From d9db4929e7bd44915df169a5d0b8b561955b8b82 Mon Sep 17 00:00:00 2001 From: Joey Huchette Date: Wed, 4 Mar 2020 10:57:45 -0600 Subject: [PATCH 1/9] First pass at a new PWL API --- Project.toml | 4 +- README.md | 6 + src/PiecewiseLinearOpt.jl | 82 ++++++++++++- src/methods/incremental.jl | 22 ++++ src/types.jl | 230 +++++++++++++++++++++---------------- 5 files changed, 239 insertions(+), 105 deletions(-) create mode 100644 src/methods/incremental.jl diff --git a/Project.toml b/Project.toml index dd3d473..ffb8dfb 100644 --- a/Project.toml +++ b/Project.toml @@ -11,8 +11,8 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" [compat] Cbc = "≥ 0.6.0" -JuMP = "~0.19, ~0.20" -MathOptInterface = "~0.8, ~0.9" +JuMP = "~0.21" +MathOptInterface = "~0.9" julia = "1" [extras] diff --git a/README.md b/README.md index 9a4ebba..86c4bb3 100644 --- a/README.md +++ b/README.md @@ -1,5 +1,11 @@ # PiecewiseLinearOpt +TODO: Need to support: +* Discontinuous functions +* Multidim inputs and outputs +* Arbitrary dimensions +* Representations in terms of values and affine functions + A package for modeling optimization problems containing piecewise linear functions. Current support is for (the graphs of) continuous univariate functions. This package is an accompaniment to a paper entitled [_Nonconvex piecewise linear functions: Advanced formulations and simple modeling tools_](https://arxiv.org/abs/1708.00050), by Joey Huchette and Juan Pablo Vielma. diff --git a/src/PiecewiseLinearOpt.jl b/src/PiecewiseLinearOpt.jl index e3ca131..447e95e 100644 --- a/src/PiecewiseLinearOpt.jl +++ b/src/PiecewiseLinearOpt.jl @@ -2,15 +2,93 @@ __precompile__() module PiecewiseLinearOpt -using JuMP +import JuMP import MathOptInterface const MOI = MathOptInterface using LinearAlgebra using Random -export PWLFunction, UnivariatePWLFunction, BivariatePWLFunction, piecewiselinear +export piecewiselinear + +abstract type Method end +abstract type UnivariateMethod <: Method end + +@enum DIRECTION Graph Epigraph Hypograph + +# include(joinpath("methods", "sos2.jl")) include("types.jl") include("jump.jl") +function _formulate!(model::JuMP.Model, input_vars::Vector{NTuple{D,Float64}}, output_vars::Vector{NTuple{F,Float64}}, pwl::PWLFunction, method::Method, direction::DIRECTION) + error("No support for a R^$D -> R^$F piecewise linear function using the $method method.") +end + +function _constrain_output_var(model::JuMP.Model, output_var::VarOrAff, rhs::VarOrAff, direction::DIRECTION) + if direction == Graph + JuMP.@constraint(model, output_var == rhs) + elseif direction == Hypograph + JuMP.@constraint(model, output_var <= rhs) + else + @assert direction == Epigraph + JuMP.@constraint(model, output_var >= rhs) + end + return +end + +function _assert_continuous_or_die(pwl::UnivariatePWLFunction) + V = union(pwl.segments.input_vals) + for segment in pwl.segments + +end + +function _continuous_breakpoints_or_die(pwl::UnivariatePWLFunction{F}) where {F} + V = union(pwl.segments.input_vals) + sort!(V) + fds = Array{Float64}(undef, length(V)) + _fds = Dict{Float64, NTuple{F,Float64}}() + for segment in pwl.segments + for input_val in segment.input_vals + if haskey(_fds, segment.input_vals) + if fds[input_val] != segment.output_vals + error("Encountered an discontinuous piecewise linear function; aborting.") + end + else + _fds[input_val] = segment.ouput_vals + end + end + end + fds = [_fds[x] for x in V] + return d, fds +end + +function piecewiselinear(model::JuMP.Model, + input_var::VarOrAff, + pwl::UnivariatePWLFunction; + method = Logarithmic(), + direction::DIRECTION = Graph, + output_var::Union{VarOrAff,Nothing} = nothing) + initPWL!(model) + counter = model.ext[:PWL].counter + counter += 1 + model.ext[:PWL].counter = counter + + if isempty(pwl.segments) + error( + "I don't know how to handle a piecewise linear function with no" + "breakpoints." + ) + end + + output_lb = minimum(output_val[1] for output_val in pwl.segments.output_vals) + output_ub = maximum(output_val[1] for output_val in pwl.segments.output_vals) + + if output_var === nothing + output_var = JuMP.@variable(model, lower_bound=output_ub, upper_bound=output_lb, base_name="y_$counter") + end + + _formulate!(model, input_var, output_var, pwl, method, direction) + return output_var +end + end # module diff --git a/src/methods/incremental.jl b/src/methods/incremental.jl new file mode 100644 index 0000000..2042cdb --- /dev/null +++ b/src/methods/incremental.jl @@ -0,0 +1,22 @@ +struct Incremental <: Method end + +function _formulate!(model::JuMP.Model, input_var::VarOrAff, output_vars::NTuple{F,VarOrAff}, pwl::UnivariatePWLFunction, method::Incremental, direction::DIRECTION) where {F} + + d, fds = _continuous_breakpoints_or_die(pwl) + + counter = model.ext[:PWL].counter + n = length(pwl.segments) + + δ = JuMP.@variable(model, [1:n], lower_bound=0, upper_bound=1, base_name="δ_$counter") + z = JuMP.@variable(model, [1:n-1], Bin, base_name="z_$counter") + JuMP.@constraint(model, input_var == d[1] + sum(δ[i]*( d[i+1]- d[i]) for i in 1:n-1)) + for j in 1:F + rhs = fds[j][1] + sum(δ[i]*(fd[j][i+1]-fd[j][i]) for i in 1:n-1) + _constrain_output_var(model, output_vars[j], rhs, direction) + end + for i in 1:n-1 + JuMP.@constraint(model, δ[i+1] ≤ z[i]) + JuMP.@constraint(model, z[i] ≤ δ[i]) + end + return +end diff --git a/src/types.jl b/src/types.jl index a3730f0..5557ede 100644 --- a/src/types.jl +++ b/src/types.jl @@ -1,110 +1,138 @@ -struct PWLFunction{D} - x::Vector{NTuple{D,Float64}} - z::Vector{Float64} - T::Vector{Vector{Int}} - meta::Dict -end - -function PWLFunction{D}(x::Vector{NTuple{D}}, z::Vector, T::Vector{Vector}, meta::Dict) where {D} - @assert length(x) == length(z) - for t in T - @assert minimum(t) > 0 && maximum(t) <= length(x) - end - return PWLFunction{D}(x, z, T, meta) -end - -PWLFunction(x, z, T) = PWLFunction(x, z, T, Dict()) +abstract type Segment{D,F} end -const UnivariatePWLFunction = PWLFunction{1} +struct SegmentPointRep{D,F} <: Segment{D,F} + input_vals::Vector{NTuple{D,Float64}} + output_vals::Vector{NTuple{D,Float64}} -function UnivariatePWLFunction(x, z) - @assert issorted(x) - return PWLFunction(Tuple{Float64}[(xx,) for xx in x], convert(Vector{Float64}, z), [[i,i+1] for i in 1:length(x)-1]) + function SegmentPointRep{D,F}(input_vals::Vector{NTuple{D,Float64}}, output_vals::Vector{NTuple{F,Float64}}) where {D,F} + if length(input_vals) != length(output_vals) + error("Must specify the same number of input and output values.") + end + return new{D,F}(input_vals, output_vals) + end end -function UnivariatePWLFunction(x, fz::Function) - @assert issorted(x) - return PWLFunction(Tuple{Float64}[(xx,) for xx in x], map(t->convert(Float64,fz(t)), x), [[i,i+1] for i in 1:length(x)-1]) +struct SegmentHyperplaneRep{D,F} <: Segment{D,F} + breakpoints::Vector{NTuple{D,Float64}} + coeffs::NTuple{F,NTuple{D,Float64}} + offsets::NTuple{F,Float64} end -const BivariatePWLFunction = PWLFunction{2} - -function BivariatePWLFunction(x, y, fz::Function; pattern=:BestFit, seed=hash((length(x),length(y)))) - @assert issorted(x) - @assert issorted(y) - X = vec(collect(Base.product(x,y))) - # X = vec(Tuple{Float64,Float64}[(_x,_y) for _x in x, _y in y]) - Z = map(t -> convert(Float64,fz(t...)), X) - T = Vector{Vector{Int}}() - m = length(x) - n = length(y) - - mt = MersenneTwister(seed) - # run for each square on [x[i],x[i+1]] × [y[i],y[i+1]] - for i in 1:length(x)-1, j in 1:length(y)-1 - SWt, NWt, NEt, SEt = LinearIndices((m,n))[i,j], LinearIndices((m,n))[i,j+1], LinearIndices((m,n))[i+1,j+1], LinearIndices((m,n))[i+1,j] - xL, xU, yL, yU = x[i], x[i+1], y[j], y[j+1] - @assert xL == X[SWt][1] == X[NWt][1] - @assert xU == X[SEt][1] == X[NEt][1] - @assert yL == X[SWt][2] == X[SEt][2] - @assert yU == X[NWt][2] == X[NEt][2] - SW, NW, NE, SE = fz(xL,yL), fz(xL,yU), fz(xU,yU), fz(xU,yL) - mid1 = 0.5*(SW+NE) - mid2 = 0.5*(NW+SE) - - if pattern == :Upper - if mid1 > mid2 - t1 = [SWt,NWt,NEt] - t2 = [SWt,NEt,SEt] - else - t1 = [SWt,NWt,SEt] - t2 = [SEt,NWt,NEt] - end - elseif pattern == :Lower - if mid1 > mid2 - t1 = [SWt,NWt,SEt] - t2 = [SEt,NWt,NEt] - else - t1 = [SWt,NWt,NEt] - t2 = [SWt,NEt,SEt] - end - elseif pattern == :BestFit - mid3 = fz(0.5*(xL+xU), 0.5*(yL+yU)) - if abs(mid1-mid3) < abs(mid2-mid3) - t1 = [SWt,NWt,NEt] - t2 = [SWt,NEt,SEt] - else - t1 = [SWt,NWt,SEt] - t2 = [SEt,NWt,NEt] - end - elseif pattern == :UnionJack - t1 = [SWt,SEt] - t2 = [NWt,NEt] - if iseven(i+j) - push!(t1, NWt) - push!(t2, SEt) - else - push!(t1, NEt) - push!(t2, SWt) - end - elseif pattern == :K1 - t1 = [SEt,SWt,NWt] - t2 = [NWt,NEt,SEt] - elseif pattern == :Random - if rand(mt, Bool) - t1 = [NWt,NEt,SEt] - t2 = [SEt,SWt,NWt] - else - t1 = [SWt,NWt,NEt] - t2 = [NEt,SEt,SWt] - end - else - error("pattern $pattern not currently supported") - end +struct PWLFunction{D, F, T <: Segment{D, F}} + segments::Vector{T} + meta::Dict - push!(T, t1) - push!(T, t2) + function PWLFunction{T}(segments::Vector{T}) where {T <: Segment} + return new(segments, Dict()) end - - return PWLFunction{2}(X, Z, T, Dict(:structure=>pattern)) end + +const UnivariatePWLFunction{F} = PWLFunction{SegmentPointRep{1,F}} +const BivariatePWLFunction{F} = PWLFunction{SegmentPointRep{2,F}} + +# +# struct +# +# function PWLFunction{D}(x::Vector{NTuple{D}}, z::Vector, T::Vector{Vector}, meta::Dict) where {D} +# @assert length(x) == length(z) +# for t in T +# @assert minimum(t) > 0 && maximum(t) <= length(x) +# end +# return PWLFunction{D}(x, z, T, meta) +# end +# +# PWLFunction(inputs) = PWLFunction(x, z, T, Dict()) +# +# const UnivariatePWLFunction = PWLFunction{1} +# +# function UnivariatePWLFunction(x, z) +# @assert issorted(x) +# return PWLFunction(Tuple{Float64}[(xx,) for xx in x], convert(Vector{Float64}, z), [[i,i+1] for i in 1:length(x)-1]) +# end +# +# function UnivariatePWLFunction(x, fz::Function) +# @assert issorted(x) +# return PWLFunction(Tuple{Float64}[(xx,) for xx in x], map(t->convert(Float64,fz(t)), x), [[i,i+1] for i in 1:length(x)-1]) +# end +# +# const BivariatePWLFunction = PWLFunction{2} +# +# function BivariatePWLFunction(x, y, fz::Function; pattern=:BestFit, seed=hash((length(x),length(y)))) +# @assert issorted(x) +# @assert issorted(y) +# X = vec(collect(Base.product(x,y))) +# # X = vec(Tuple{Float64,Float64}[(_x,_y) for _x in x, _y in y]) +# Z = map(t -> convert(Float64,fz(t...)), X) +# T = Vector{Vector{Int}}() +# m = length(x) +# n = length(y) +# +# mt = MersenneTwister(seed) +# # run for each square on [x[i],x[i+1]] × [y[i],y[i+1]] +# for i in 1:length(x)-1, j in 1:length(y)-1 +# SWt, NWt, NEt, SEt = LinearIndices((m,n))[i,j], LinearIndices((m,n))[i,j+1], LinearIndices((m,n))[i+1,j+1], LinearIndices((m,n))[i+1,j] +# xL, xU, yL, yU = x[i], x[i+1], y[j], y[j+1] +# @assert xL == X[SWt][1] == X[NWt][1] +# @assert xU == X[SEt][1] == X[NEt][1] +# @assert yL == X[SWt][2] == X[SEt][2] +# @assert yU == X[NWt][2] == X[NEt][2] +# SW, NW, NE, SE = fz(xL,yL), fz(xL,yU), fz(xU,yU), fz(xU,yL) +# mid1 = 0.5*(SW+NE) +# mid2 = 0.5*(NW+SE) +# +# if pattern == :Upper +# if mid1 > mid2 +# t1 = [SWt,NWt,NEt] +# t2 = [SWt,NEt,SEt] +# else +# t1 = [SWt,NWt,SEt] +# t2 = [SEt,NWt,NEt] +# end +# elseif pattern == :Lower +# if mid1 > mid2 +# t1 = [SWt,NWt,SEt] +# t2 = [SEt,NWt,NEt] +# else +# t1 = [SWt,NWt,NEt] +# t2 = [SWt,NEt,SEt] +# end +# elseif pattern == :BestFit +# mid3 = fz(0.5*(xL+xU), 0.5*(yL+yU)) +# if abs(mid1-mid3) < abs(mid2-mid3) +# t1 = [SWt,NWt,NEt] +# t2 = [SWt,NEt,SEt] +# else +# t1 = [SWt,NWt,SEt] +# t2 = [SEt,NWt,NEt] +# end +# elseif pattern == :UnionJack +# t1 = [SWt,SEt] +# t2 = [NWt,NEt] +# if iseven(i+j) +# push!(t1, NWt) +# push!(t2, SEt) +# else +# push!(t1, NEt) +# push!(t2, SWt) +# end +# elseif pattern == :K1 +# t1 = [SEt,SWt,NWt] +# t2 = [NWt,NEt,SEt] +# elseif pattern == :Random +# if rand(mt, Bool) +# t1 = [NWt,NEt,SEt] +# t2 = [SEt,SWt,NWt] +# else +# t1 = [SWt,NWt,NEt] +# t2 = [NEt,SEt,SWt] +# end +# else +# error("pattern $pattern not currently supported") +# end +# +# push!(T, t1) +# push!(T, t2) +# end +# +# return PWLFunction{2}(X, Z, T, Dict(:structure=>pattern)) +# end From a1b236b1732a3bac4b46c68a99845a5751cf35df Mon Sep 17 00:00:00 2001 From: Joey Huchette Date: Wed, 11 Mar 2020 21:22:19 -0500 Subject: [PATCH 2/9] Working port of incremental and log 1D formulations --- Project.toml | 3 +- src/PiecewiseLinearOpt.jl | 67 ++++-------- src/methods/incremental.jl | 12 +-- src/methods/logarithmic.jl | 28 +++++ src/methods/util.jl | 213 +++++++++++++++++++++++++++++++++++++ src/types.jl | 14 ++- test/runtests.jl | 103 +++++++----------- 7 files changed, 319 insertions(+), 121 deletions(-) create mode 100644 src/methods/logarithmic.jl create mode 100644 src/methods/util.jl diff --git a/Project.toml b/Project.toml index ffb8dfb..a65be4e 100644 --- a/Project.toml +++ b/Project.toml @@ -17,7 +17,8 @@ julia = "1" [extras] Cbc = "9961bab8-2fa3-5c5a-9d89-47fab24efd76" +Gurobi = "2e9cd046-0924-5485-92f1-d5272153d98b" Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" [targets] -test = ["Test", "Cbc"] +test = ["Test", "Cbc", "Gurobi"] diff --git a/src/PiecewiseLinearOpt.jl b/src/PiecewiseLinearOpt.jl index 447e95e..0ecef6a 100644 --- a/src/PiecewiseLinearOpt.jl +++ b/src/PiecewiseLinearOpt.jl @@ -10,56 +10,30 @@ using Random export piecewiselinear -abstract type Method end -abstract type UnivariateMethod <: Method end - -@enum DIRECTION Graph Epigraph Hypograph - -# include(joinpath("methods", "sos2.jl")) - include("types.jl") -include("jump.jl") -function _formulate!(model::JuMP.Model, input_vars::Vector{NTuple{D,Float64}}, output_vars::Vector{NTuple{F,Float64}}, pwl::PWLFunction, method::Method, direction::DIRECTION) - error("No support for a R^$D -> R^$F piecewise linear function using the $method method.") +mutable struct PWLData + counter::Int + PWLData() = new(0) end -function _constrain_output_var(model::JuMP.Model, output_var::VarOrAff, rhs::VarOrAff, direction::DIRECTION) - if direction == Graph - JuMP.@constraint(model, output_var == rhs) - elseif direction == Hypograph - JuMP.@constraint(model, output_var <= rhs) - else - @assert direction == Epigraph - JuMP.@constraint(model, output_var >= rhs) +function initPWL!(m::JuMP.Model) + if !haskey(m.ext, :PWL) + m.ext[:PWL] = PWLData() end - return + return nothing end -function _assert_continuous_or_die(pwl::UnivariatePWLFunction) - V = union(pwl.segments.input_vals) - for segment in pwl.segments +const VarOrAff = Union{JuMP.VariableRef,JuMP.AffExpr} -end +include(joinpath("methods", "util.jl")) -function _continuous_breakpoints_or_die(pwl::UnivariatePWLFunction{F}) where {F} - V = union(pwl.segments.input_vals) - sort!(V) - fds = Array{Float64}(undef, length(V)) - _fds = Dict{Float64, NTuple{F,Float64}}() - for segment in pwl.segments - for input_val in segment.input_vals - if haskey(_fds, segment.input_vals) - if fds[input_val] != segment.output_vals - error("Encountered an discontinuous piecewise linear function; aborting.") - end - else - _fds[input_val] = segment.ouput_vals - end - end - end - fds = [_fds[x] for x in V] - return d, fds +export Incremental, Logarithmic +include(joinpath("methods", "incremental.jl")) +include(joinpath("methods", "logarithmic.jl")) + +function _formulate!(model::JuMP.Model, input_vals::Vector{NTuple{D,VarOrAff}}, output_vals::Vector{NTuple{F,VarOrAff}}, pwl::PWLFunction, method::Method, direction::DIRECTION) where {D,F} + error("No support for a R^$D -> R^$F piecewise linear function using the $method method.") end function piecewiselinear(model::JuMP.Model, @@ -75,19 +49,18 @@ function piecewiselinear(model::JuMP.Model, if isempty(pwl.segments) error( - "I don't know how to handle a piecewise linear function with no" - "breakpoints." + "I don't know how to handle a piecewise linear function with no breakpoints." ) end - output_lb = minimum(output_val[1] for output_val in pwl.segments.output_vals) - output_ub = maximum(output_val[1] for output_val in pwl.segments.output_vals) + output_lb = minimum(minimum(segment.output_vals) for segment in pwl.segments)[1] + output_ub = maximum(maximum(segment.output_vals) for segment in pwl.segments)[1] if output_var === nothing - output_var = JuMP.@variable(model, lower_bound=output_ub, upper_bound=output_lb, base_name="y_$counter") + output_var = JuMP.@variable(model, lower_bound=output_lb, upper_bound=output_ub, base_name="y_$counter") end - _formulate!(model, input_var, output_var, pwl, method, direction) + _formulate!(model, (input_var,), (output_var,), pwl, method, direction) return output_var end diff --git a/src/methods/incremental.jl b/src/methods/incremental.jl index 2042cdb..9f48e7e 100644 --- a/src/methods/incremental.jl +++ b/src/methods/incremental.jl @@ -1,17 +1,17 @@ struct Incremental <: Method end -function _formulate!(model::JuMP.Model, input_var::VarOrAff, output_vars::NTuple{F,VarOrAff}, pwl::UnivariatePWLFunction, method::Incremental, direction::DIRECTION) where {F} - - d, fds = _continuous_breakpoints_or_die(pwl) +function _formulate!(model::JuMP.Model, input_vars::Tuple{VarOrAff}, output_vars::NTuple{F,VarOrAff}, pwl::UnivariatePWLFunction, method::Incremental, direction::DIRECTION) where {F} + xs, ys = _continuous_breakpoints_or_die(pwl) counter = model.ext[:PWL].counter - n = length(pwl.segments) + n = length(pwl.segments) + 1 + @assert length(xs) == length(ys) == n δ = JuMP.@variable(model, [1:n], lower_bound=0, upper_bound=1, base_name="δ_$counter") z = JuMP.@variable(model, [1:n-1], Bin, base_name="z_$counter") - JuMP.@constraint(model, input_var == d[1] + sum(δ[i]*( d[i+1]- d[i]) for i in 1:n-1)) + JuMP.@constraint(model, input_vars[1] == xs[1][1] + sum(δ[i]*(xs[i+1][1] - xs[i][1]) for i in 1:n-1)) for j in 1:F - rhs = fds[j][1] + sum(δ[i]*(fd[j][i+1]-fd[j][i]) for i in 1:n-1) + rhs = ys[1][j] + sum(δ[i]*(ys[i+1][j] - ys[i][j]) for i in 1:n-1) _constrain_output_var(model, output_vars[j], rhs, direction) end for i in 1:n-1 diff --git a/src/methods/logarithmic.jl b/src/methods/logarithmic.jl new file mode 100644 index 0000000..808774b --- /dev/null +++ b/src/methods/logarithmic.jl @@ -0,0 +1,28 @@ +struct Logarithmic <: Method end + +function _reflected_gray_codes(k::Int) + if k == 0 + return Vector{Float64}[] + elseif k == 1 + return [[0.0], [1.0]] + else + codes′ = _reflected_gray_codes(k-1) + return vcat([vcat(code, 0.0) for code in codes′], + [vcat(code, 1.0) for code in reverse(codes′)]) + end +end + +function _formulate!(model::JuMP.Model, input_vars::Tuple{VarOrAff}, output_vars::NTuple{F,VarOrAff}, pwl::UnivariatePWLFunction, method::Logarithmic, direction::DIRECTION) where {F} + xs, ys = _continuous_breakpoints_or_die(pwl) + + n = length(xs) + d = n - 1 + k = ceil(Int, log2(n)) + counter = model.ext[:PWL].counter + y = JuMP.@variable(model, [1:k], Bin, base_name="y_$counter") + + λ = _create_convex_multiplier_vars(model, xs, ys, input_vars, output_vars, direction) + + _sos2_encoding_constraints!(model, λ, y, _reflected_gray_codes(k), _unit_vector_hyperplanes(k)) + return +end diff --git a/src/methods/util.jl b/src/methods/util.jl new file mode 100644 index 0000000..18bb77b --- /dev/null +++ b/src/methods/util.jl @@ -0,0 +1,213 @@ +function _continuous_breakpoints_or_die(pwl::UnivariatePWLFunction{F}) where {F} + xs = Set{Tuple{Float64}}() + for segment in pwl.segments + for val in segment.input_vals + push!(xs, val) + end + end + ys = Dict{Tuple{Float64},NTuple{F,Float64}}() + for segment in pwl.segments + for i in 1:length(segment.input_vals) + x = segment.input_vals[i] + y = segment.output_vals[i] + if haskey(ys, x) + if y != ys[x] + error("Expected piecewise linear function to be continuous.") + end + else + ys[x] = y + end + end + end + X = sort!(collect(xs)) + Y = [ys[x] for x in X] + return X, Y +end + +function _constrain_output_var(model::JuMP.Model, output_var::VarOrAff, func_val::VarOrAff, direction::DIRECTION) + if direction == Graph + JuMP.@constraint(model, output_var == func_val) + elseif direction == Hypograph + JuMP.@constraint(model, output_var <= func_val) + else + @assert direction == Epigraph + JuMP.@constraint(model, output_var >= func_val) + end + return +end + +function _create_convex_multiplier_vars(model::JuMP.Model, xs::Vector{NTuple{D,Float64}}, ys::Vector{NTuple{F,Float64}}, input_vars::NTuple{D,JuMP.VariableRef}, output_vars::NTuple{F,JuMP.VariableRef}, direction::DIRECTION) where {D,F} + counter = model.ext[:PWL].counter + n = length(xs) + @assert n == length(ys) + + λ = JuMP.@variable(model, [1:n], lower_bound=0, upper_bound=1, base_name="λ_$counter") + JuMP.@constraint(model, sum(λ) == 1) + for j in 1:D + JuMP.@constraint(model, sum(λ[i]* xs[i][j] for i in 1:n) == input_vars[j]) + end + for j in 1:F + _constrain_output_var(model, output_vars[j], sum(λ[i]*ys[i][j] for i in 1:n), direction) + end + return λ +end + +function _sos2_encoding_constraints!(m::JuMP.Model, λ::Vector{JuMP.VariableRef}, y::Vector{JuMP.VariableRef}, h::Vector{Vector{Float64}}, B::Vector{Vector{Float64}}) + n = length(λ) - 1 + for b in B + JuMP.@constraints(m, begin + dot(b,h[1])*λ[1] + sum(min(dot(b,h[v]),dot(b,h[v-1]))*λ[v] for v in 2:n) + dot(b,h[n])*λ[n+1] ≤ dot(b,y) + dot(b,h[1])*λ[1] + sum(max(dot(b,h[v]),dot(b,h[v-1]))*λ[v] for v in 2:n) + dot(b,h[n])*λ[n+1] ≥ dot(b,y) + end) + end + return nothing +end + +function _zigzag_codes(k::Int) + if k <= 0 + error("Invalid code length $k") + elseif k == 1 + return [[0],[1]] + else + codes′ = _zigzag_codes(k-1) + return vcat([vcat(code,0) for code in codes′], + [vcat(code,1) for code in codes′]) + end +end + +function _integer_zigzag_codes(k::Int) + if k <= 0 + error("Invalid code length $k") + elseif k == 1 + return [[0],[1]] + else + codes′ = _integer_zigzag_codes(k-1) + offset = [2^(j-2) for j in k:-1:2] + return vcat([vcat(code, 0) for code in codes′], + [vcat(code.+offset,1) for code in codes′]) + end +end + +function _zigzag_hyperplanes(k::Int) + hps = Vector{Int}[] + for i in 1:k + hp = zeros(Int, k) + hp[i] = 1 + for j in (i+1):k + hp[j] = 2^(j-i-1) + end + push!(hps, hp) + end + return hps +end + +function _unit_vector_hyperplanes(k::Int) + hps = Vector{Float64}[] + for i in 1:k + hp = zeros(Int,k) + hp[i] = 1 + push!(hps, hp) + end + return hps +end + +_generalized_celaya_hyperplanes(k::Int) = _compute_hyperplanes(_generalized_celaya_codes(k)) + +_symmetric_celaya_hyperplanes(k::Int) = _compute_hyperplanes(_symmetric_celaya_codes(k)) + +# TODO: Figure out assumptions at play here +function _compute_hyperplanes(C::Vector{Vector{T}}) where T <: Number + n = length(C) + k = length(C[1]) + + d = zeros(n-1,k) + for i in 1:n-1 + d[i,:] = C[i+1] - C[i] + end + + if k <= 1 + error("Cannot process codes of length $k") + elseif k == 2 + @assert n == 4 + spanners = Vector{Float64}[] + for i in 1:n-1 + v = canonical!(d[i,:]) + v = [v[2], -v[1]] + push!(spanners, v) + end + indices = [1] + approx12 = isapprox(spanners[1],spanners[2]) + approx13 = isapprox(spanners[1],spanners[3]) + approx23 = isapprox(spanners[2],spanners[3]) + if !approx12 + push!(indices,2) + end + if !approx13 && !(!approx12 && approx23) + push!(indices,3) + end + return spanners[indices] + end + + indices = [1,2] + spanners = Vector{Float64}[] + while !isempty(indices) + if indices == [n-1] + break + end + if rank(d[indices,:]) == length(indices) && length(indices) <= k-1 + if length(indices) == k-1 + nullsp = nullspace(d[indices,:]) + @assert size(nullsp,2) == 1 + v = vec(nullsp) + push!(spanners, canonical!(v)) + end + if indices[end] != n-1 + push!(indices, indices[end]+1) + else + pop!(indices) + indices[end] += 1 + end + else + if indices[end] != n-1 + indices[end] += 1 + else + pop!(indices) + indices[end] += 1 + end + end + end + + keepers = [1] + for i in 2:length(spanners) + alreadyin = false + for j in keepers + if isapprox(spanners[i], spanners[j]) + alreadyin = true + break + end + end + if !alreadyin + push!(keepers, i) + end + end + + return spanners[keepers] +end + +function _canonical!(v::Vector{Float64}) + normalize!(v) + for j in 1:length(v) + if abs(v[j]) < 1e-8 + v[j] = 0 + end + end + sgn = sign(v[findfirst([x!=0 for x in v])]) + for j in 1:length(v) + if abs(v[j]) < 1e-8 + v[j] = 0 + else + v[j] *= sgn + end + end + return v +end diff --git a/src/types.jl b/src/types.jl index 5557ede..79eb69a 100644 --- a/src/types.jl +++ b/src/types.jl @@ -1,13 +1,19 @@ +abstract type Method end +abstract type UnivariateMethod <: Method end + +@enum DIRECTION Graph Epigraph Hypograph + abstract type Segment{D,F} end struct SegmentPointRep{D,F} <: Segment{D,F} input_vals::Vector{NTuple{D,Float64}} - output_vals::Vector{NTuple{D,Float64}} + output_vals::Vector{NTuple{F,Float64}} function SegmentPointRep{D,F}(input_vals::Vector{NTuple{D,Float64}}, output_vals::Vector{NTuple{F,Float64}}) where {D,F} if length(input_vals) != length(output_vals) error("Must specify the same number of input and output values.") end + # TODO: Run verifier to ensure this is actually a PWL function return new{D,F}(input_vals, output_vals) end end @@ -22,13 +28,13 @@ struct PWLFunction{D, F, T <: Segment{D, F}} segments::Vector{T} meta::Dict - function PWLFunction{T}(segments::Vector{T}) where {T <: Segment} + function PWLFunction{D, F, T}(segments::Vector{T}) where {D, F, T <: Segment} return new(segments, Dict()) end end -const UnivariatePWLFunction{F} = PWLFunction{SegmentPointRep{1,F}} -const BivariatePWLFunction{F} = PWLFunction{SegmentPointRep{2,F}} +const UnivariatePWLFunction{F} = PWLFunction{1, F, SegmentPointRep{1,F}} +const BivariatePWLFunction{F} = PWLFunction{2, F, SegmentPointRep{2,F}} # # struct diff --git a/test/runtests.jl b/test/runtests.jl index db0154c..87b37f1 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -1,32 +1,40 @@ -using Cbc +using Cbc, Gurobi using Test using LinearAlgebra -# using Gurobi -# solver = GurobiSolver(OutputFlag=0) - -# using CPLEX -# solver = CplexSolver(CPX_PARAM_SCRIND=0) - - import JuMP import MathOptInterface const MOI = MathOptInterface using PiecewiseLinearOpt +const PLO = PiecewiseLinearOpt # TODO: Add :SOS2 to this list, once Cbc supports it -methods_1D = (:CC,:MC,:Logarithmic,:LogarithmicIB,:ZigZag,:ZigZagInteger,:GeneralizedCelaya,:SymmetricCelaya,:Incremental,:DisaggLogarithmic) -# TODO: Add :SOS2 to this list, once Cbc supports it -# TODO: Add :MC to this list, Cbc (but not Gurobi) gives a different answer below, only for :MC (maybe a bug in Cbc?) -methods_2D = (:CC,:Logarithmic,:LogarithmicIB,:ZigZag,:ZigZagInteger,:GeneralizedCelaya,:SymmetricCelaya,:DisaggLogarithmic) -patterns_2D = (:Upper,:Lower,:BestFit,:UnionJack,:K1,:Random) # :OptimalTriangleSelection and :Stencil not supported currently +methods_1D = (Incremental(), Logarithmic()) +@testset "Simple univariate" begin + m = JuMP.Model(Gurobi.Optimizer) + JuMP.@variable(m, x) + + s1 = PLO.SegmentPointRep{1,1}([(1.,), (2.,)], [(2.5,), (3.5,)]) + s2 = PLO.SegmentPointRep{1,1}([(2.,), (3.,)], [(3.5,), (1.0,)]) + pwl = PLO.PWLFunction{1,1,PLO.SegmentPointRep{1,1}}([s1, s2]) + + piecewiselinear(m, x, pwl, method=PLO.Incremental()) +end -println("\nunivariate tests") @testset "1D: $method" for method in methods_1D - model = JuMP.Model(JuMP.with_optimizer(Cbc.Optimizer)) + model = JuMP.Model(Gurobi.Optimizer) JuMP.@variable(model, x) - z = piecewiselinear(model, x, range(1,stop=2π, length=8), sin, method=method) + segments = PLO.SegmentPointRep{1,1}[] + d = 7 + xs = range(1,stop=2π, length=(d + 1)) + for i in 1:d + x_l = xs[i] + x_r = xs[i+1] + push!(segments, PLO.SegmentPointRep{1,1}([(x_l,), (x_r,)], [(sin(x_l),), (sin(x_r),)])) + end + pwl = PLO.PWLFunction{1,1,PLO.SegmentPointRep{1,1}}(segments) + z = piecewiselinear(model, x, pwl, method=method) JuMP.@objective(model, Max, z) JuMP.optimize!(model) @@ -46,63 +54,32 @@ println("\nunivariate tests") @test JuMP.objective_value(model) ≈ JuMP.value(z) rtol=1e-4 end -println("\nbivariate tests") -@testset "2D: $method, $pattern" for method in methods_2D, pattern in patterns_2D - model = JuMP.Model(JuMP.with_optimizer(Cbc.Optimizer)) - JuMP.@variable(model, x[1:2]) - d = range(0,stop=1,length=8) - f = (x1,x2) -> 2*(x1-1/3)^2 + 3*(x2-4/7)^4 - z = piecewiselinear(model, x[1], x[2], BivariatePWLFunction(d, d, f, pattern=pattern), method=method) - JuMP.@objective(model, Min, z) - - JuMP.optimize!(model) - - @test JuMP.termination_status(model) == MOI.OPTIMAL - @test JuMP.value(x[1]) ≈ 0.285714 rtol=1e-4 - @test JuMP.value(x[2]) ≈ 0.571429 rtol=1e-4 - @test JuMP.value(z) ≈ 0.004535 rtol=1e-3 - @test JuMP.objective_value(model) ≈ 0.004535 rtol=1e-3 - @test JuMP.objective_value(model) ≈ JuMP.value(z) rtol=1e-3 - - JuMP.@constraint(model, x[1] ≥ 0.6) - - JuMP.optimize!(model) - - @test JuMP.termination_status(model) == MOI.OPTIMAL - @test JuMP.value(x[1]) ≈ 0.6 rtol=1e-4 - @test JuMP.value(x[2]) ≈ 0.571428 rtol=1e-4 - @test JuMP.value(z) ≈ 0.148753 rtol=1e-4 - @test JuMP.objective_value(model) ≈ 0.148753 rtol=1e-3 - @test JuMP.objective_value(model) ≈ JuMP.value(z) rtol=1e-3 -end -# -# println("\nbivariate optimal IB scheme tests") -# @testset "2D: optimal IB, UnionJack" begin +# println("\nbivariate tests") +# @testset "2D: $method, $pattern" for method in methods_2D, pattern in patterns_2D # model = JuMP.Model(JuMP.with_optimizer(Cbc.Optimizer)) -# JuMP.@variable(model, x) -# JuMP.@variable(model, y) -# d = range(0,stop=1,length=3) -# f = (x,y) -> 2*(x-1/3)^2 + 3*(y-4/7)^4 -# z = piecewiselinear(model, x, y, BivariatePWLFunction(d, d, f, pattern=:UnionJack), method=:OptimalIB, subsolver=solver) +# JuMP.@variable(model, x[1:2]) +# d = range(0,stop=1,length=8) +# f = (x1,x2) -> 2*(x1-1/3)^2 + 3*(x2-4/7)^4 +# z = piecewiselinear(model, x[1], x[2], BivariatePWLFunction(d, d, f, pattern=pattern), method=method) # JuMP.@objective(model, Min, z) # # JuMP.optimize!(model) # # @test JuMP.termination_status(model) == MOI.OPTIMAL -# @test JuMP.value(x) ≈ 0.5 rtol=1e-4 -# @test JuMP.value(y) ≈ 0.5 rtol=1e-4 -# @test JuMP.value(z) ≈ 0.055634 rtol=1e-3 -# @test getobjectivevalue(model) ≈ 0.055634 rtol=1e-3 -# @test getobjectivevalue(model) ≈ JuMP.value(z) rtol=1e-3 +# @test JuMP.value(x[1]) ≈ 0.285714 rtol=1e-4 +# @test JuMP.value(x[2]) ≈ 0.571429 rtol=1e-4 +# @test JuMP.value(z) ≈ 0.004535 rtol=1e-3 +# @test JuMP.objective_value(model) ≈ 0.004535 rtol=1e-3 +# @test JuMP.objective_value(model) ≈ JuMP.value(z) rtol=1e-3 # -# JuMP.@constraint(model, x ≥ 0.6) +# JuMP.@constraint(model, x[1] ≥ 0.6) # # JuMP.optimize!(model) # # @test JuMP.termination_status(model) == MOI.OPTIMAL -# @test JuMP.value(x) ≈ 0.6 rtol=1e-4 -# @test JuMP.value(y) ≈ 0.5 rtol=1e-4 -# @test JuMP.value(z) ≈ 0.222300 rtol=1e-3 -# @test JuMP.objective_value(model) ≈ 0.222300 rtol=1e-3 +# @test JuMP.value(x[1]) ≈ 0.6 rtol=1e-4 +# @test JuMP.value(x[2]) ≈ 0.571428 rtol=1e-4 +# @test JuMP.value(z) ≈ 0.148753 rtol=1e-4 +# @test JuMP.objective_value(model) ≈ 0.148753 rtol=1e-3 # @test JuMP.objective_value(model) ≈ JuMP.value(z) rtol=1e-3 # end From 484ce2033db0296d4675ce0c99e132a51df40bf7 Mon Sep 17 00:00:00 2001 From: Joey Huchette Date: Sun, 5 Apr 2020 21:02:36 -0500 Subject: [PATCH 3/9] Port over bivariate code --- README.md | 7 -- src/PiecewiseLinearOpt.jl | 56 +++++++++--- src/methods/incremental.jl | 5 +- src/methods/logarithmic.jl | 21 +++-- src/methods/six_stencil.jl | 169 +++++++++++++++++++++++++++++++++++++ src/methods/util.jl | 107 +++++++++++++++++++---- test/runtests.jl | 50 ++++++++--- 7 files changed, 358 insertions(+), 57 deletions(-) create mode 100644 src/methods/six_stencil.jl diff --git a/README.md b/README.md index 86c4bb3..0b50008 100644 --- a/README.md +++ b/README.md @@ -1,11 +1,4 @@ # PiecewiseLinearOpt - -TODO: Need to support: -* Discontinuous functions -* Multidim inputs and outputs -* Arbitrary dimensions -* Representations in terms of values and affine functions - A package for modeling optimization problems containing piecewise linear functions. Current support is for (the graphs of) continuous univariate functions. This package is an accompaniment to a paper entitled [_Nonconvex piecewise linear functions: Advanced formulations and simple modeling tools_](https://arxiv.org/abs/1708.00050), by Joey Huchette and Juan Pablo Vielma. diff --git a/src/PiecewiseLinearOpt.jl b/src/PiecewiseLinearOpt.jl index 0ecef6a..ee36c15 100644 --- a/src/PiecewiseLinearOpt.jl +++ b/src/PiecewiseLinearOpt.jl @@ -28,20 +28,25 @@ const VarOrAff = Union{JuMP.VariableRef,JuMP.AffExpr} include(joinpath("methods", "util.jl")) -export Incremental, Logarithmic +export Incremental, Logarithmic, SixStencil include(joinpath("methods", "incremental.jl")) include(joinpath("methods", "logarithmic.jl")) +include(joinpath("methods", "six_stencil.jl")) -function _formulate!(model::JuMP.Model, input_vals::Vector{NTuple{D,VarOrAff}}, output_vals::Vector{NTuple{F,VarOrAff}}, pwl::PWLFunction, method::Method, direction::DIRECTION) where {D,F} +function formulate_pwl!(model::JuMP.Model, input_vals::Vector{NTuple{D,VarOrAff}}, output_vals::Vector{NTuple{F,VarOrAff}}, pwl::PWLFunction, method::Method, direction::DIRECTION) where {D,F} error("No support for a R^$D -> R^$F piecewise linear function using the $method method.") end +_default_method(::Val{1}) = Logarithmic() +_default_method(::Val{2}) = SixStencil() +# _default_method(::Val) = MultipleChoice() + function piecewiselinear(model::JuMP.Model, - input_var::VarOrAff, - pwl::UnivariatePWLFunction; - method = Logarithmic(), + input_vars::NTuple{D,VarOrAff}, + pwl::PWLFunction{D,F,SegmentPointRep{D,F}}; + method::Method = _default_method(Val(D)), direction::DIRECTION = Graph, - output_var::Union{VarOrAff,Nothing} = nothing) + output_vars::Union{Nothing,NTuple{F,VarOrAff}} = nothing) where {D,F} initPWL!(model) counter = model.ext[:PWL].counter counter += 1 @@ -53,15 +58,42 @@ function piecewiselinear(model::JuMP.Model, ) end - output_lb = minimum(minimum(segment.output_vals) for segment in pwl.segments)[1] - output_ub = maximum(maximum(segment.output_vals) for segment in pwl.segments)[1] + output_lb = minimum(minimum(segment.output_vals) for segment in pwl.segments) + output_ub = maximum(maximum(segment.output_vals) for segment in pwl.segments) - if output_var === nothing - output_var = JuMP.@variable(model, lower_bound=output_lb, upper_bound=output_ub, base_name="y_$counter") + if output_vars === nothing + output_vars = tuple(JuMP.@variable(model, [i in 1:F], lower_bound=output_lb[i], upper_bound=output_ub[i], base_name="y_$counter")...) end - _formulate!(model, (input_var,), (output_var,), pwl, method, direction) - return output_var + formulate_pwl!(model, input_vars, output_vars, pwl, method, direction) + return output_vars end +# function piecewiselinear(model::JuMP.Model, +# input_vars::Tuple{VarOrAff,VarOrAff}, +# pwl::BivariatePWLFunction{1}, +# method::Method = SixStencil(), +# direction::DIRECTION = Graph, +# output_var::Union{Nothing,VarOrAff} = nothing) +# initPWL!(model) +# counter = model.ext[:PWL].counter +# counter += 1 +# model.ext[:PWL].counter = counter +# +# if isempty(pwl.segments) +# error( +# "I don't know how to handle a piecewise linear function with no breakpoints." +# ) +# end +# +# output_lb = minimum(minimum(segment.output_vals) for segment in pwl.segments)[1] +# output_ub = maximum(maximum(segment.output_vals) for segment in pwl.segments)[1] +# +# if output_var === nothing +# output_var = JuMP.@variable(model, lower_bound=output_lb, upper_bound=output_ub, base_name="y_$counter") +# end +# formulate_pwl!(model, (input_var,), (output_var,), pwl, method, direction) +# return output_var +# end + end # module diff --git a/src/methods/incremental.jl b/src/methods/incremental.jl index 9f48e7e..0687223 100644 --- a/src/methods/incremental.jl +++ b/src/methods/incremental.jl @@ -1,7 +1,8 @@ struct Incremental <: Method end -function _formulate!(model::JuMP.Model, input_vars::Tuple{VarOrAff}, output_vars::NTuple{F,VarOrAff}, pwl::UnivariatePWLFunction, method::Incremental, direction::DIRECTION) where {F} - xs, ys = _continuous_breakpoints_or_die(pwl) +function formulate_pwl!(model::JuMP.Model, input_vars::Tuple{VarOrAff}, output_vars::NTuple{F,VarOrAff}, pwl::UnivariatePWLFunction, method::Incremental, direction::DIRECTION) where {F} + grid = _continuous_gridpoints_or_die(pwl) + @show xs, ys = grid.input_vals, grid.output_vals counter = model.ext[:PWL].counter n = length(pwl.segments) + 1 diff --git a/src/methods/logarithmic.jl b/src/methods/logarithmic.jl index 808774b..54b6b29 100644 --- a/src/methods/logarithmic.jl +++ b/src/methods/logarithmic.jl @@ -12,17 +12,20 @@ function _reflected_gray_codes(k::Int) end end -function _formulate!(model::JuMP.Model, input_vars::Tuple{VarOrAff}, output_vars::NTuple{F,VarOrAff}, pwl::UnivariatePWLFunction, method::Logarithmic, direction::DIRECTION) where {F} - xs, ys = _continuous_breakpoints_or_die(pwl) +function formulate_pwl!(model::JuMP.Model, input_vars::Tuple{VarOrAff}, output_vars::NTuple{F,VarOrAff}, pwl::UnivariatePWLFunction{F}, method::Logarithmic, direction::DIRECTION) where {F} + grid = _continuous_gridpoints_or_die(pwl) - n = length(xs) - d = n - 1 - k = ceil(Int, log2(n)) + λ = _create_convex_multiplier_vars(model, grid, input_vars, output_vars, direction) + formulate_sos2!(model, λ, method) + return +end + +function formulate_sos2!(model::JuMP.Model, λ::Vector{T}, method::Logarithmic) where {T <: VarOrAff} counter = model.ext[:PWL].counter + n = length(λ) + d = n - 1 + k = ceil(Int, log2(d)) y = JuMP.@variable(model, [1:k], Bin, base_name="y_$counter") - - λ = _create_convex_multiplier_vars(model, xs, ys, input_vars, output_vars, direction) - _sos2_encoding_constraints!(model, λ, y, _reflected_gray_codes(k), _unit_vector_hyperplanes(k)) - return + return nothing end diff --git a/src/methods/six_stencil.jl b/src/methods/six_stencil.jl new file mode 100644 index 0000000..d1ff3f3 --- /dev/null +++ b/src/methods/six_stencil.jl @@ -0,0 +1,169 @@ +struct SixStencil <: Method + axis_method::Method +end + +# Logarithmic is default method for x_1 and x_2 axis sos2 constraints. +SixStencil() = SixStencil(Logarithmic()) + +# TODO: Unit tests for biclique cover +function formulate_pwl!(model::JuMP.Model, input_vars::NTuple{2, VarOrAff}, output_vars::NTuple{F,VarOrAff}, pwl::BivariatePWLFunction{F}, method::SixStencil, direction::DIRECTION) where {F} + # Verify we have a triangulation + _check_triangulation(pwl) + + initPWL!(model) + counter = model.ext[:PWL].counter + counter += 1 + model.ext[:PWL].counter = counter + + grid = _continuous_gridpoints_or_die(pwl) + xs, ys = grid.input_vals, grid.output_vals + u_1 = unique(x[1] for x in xs) + u_2 = unique(x[2] for x in xs) + @assert issorted(u_1) + @assert issorted(u_2) + + n_1, n_2 = size(xs) + + x_1_to_i = Dict(u_1[i] => i for i in 1:n_1) + x_2_to_j = Dict(u_2[j] => j for j in 1:n_2) + + λ = JuMP.@variable(model, [1:n_1,1:n_2], lower_bound=0, upper_bound=1, base_name="λ_$counter") + JuMP.@constraint(model, sum(λ) == 1) + JuMP.@constraint(model, sum(λ[i,j]*u_1[i] for i in 1:n_1, j in 1:n_2) == input_vars[1]) + JuMP.@constraint(model, sum(λ[i,j]*u_2[j] for i in 1:n_1, j in 1:n_2) == input_vars[2]) + for k in 1:F + rhs = sum(λ[i,j]*ys[i,j][k] for i in 1:n_1, j in 1:n_2) + _constrain_output_var(model, output_vars[k], rhs, direction) + end + + # formulations with SOS2 along each dimension + T_x = [sum(λ[i,j] for i in 1:n_1) for j in 1:n_2] + T_y = [sum(λ[i,j] for j in 1:n_2) for i in 1:n_1] + + formulate_sos2!(model, T_x, method.axis_method) + formulate_sos2!(model, T_y, method.axis_method) + + # Eⁿᵉ[i,j] = true means that we must cover the edge {(i,j),(i+1,j+1)}. + # Otherwise, we must cover the edge {(i+1,j),(i,j+1)}. + E_sw_ne = fill(false, n_1 - 1, n_2 - 1) + for segment in pwl.segments + # TODO: Remove; assertion redundant with _check_triangulation above. + @assert length(segment.input_vals) == length(segment.output_vals) == 3 + i_a = x_1_to_i[segment.input_vals[1][1]] + i_b = x_1_to_i[segment.input_vals[2][1]] + i_c = x_1_to_i[segment.input_vals[3][1]] + j_a = x_2_to_j[segment.input_vals[1][2]] + j_b = x_2_to_j[segment.input_vals[2][2]] + j_c = x_2_to_j[segment.input_vals[3][2]] + IJ = Set([(i_a, j_a), (i_a, j_a), (i_c, j_c)]) + i_min, i_max = extrema([i_a, i_b, i_c]) + j_min, j_max = extrema([j_a, j_b, j_c]) + if ((i_min, j_max) in IJ) && ((i_max, j_min) in IJ) + E_sw_ne[i_min, j_min] = true + else + @assert (i_min, j_min) in IJ + @assert (i_max, j_max) in IJ + end + end + + # diagonal lines running from SW to NE. Grouped with an offset of 3. + w_sw_ne = JuMP.@variable(model, [0:2], Bin, base_name="w_sw_ne_$counter") + for o in 0:2 + A_o = Set{Tuple{Int,Int}}() + B_o = Set{Tuple{Int,Int}}() + for off_1 in o:3:(n_1 - 2) + sw_in_A = true # whether we put the SW corner of the next triangle to cover in set A + for i in (1 + off_1):(n_1 - 1) + j = i - off_1 + if !(1 ≤ i ≤ n_1 - 1) + continue + end + if !(1 ≤ j ≤ n_2-1) + continue # should never happen + end + if E_sw_ne[i,j] # if we need to cover the edge... + if sw_in_A # figure out which set we need to put it in; this depends on previous triangle in our current line + push!(A_o, (i ,j )) + push!(B_o, (i+1,j+1)) + else + push!(A_o, (i+1,j+1)) + push!(B_o, (i ,j )) + end + sw_in_A = !sw_in_A + end + end + end + for off_2 in (3-o):3:(n_2-1) + sw_in_A = true + for j in (off_2+1):(n_2-1) + i = j - off_2 + if !(1 ≤ i ≤ n_1-1) + continue + end + if E_sw_ne[i,j] + if sw_in_A + push!(A_o, (i ,j )) + push!(B_o, (i+1,j+1)) + else + push!(A_o, (i+1,j+1)) + push!(B_o, (i ,j )) + end + sw_in_A = !sw_in_A + end + end + end + JuMP.@constraints(model, begin + sum(λ[i,j] for (i,j) in A_o) ≤ w_sw_ne[o] + sum(λ[i,j] for (i,j) in B_o) ≤ 1 - w_sw_ne[o] + end) + end + + w_se_nw = JuMP.@variable(model, [0:2], Bin, base_name="w_se_nw_$counter") + for o in 0:2 + A_o = Set{Tuple{Int,Int}}() + B_o = Set{Tuple{Int,Int}}() + for off_1 in o:3:(n_1 - 2) + se_in_A = true + for j in 1:(n_2-1) + i = n_1 - j - off_1 + if !(1 ≤ i ≤ n_1-1) + continue + end + if !E_sw_ne[i,j] + if se_in_A + push!(A_o, (i+1,j )) + push!(B_o, (i ,j+1)) + else + push!(A_o, (i ,j+1)) + push!(B_o, (i+1,j )) + end + se_in_A = !se_in_A + end + end + end + for off_2 in (3-o):3:(n_2-1) + se_in_A = true + for j in (off_2+1):(n_2-1) + i = n_1 - j + off_2 + if !(1 ≤ i ≤ n_1-1) + continue + end + if !E_sw_ne[i,j] + if se_in_A + push!(A_o, (i+1,j )) + push!(B_o, (i ,j+1)) + else + push!(A_o, (i ,j+1)) + push!(B_o, (i+1,j )) + end + se_in_A = !se_in_A + end + end + end + JuMP.@constraints(model, begin + sum(λ[i,j] for (i,j) in A_o) ≤ w_se_nw[o] + sum(λ[i,j] for (i,j) in B_o) ≤ 1 - w_se_nw[o] + end) + end + return +end diff --git a/src/methods/util.jl b/src/methods/util.jl index 18bb77b..d810c07 100644 --- a/src/methods/util.jl +++ b/src/methods/util.jl @@ -1,15 +1,42 @@ -function _continuous_breakpoints_or_die(pwl::UnivariatePWLFunction{F}) where {F} - xs = Set{Tuple{Float64}}() +# function _continuous_gridpoints_or_die(pwl::UnivariatePWLFunction{F}) where {F} +# xs = Set{Tuple{Float64}}() +# for segment in pwl.segments +# for val in segment.input_vals +# push!(xs, val) +# end +# end +# ys = Dict{Tuple{Float64},NTuple{F,Float64}}() +# for segment in pwl.segments +# for i in 1:length(segment.input_vals) +# x = segment.input_vals[i] +# y = segment.output_vals[i] +# if haskey(ys, x) +# if y != ys[x] +# error("Expected piecewise linear function to be continuous.") +# end +# else +# ys[x] = y +# end +# end +# end +# X = sort!(collect(xs)) +# Y = [ys[x] for x in X] +# return X, Y +# end + +function _continuous_gridpoints_or_die(pwl:: PWLFunction{D, F, SegmentPointRep{D, F}}) where {D, F} + # Step 1: Collect all input points + xs = Set{NTuple{D, Float64}}() for segment in pwl.segments for val in segment.input_vals push!(xs, val) end end - ys = Dict{Tuple{Float64},NTuple{F,Float64}}() + + # Step 2: Verify continuity + ys = Dict{NTuple{D, Float64}, NTuple{F, Float64}}() for segment in pwl.segments - for i in 1:length(segment.input_vals) - x = segment.input_vals[i] - y = segment.output_vals[i] + for (x, y) in zip(segment.input_vals, segment.output_vals) if haskey(ys, x) if y != ys[x] error("Expected piecewise linear function to be continuous.") @@ -19,9 +46,20 @@ function _continuous_breakpoints_or_die(pwl::UnivariatePWLFunction{F}) where {F} end end end - X = sort!(collect(xs)) - Y = [ys[x] for x in X] - return X, Y + + @assert length(xs) == length(ys) + + # Step 3: Build grid, and verify every point is included in PWL function + axes = [sort!(unique(x[i] for x in xs)) for i in 1:D] + + x_grid = collect(Base.Iterators.product(axes...)) + y_grid = map(x -> get(ys, x, nothing), x_grid) + + if length(x_grid) != length(xs) + error("Decomposition is not aligned along a grid.") + end + + return Grid(x_grid, y_grid) end function _constrain_output_var(model::JuMP.Model, output_var::VarOrAff, func_val::VarOrAff, direction::DIRECTION) @@ -36,23 +74,60 @@ function _constrain_output_var(model::JuMP.Model, output_var::VarOrAff, func_val return end -function _create_convex_multiplier_vars(model::JuMP.Model, xs::Vector{NTuple{D,Float64}}, ys::Vector{NTuple{F,Float64}}, input_vars::NTuple{D,JuMP.VariableRef}, output_vars::NTuple{F,JuMP.VariableRef}, direction::DIRECTION) where {D,F} +struct Grid{D, F} + input_vals::Array{NTuple{D, Float64}, D} + output_vals::Array{NTuple{F, Float64}, D} + + function Grid(input_vals::Array{NTuple{D, Float64}, D}, output_vals::Array{NTuple{F, Float64}, D}) where {D, F} + if size(input_vals) != size(output_vals) + error("Incompatible input/output sizes $(size(input_vals)) and $(size(output_vals)). Must be the same.") + end + return new{D, F}(input_vals, output_vals) + end +end + +function _create_convex_multiplier_vars(model::JuMP.Model, grid::Grid{D, F}, input_vars::NTuple{D,JuMP.VariableRef}, output_vars::NTuple{F,JuMP.VariableRef}, direction::DIRECTION) where {D,F} counter = model.ext[:PWL].counter - n = length(xs) - @assert n == length(ys) - λ = JuMP.@variable(model, [1:n], lower_bound=0, upper_bound=1, base_name="λ_$counter") + # TODO: Name λ variables + λ = similar(Array{JuMP.VariableRef}, axes(grid.input_vals)) + for I in eachindex(λ) + λ[I] = JuMP.@variable(model, lower_bound=0, upper_bound=1) + end + JuMP.@constraint(model, sum(λ) == 1) for j in 1:D - JuMP.@constraint(model, sum(λ[i]* xs[i][j] for i in 1:n) == input_vars[j]) + JuMP.@constraint(model, sum(λ[I] * grid.input_vals[I][j] for I in eachindex(λ)) == input_vars[j]) end for j in 1:F - _constrain_output_var(model, output_vars[j], sum(λ[i]*ys[i][j] for i in 1:n), direction) + _constrain_output_var(model, output_vars[j], sum(λ[I]*grid.output_vals[I][j] for I in eachindex(λ)), direction) end return λ end -function _sos2_encoding_constraints!(m::JuMP.Model, λ::Vector{JuMP.VariableRef}, y::Vector{JuMP.VariableRef}, h::Vector{Vector{Float64}}, B::Vector{Vector{Float64}}) +function _check_triangle(segment::SegmentPointRep{D}) where {D} + if !(length(segment.input_vals) == length(segment.output_vals) == D + 1) + error("Encountered something that was not a simplex while expecting a trianglulation.") + end + return +end + +function _check_triangle(segment::SegmentHyperplaneRep{D}) where {D} + if length(segment.breakpoints) != D + 1 + error("Encountered something that was not a simplex while expecting a trianglulation.") + end + return +end + +function _check_triangulation(pwl::PWLFunction) where {D, F} + # TODO: Add check that segments lie in a single subrectangle + for segment in pwl.segments + _check_triangle(segment) + end + return +end + +function _sos2_encoding_constraints!(m::JuMP.Model, λ::Vector{T}, y::Vector{JuMP.VariableRef}, h::Vector{Vector{Float64}}, B::Vector{Vector{Float64}}) where {T <: VarOrAff} n = length(λ) - 1 for b in B JuMP.@constraints(m, begin diff --git a/test/runtests.jl b/test/runtests.jl index 87b37f1..1560436 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -9,17 +9,43 @@ const MOI = MathOptInterface using PiecewiseLinearOpt const PLO = PiecewiseLinearOpt -# TODO: Add :SOS2 to this list, once Cbc supports it -methods_1D = (Incremental(), Logarithmic()) +const methods_1D = (Incremental(), Logarithmic()) @testset "Simple univariate" begin - m = JuMP.Model(Gurobi.Optimizer) - JuMP.@variable(m, x) + model = JuMP.Model(Gurobi.Optimizer) + JuMP.@variable(model, x) s1 = PLO.SegmentPointRep{1,1}([(1.,), (2.,)], [(2.5,), (3.5,)]) s2 = PLO.SegmentPointRep{1,1}([(2.,), (3.,)], [(3.5,), (1.0,)]) pwl = PLO.PWLFunction{1,1,PLO.SegmentPointRep{1,1}}([s1, s2]) - piecewiselinear(m, x, pwl, method=PLO.Incremental()) + y = piecewiselinear(model, (x,), pwl, method=PLO.Incremental()) + JuMP.@objective(model, Min, y[1]) + + JuMP.optimize!(model) + + @test JuMP.termination_status(model) == MOI.OPTIMAL + @test JuMP.value(x) ≈ 3.0 rtol=1e-4 + @test JuMP.value(y[1]) ≈ 1.0 rtol=1e-4 +end + +const methods_2D = (Incremental(), Logarithmic()) +@testset "Simple bivariate" begin + model = JuMP.Model(Gurobi.Optimizer) + JuMP.@variable(model, x[1:2]) + + s1 = PLO.SegmentPointRep{2,1}([(0.0, 0.0), (0.0, 1.0), (1.0, 1.0)], [(0.0,), (1.0,), (2.0,)]) + s2 = PLO.SegmentPointRep{2,1}([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0)], [(0.0,), (3.0,), (2.0,)]) + pwl = PLO.PWLFunction{2,1,PLO.SegmentPointRep{2,1}}([s1, s2]) + + y = piecewiselinear(model, (x[1], x[2]), pwl) + JuMP.@objective(model, Min, y[1]) + + JuMP.optimize!(model) + + @test JuMP.termination_status(model) == MOI.OPTIMAL + @test JuMP.value(x[1]) ≈ 0.0 rtol=1e-4 + @test JuMP.value(x[2]) ≈ 0.0 rtol=1e-4 + @test JuMP.value(y[1]) ≈ 0.0 rtol=1e-4 end @testset "1D: $method" for method in methods_1D @@ -34,24 +60,26 @@ end push!(segments, PLO.SegmentPointRep{1,1}([(x_l,), (x_r,)], [(sin(x_l),), (sin(x_r),)])) end pwl = PLO.PWLFunction{1,1,PLO.SegmentPointRep{1,1}}(segments) - z = piecewiselinear(model, x, pwl, method=method) - JuMP.@objective(model, Max, z) + y = piecewiselinear(model, (x,), pwl, method=method) + JuMP.@objective(model, Max, y[1]) JuMP.optimize!(model) @test JuMP.termination_status(model) == MOI.OPTIMAL @test JuMP.value(x) ≈ 1.75474 rtol=1e-4 - @test JuMP.value(z) ≈ 0.98313 rtol=1e-4 + @test JuMP.value(y[1]) ≈ 0.98313 rtol=1e-4 + @test JuMP.objective_value(model) ≈ 0.98313 rtol=1e-4 + @test JuMP.objective_value(model) ≈ JuMP.value(y[1]) rtol=1e-4 - JuMP.@constraint(model, x ≤ 1.5z) + JuMP.@constraint(model, x ≤ 1.5y[1]) JuMP.optimize!(model) @test JuMP.termination_status(model) == MOI.OPTIMAL @test JuMP.value(x) ≈ 1.36495 rtol=1e-4 - @test JuMP.value(z) ≈ 0.90997 rtol=1e-4 + @test JuMP.value(y[1]) ≈ 0.90997 rtol=1e-4 @test JuMP.objective_value(model) ≈ 0.90997 rtol=1e-4 - @test JuMP.objective_value(model) ≈ JuMP.value(z) rtol=1e-4 + @test JuMP.objective_value(model) ≈ JuMP.value(y[1]) rtol=1e-4 end # println("\nbivariate tests") From 05d0783105ec35c65b79693f00d0e3bfe774bbb7 Mon Sep 17 00:00:00 2001 From: Joey Huchette Date: Mon, 6 Apr 2020 11:25:32 -0500 Subject: [PATCH 4/9] Add disaggregated logarithmic formulation --- src/PiecewiseLinearOpt.jl | 32 +- src/jump.jl | 949 ----------------------- src/methods/disaggregated_logarithmic.jl | 28 + src/methods/logarithmic.jl | 12 - src/methods/six_stencil.jl | 2 +- src/methods/util.jl | 38 +- src/types.jl | 112 +-- test/1D-pwl-instances.h5 | Bin 24859632 -> 0 bytes test/2D-pwl-instances.h5 | Bin 34281328 -> 0 bytes test/exhaustive-tests.jl | 92 --- test/runtests.jl | 13 +- 11 files changed, 56 insertions(+), 1222 deletions(-) delete mode 100644 src/jump.jl create mode 100644 src/methods/disaggregated_logarithmic.jl delete mode 100644 test/1D-pwl-instances.h5 delete mode 100644 test/2D-pwl-instances.h5 delete mode 100644 test/exhaustive-tests.jl diff --git a/src/PiecewiseLinearOpt.jl b/src/PiecewiseLinearOpt.jl index ee36c15..57010c4 100644 --- a/src/PiecewiseLinearOpt.jl +++ b/src/PiecewiseLinearOpt.jl @@ -28,9 +28,12 @@ const VarOrAff = Union{JuMP.VariableRef,JuMP.AffExpr} include(joinpath("methods", "util.jl")) -export Incremental, Logarithmic, SixStencil +export Incremental, Logarithmic, DisaggregatedLogarithmic, SixStencil include(joinpath("methods", "incremental.jl")) include(joinpath("methods", "logarithmic.jl")) +include(joinpath("methods", "disaggregated_logarithmic.jl")) + +const SOS2Method = Union{Logarithmic} include(joinpath("methods", "six_stencil.jl")) function formulate_pwl!(model::JuMP.Model, input_vals::Vector{NTuple{D,VarOrAff}}, output_vals::Vector{NTuple{F,VarOrAff}}, pwl::PWLFunction, method::Method, direction::DIRECTION) where {D,F} @@ -69,31 +72,4 @@ function piecewiselinear(model::JuMP.Model, return output_vars end -# function piecewiselinear(model::JuMP.Model, -# input_vars::Tuple{VarOrAff,VarOrAff}, -# pwl::BivariatePWLFunction{1}, -# method::Method = SixStencil(), -# direction::DIRECTION = Graph, -# output_var::Union{Nothing,VarOrAff} = nothing) -# initPWL!(model) -# counter = model.ext[:PWL].counter -# counter += 1 -# model.ext[:PWL].counter = counter -# -# if isempty(pwl.segments) -# error( -# "I don't know how to handle a piecewise linear function with no breakpoints." -# ) -# end -# -# output_lb = minimum(minimum(segment.output_vals) for segment in pwl.segments)[1] -# output_ub = maximum(maximum(segment.output_vals) for segment in pwl.segments)[1] -# -# if output_var === nothing -# output_var = JuMP.@variable(model, lower_bound=output_lb, upper_bound=output_ub, base_name="y_$counter") -# end -# formulate_pwl!(model, (input_var,), (output_var,), pwl, method, direction) -# return output_var -# end - end # module diff --git a/src/jump.jl b/src/jump.jl deleted file mode 100644 index 1eba2d6..0000000 --- a/src/jump.jl +++ /dev/null @@ -1,949 +0,0 @@ -# TODO: choose method based on problem size -defaultmethod() = :Logarithmic - -mutable struct PWLData - counter::Int - PWLData() = new(0) -end - -function initPWL!(m::JuMP.Model) - if !haskey(m.ext, :PWL) - m.ext[:PWL] = PWLData() - end - return nothing -end - -const VarOrAff = Union{JuMP.VariableRef,JuMP.AffExpr} - -function piecewiselinear(m::JuMP.Model, x::VarOrAff, d, f::Function; method=defaultmethod()) - initPWL!(m) - fd = [f(xx) for xx in d] - return piecewiselinear(m, x, d, fd; method=method) -end - -piecewiselinear(m::JuMP.Model, x::VarOrAff, d, fd; method=defaultmethod()) = - piecewiselinear(m, x, UnivariatePWLFunction(d, fd); method=method) - -function piecewiselinear(m::JuMP.Model, x::VarOrAff, pwl::UnivariatePWLFunction; method=defaultmethod()) - initPWL!(m) - counter = m.ext[:PWL].counter - counter += 1 - m.ext[:PWL].counter = counter - d = [_x[1] for _x in pwl.x] - fd = pwl.z - n = length(d) - - if n != length(fd) - error("You provided a different number of breakpoints ($n) and function values at the breakpoints ($(length(fd)))") - end - if n == 0 - error("I don't know how to handle a piecewise linear function with no breakpoints") - end - - z = JuMP.@variable(m, lower_bound=minimum(fd), upper_bound=maximum(fd), base_name="z_$counter") - - if n == 1 - JuMP.@constraint(m, x == d[1]) - JuMP.@constraint(m, z == fd[1]) - return z - end - - if method == :Incremental - δ = JuMP.@variable(m, [1:n], lower_bound=0, upper_bound=1, base_name="δ_$counter") - y = JuMP.@variable(m, [1:n-1], Bin, base_name="y_$counter") - JuMP.@constraint(m, x == d[1] + sum(δ[i]*( d[i+1]- d[i]) for i in 1:n-1)) - JuMP.@constraint(m, z == fd[1] + sum(δ[i]*(fd[i+1]-fd[i]) for i in 1:n-1)) - for i in 1:n-1 - JuMP.@constraint(m, δ[i+1] ≤ y[i]) - JuMP.@constraint(m, y[i] ≤ δ[i]) - end - elseif method == :MC - x̂ = JuMP.@variable(m, [1:n-1], base_name="x̂_$counter") - ẑ = JuMP.@variable(m, [1:n-1], base_name="ẑ_$counter") - y = JuMP.@variable(m, [1:n-1], Bin, base_name="y_$counter") - JuMP.@constraint(m, sum(y) == 1) - JuMP.@constraint(m, sum(x̂) == x) - JuMP.@constraint(m, sum(ẑ) == z) - Δ = [(fd[i+1]-fd[i])/(d[i+1]-d[i]) for i in 1:n-1] - for i in 1:n-1 - JuMP.@constraints(m, begin - x̂[i] ≥ d[i] *y[i] - x̂[i] ≤ d[i+1]*y[i] - ẑ[i] == fd[i]*y[i] + Δ[i]*(x̂[i]-d[i]*y[i]) - end) - end - elseif method in (:DisaggLogarithmic,:DLog) - γ = JuMP.@variable(m, [i=1:n,j=max(1,i-1):min(n-1,i)], lower_bound=0, upper_bound=1) - JuMP.@constraint(m, sum(γ) == 1) - JuMP.@constraint(m, γ[1,1]* d[1] + sum((γ[i,i-1]+γ[i,i])* d[i] for i in 2:n-1) + γ[n,n-1]* d[n] == x) - JuMP.@constraint(m, γ[1,1]*fd[1] + sum((γ[i,i-1]+γ[i,i])*fd[i] for i in 2:n-1) + γ[n,n-1]*fd[n] == z) - r = ceil(Int, log2(n-1)) - H = reflected_gray_codes(r) - y = JuMP.@variable(m, [1:r], Bin) - for j in 1:r - JuMP.@constraint(m, sum((γ[i,i]+γ[i+1,i])*H[i][j] for i in 1:(n-1)) == y[j]) - end - else - # V-formulation methods - λ = JuMP.@variable(m, [1:n], lower_bound=0, upper_bound=1, base_name="λ_$counter") - JuMP.@constraint(m, sum(λ) == 1) - JuMP.@constraint(m, sum(λ[i]* d[i] for i in 1:n) == x) - JuMP.@constraint(m, sum(λ[i]*fd[i] for i in 1:n) == z) - - if method in (:Logarithmic,:Log) - sos2_logarithmic_formulation!(m, λ) - elseif method in (:LogarithmicIB,:LogIB) - sos2_logarithmic_IB_formulation!(m, λ) - elseif method == :CC - sos2_cc_formulation!(m, λ) - elseif method in (:ZigZag,:ZZB) - sos2_zigzag_formulation!(m, λ) - elseif method in (:ZigZagInteger,:ZZI) - sos2_zigzag_general_integer_formulation!(m, λ) - elseif method == :GeneralizedCelaya - sos2_generalized_celaya_formulation!(m, λ) - elseif method == :SymmetricCelaya - sos2_symmetric_celaya_formulation!(m, λ) - elseif method == :SOS2 - JuMP.@constraint(m, λ in MOI.SOS2([i for i in 1:n])) - else - error("Unrecognized method $method") - end - end - - return z -end - -function sos2_cc_formulation!(m::JuMP.Model, λ) - counter = m.ext[:PWL].counter - n = length(λ) - y = JuMP.@variable(m, [1:n-1], Bin, base_name="y_$counter") - JuMP.@constraint(m, sum(y) == 1) - JuMP.@constraint(m, λ[1] ≤ y[1]) - for i in 2:n-1 - JuMP.@constraint(m, λ[i] ≤ y[i-1] + y[i]) - end - JuMP.@constraint(m, λ[n] ≤ y[n-1]) - return nothing -end - -# function sos2_mc_formulation!(m::JuMP.Model, λ) # not currently used -# counter = m.ext[:PWL].counter -# n = length(λ) -# γ = JuMP.@variable(m, [1:n-1, 1:n], base_name="γ_$counter") -# y = JuMP.@variable(m, [1:n-1], Bin, base_name="y_$counter") -# JuMP.@constraint(m, sum(y) == 1) -# JuMP.@constraint(m, sum(γ[i,:] for i in 1:n-1) .== λ) -# for i in 1:n-1 -# JuMP.@constraint(m, γ[i,i] + γ[i,i+1] ≥ y[i]) -# end -# return nothing -# end - -function sos2_logarithmic_formulation!(m::JuMP.Model, λ) - counter = m.ext[:PWL].counter - n = length(λ)-1 - k = ceil(Int,log2(n)) - y = JuMP.@variable(m, [1:k], Bin, base_name="y_$counter") - sos2_encoding_constraints!(m, λ, y, reflected_gray_codes(k), unit_vector_hyperplanes(k)) - return nothing -end - -function sos2_logarithmic_IB_formulation!(m::JuMP.Model, λ) # IB: independent branching - counter = m.ext[:PWL].counter - n = length(λ)-1 - k = ceil(Int,log2(n)) - y = JuMP.@variable(m, [1:k], Bin, base_name="y_$counter") - _H = reflected_gray_codes(k) - d = length(_H) - H = Dict(i => _H[i] for i in 1:d) - H[0] = H[1] - H[d+1] = H[d] - for j in 1:k - JuMP.@constraints(m, begin - sum(λ[i] for i in 1:(n+1) if H[i-1][j] == H[i][j] == 1) ≤ y[j] - sum(λ[i] for i in 1:(n+1) if H[i-1][j] == H[i][j] == 0) ≤ 1 - y[j] - end) - end - return nothing -end - -function sos2_zigzag_formulation!(m::JuMP.Model, λ) - counter = m.ext[:PWL].counter - n = length(λ)-1 - k = ceil(Int,log2(n)) - y = JuMP.@variable(m, [1:k], Bin, base_name="y_$counter") - sos2_encoding_constraints!(m, λ, y, zigzag_codes(k), zigzag_hyperplanes(k)) - return nothing -end - -function sos2_zigzag_general_integer_formulation!(m::JuMP.Model, λ) - counter = m.ext[:PWL].counter - n = length(λ)-1 - k = ceil(Int,log2(n)) - # TODO: tighter upper_bounds - y = JuMP.@variable(m, [i=1:k], Int, lower_bound=0, upper_bound=2^(k-i), base_name="y_$counter") - sos2_encoding_constraints!(m, λ, y, integer_zigzag_codes(k), unit_vector_hyperplanes(k)) - return nothing -end - -function sos2_generalized_celaya_formulation!(m::JuMP.Model, λ) - counter = m.ext[:PWL].counter - n = length(λ)-1 - k = ceil(Int,log2(n)) - codes = generalized_celaya_codes(k) - lb = [minimum(t[i] for t in codes) for i in 1:k] - ub = [maximum(t[i] for t in codes) for i in 1:k] - y = JuMP.@variable(m, [i=1:k], Int, lower_bound=lb[i], upper_bound=ub[i], base_name="y_$counter") - sos2_encoding_constraints!(m, λ, y, codes, generalized_celaya_hyperplanes(k)) - return nothing -end - -function sos2_symmetric_celaya_formulation!(m::JuMP.Model, λ) - counter = m.ext[:PWL].counter - n = length(λ)-1 - k = ceil(Int,log2(n)) - codes = symmetric_celaya_codes(k) - lb = [minimum(t[i] for t in codes) for i in 1:k] - ub = [maximum(t[i] for t in codes) for i in 1:k] - y = JuMP.@variable(m, [i=1:k], Int, lower_bound=lb[i], upper_bound=ub[i], base_name="y_$counter") - sos2_encoding_constraints!(m, λ, y, codes, symmetric_celaya_hyperplanes(k)) - return nothing -end - -function sos2_encoding_constraints!(m, λ, y, h, B) - n = length(λ)-1 - for b in B - JuMP.@constraints(m, begin - dot(b,h[1])*λ[1] + sum(min(dot(b,h[v]),dot(b,h[v-1]))*λ[v] for v in 2:n) + dot(b,h[n])*λ[n+1] ≤ dot(b,y) - dot(b,h[1])*λ[1] + sum(max(dot(b,h[v]),dot(b,h[v-1]))*λ[v] for v in 2:n) + dot(b,h[n])*λ[n+1] ≥ dot(b,y) - end) - end - return nothing -end - -function reflected_gray_codes(k::Int) - if k == 0 - return Vector{Int}[] - elseif k == 1 - return [[0],[1]] - else - codes′ = reflected_gray_codes(k-1) - return vcat([vcat(code,0) for code in codes′], - [vcat(code,1) for code in reverse(codes′)]) - end -end - -function zigzag_codes(k::Int) - if k <= 0 - error("Invalid code length $k") - elseif k == 1 - return [[0],[1]] - else - codes′ = zigzag_codes(k-1) - return vcat([vcat(code,0) for code in codes′], - [vcat(code,1) for code in codes′]) - end -end - -function integer_zigzag_codes(k::Int) - if k <= 0 - error("Invalid code length $k") - elseif k == 1 - return [[0],[1]] - else - codes′ = integer_zigzag_codes(k-1) - offset = [2^(j-2) for j in k:-1:2] - return vcat([vcat(code, 0) for code in codes′], - [vcat(code.+offset,1) for code in codes′]) - end -end - -function generalized_celaya_codes(k::Int) - if k <= 0 - error("Invalid code length $k") - elseif k == 1 - return [[0],[1]] - elseif k == 2 - return [[0,0],[1,1],[1,0],[0,1]] - else - codes′ = generalized_celaya_codes(k-1) - n = length(codes′) - hp = Int(n/2) - firstcodes = [codes′[i] for i in 1:hp] - secondcodes = [codes′[i] for i in (hp+1):n] - return vcat([vcat(codes′[i], 0) for i in 1 : n], - [vcat(codes′[i], 1) for i in 1 : hp], - [vcat(codes′[i],-1) for i in (hp+1): n]) - end -end - -function symmetric_celaya_codes(k::Int) - if k <= 0 - error("Invalid code length $k") - elseif k == 1 - return [[0],[1]] - else - codes′ = generalized_celaya_codes(k-1) - n = length(codes′) - hp = Int(n/2) - firstcodes = [codes′[i] for i in 1:hp] - secondcodes = [codes′[i] for i in (hp+1):n] - return vcat([vcat(codes′[i], 0) for i in 1 : n], - [vcat(codes′[i], 1) for i in 1 : hp], - [vcat(codes′[i],-1) for i in (hp+1): n]) - end -end - -function zigzag_hyperplanes(k::Int) - hps = Vector{Int}[] - for i in 1:k - hp = zeros(Int, k) - hp[i] = 1 - for j in (i+1):k - hp[j] = 2^(j-i-1) - end - push!(hps, hp) - end - return hps -end - -function unit_vector_hyperplanes(k::Int) - hps = Vector{Int}[] - for i in 1:k - hp = zeros(Int,k) - hp[i] = 1 - push!(hps, hp) - end - return hps -end - -generalized_celaya_hyperplanes(k::Int) = compute_hyperplanes(generalized_celaya_codes(k)) - -symmetric_celaya_hyperplanes(k::Int) = compute_hyperplanes(symmetric_celaya_codes(k)) - -function compute_hyperplanes(C::Vector{Vector{T}}) where T <: Number - n = length(C) - k = length(C[1]) - - d = zeros(n-1,k) - for i in 1:n-1 - d[i,:] = C[i+1] - C[i] - end - - if k <= 1 - error("Cannot process codes of length $k") - elseif k == 2 - @assert n == 4 - spanners = Vector{Float64}[] - for i in 1:n-1 - v = canonical!(d[i,:]) - v = [v[2], -v[1]] - push!(spanners, v) - end - indices = [1] - approx12 = isapprox(spanners[1],spanners[2]) - approx13 = isapprox(spanners[1],spanners[3]) - approx23 = isapprox(spanners[2],spanners[3]) - if !approx12 - push!(indices,2) - end - if !approx13 && !(!approx12 && approx23) - push!(indices,3) - end - return spanners[indices] - end - - indices = [1,2] - spanners = Vector{Float64}[] - while !isempty(indices) - if indices == [n-1] - break - end - if rank(d[indices,:]) == length(indices) && length(indices) <= k-1 - if length(indices) == k-1 - nullsp = nullspace(d[indices,:]) - @assert size(nullsp,2) == 1 - v = vec(nullsp) - push!(spanners, canonical!(v)) - end - if indices[end] != n-1 - push!(indices, indices[end]+1) - else - pop!(indices) - indices[end] += 1 - end - else - if indices[end] != n-1 - indices[end] += 1 - else - pop!(indices) - indices[end] += 1 - end - end - end - - keepers = [1] - for i in 2:length(spanners) - alreadyin = false - for j in keepers - if isapprox(spanners[i], spanners[j]) - alreadyin = true - break - end - end - if !alreadyin - push!(keepers, i) - end - end - - return spanners[keepers] -end - -function canonical!(v::Vector{Float64}) - normalize!(v) - for j in 1:length(v) - if abs(v[j]) < 1e-8 - v[j] = 0 - end - end - sgn = sign(v[findfirst([x!=0 for x in v])]) - for j in 1:length(v) - if abs(v[j]) < 1e-8 - v[j] = 0 - else - v[j] *= sgn - end - end - return v -end - -function optimal_IB_scheme!(m::JuMP.Model, λ, pwl, subsolver) # IB: independent branching - m.ext[:OptimalIB] = Int[] - - if !haskey(m.ext, :OptimalIBCache) - m.ext[:OptimalIBCache] = Dict() - end - - T = pwl.T - n = maximum(maximum(t) for t in T) - J = 1:n - E = fill(false, n, n) - for t in T - for i in t, j in t - E[i,j] = true - end - end - - if haskey(m.ext[:OptimalIBCache], pwl.T) - xx, yy = m.ext[:OptimalIBCache][pwl.T] - t = size(xx,1) - else - t = ceil(Int, log2(length(T))) - xx = Array{Float64,2}(undef,0,0) - yy = Array{Float64,2}(undef,0,0) - - while true - model = JuMP.Model(solver=subsolver) - JuMP.@variable(model, x[1:t,1:n], Bin) - JuMP.@variable(model, y[1:t,1:n], Bin) - JuMP.@variable(model, z[1:t,1:n,1:n], Bin) - - for j in 1:t - for r in J, s in J - if r >= s - continue - end - JuMP.@constraints(model, begin - z[j,r,s] <= x[j,r] + x[j,s] - z[j,r,s] <= x[j,r] + y[j,r] - z[j,r,s] <= x[j,s] + y[j,s] - z[j,r,s] <= y[j,r] + y[j,s] - z[j,r,s] >= x[j,r] + y[j,s] - 1 - z[j,r,s] >= x[j,s] + y[j,r] - 1 - end) - end - for r in J - JuMP.@constraint(model, x[j,r] + y[j,r] <= 1) - end - end - - for r in J, s in J - if r >= s - continue - end - if E[r,s] - JuMP.@constraint(model, sum(z[j,r,s] for j in 1:t) == 0) - else - JuMP.@constraint(model, sum(z[j,r,s] for j in 1:t) >= 1) - end - end - - JuMP.@objective(model, Min, sum(x) + sum(y)) - stat = JuMP.solve(model) - xx = JuMP.getvalue(x) - yy = JuMP.getvalue(y) - if any(isnan, xx) || any(isnan, yy) - t += 1 - else - break - end - end - m.ext[:OptimalIBCache][pwl.T] = (xx,yy) - end - - y = JuMP.@variable(m, [1:t], Bin) - - dˣ = [_x[1] for _x in pwl.x] - dʸ = [_x[2] for _x in pwl.x] - uˣ, uʸ = unique(dˣ), unique(dʸ) - @assert issorted(uˣ) - @assert issorted(uʸ) - nˣ, nʸ = length(uˣ), length(uʸ) - ˣtoⁱ = Dict(uˣ[i] => i for i in 1:nˣ) - ʸtoʲ = Dict(uʸ[i] => i for i in 1:nʸ) - - for i in 1:t - JuMP.@constraints(m, begin - sum(λ[ˣtoⁱ[pwl.x[j][1]],ʸtoʲ[pwl.x[j][2]]] for j in J if xx[i,j] == 1) ≤ y[i] - sum(λ[ˣtoⁱ[pwl.x[j][1]],ʸtoʲ[pwl.x[j][2]]] for j in J if yy[i,j] == 1) ≤ 1 - y[i] - end) - end - push!(m.ext[:OptimalIB], t) - - return nothing -end - -piecewiselinear(m::JuMP.Model, x::VarOrAff, y::VarOrAff, dˣ, dʸ, f::Function; method=defaultmethod()) = - piecewiselinear(m, x, y, BivariatePWLFunction(dˣ, dʸ, f); method=method) - -function piecewiselinear(m::JuMP.Model, x₁::VarOrAff, x₂::VarOrAff, pwl::BivariatePWLFunction; method=defaultmethod(), subsolver=nothing) - if (method == :OptimalIB) && (subsolver === nothing) - error("No MIP solver provided to construct optimal IB scheme. Pass a solver object to the piecewiselinear function, e.g. piecewiselinear(m, x₁, x₂, bivariatefunc, method=:OptimalIB, subsolver=GurobiSolver())") - end - - initPWL!(m) - counter = m.ext[:PWL].counter - counter += 1 - m.ext[:PWL].counter = counter - dˣ = [_x[1] for _x in pwl.x] - dʸ = [_x[2] for _x in pwl.x] - uˣ, uʸ = unique(dˣ), unique(dʸ) - @assert issorted(uˣ) - @assert issorted(uʸ) - - T = pwl.T - - nˣ, nʸ = length(uˣ), length(uʸ) - - if nˣ == 0 || nʸ == 0 - error("I don't know how to handle a piecewise linear function with zero breakpoints") - elseif nˣ == 1 - @assert length(dʸ) == nʸ == length(pwl.z) - return piecewiselinear(m, x₂, UnivariatePWLFunction(dʸ, [pwl.z[i] for i in 1:nʸ])) - elseif nʸ == 1 - @assert length(dˣ) == nˣ == length(pwl.z) - return piecewiselinear(m, x₁, UnivariatePWLFunction(dˣ, [pwl.z[i] for i in 1:nˣ])) - end - - ˣtoⁱ = Dict(uˣ[i] => i for i in 1:nˣ) - ʸtoʲ = Dict(uʸ[i] => i for i in 1:nʸ) - - fd = Array{Float64}(undef, nˣ, nʸ) - for (v,fv) in zip(pwl.x, pwl.z) - # i is the linear index into pwl.x...really want (i,j) pair - fd[ˣtoⁱ[v[1]],ʸtoʲ[v[2]]] = fv - end - - z = JuMP.@variable(m, lower_bound=minimum(fd), upper_bound=maximum(fd), base_name="z_$counter") - - if method == :MC - x̂₁ = JuMP.@variable(m, [T], base_name="x̂₁_$counter") - x̂₂ = JuMP.@variable(m, [T], base_name="x̂₂_$counter") - ẑ = JuMP.@variable(m, [T], base_name="ẑ_$counter") - y = JuMP.@variable(m, [T], Bin, base_name="y_$counter") - JuMP.@constraint(m, sum(y) == 1) - JuMP.@constraint(m, sum(x̂₁) == x₁) - JuMP.@constraint(m, sum(x̂₂) == x₂) - JuMP.@constraint(m, sum(ẑ) == z) - for t in T - @assert length(t) == 3 - r¹, r², r³ = pwl.x[t[1]], pwl.x[t[2]], pwl.x[t[3]] - fz¹, fz², fz³ = pwl.z[t[1]], pwl.z[t[2]], pwl.z[t[3]] - for P in ([1,2,3], [2,3,1], [3,1,2]) - p¹, p², p³ = [r¹, r², r³][P] - # p¹, p², p³ = pwl.x[t[P[1]]], pwl.x[t[P[2]]], pwl.x[t[P[3]]] - - A = [p¹[1] p¹[2] 1 - p²[1] p²[2] 1 - p³[1] p³[2] 1] - @assert rank(A) == 3 - b = [0, 0, 1] - q = A \ b - @assert isapprox(q[1]*p¹[1] + q[2]*p¹[2] + q[3], 0, atol=1e-4) - @assert isapprox(q[1]*p²[1] + q[2]*p²[2] + q[3], 0, atol=1e-4) - @assert isapprox(q[1]*p³[1] + q[2]*p³[2] + q[3], 1, atol=1e-4) - JuMP.@constraint(m, q[1]*x̂₁[t] + q[2]*x̂₂[t] + q[3]*y[t] ≥ 0) - end - A = [r¹[1] r¹[2] 1 - r²[1] r²[2] 1 - r³[1] r³[2] 1] - b = [fz¹, fz², fz³] - q = A \ b - @assert isapprox(q[1]*r¹[1] + q[2]*r¹[2] + q[3], fz¹, atol=1e-4) - @assert isapprox(q[1]*r²[1] + q[2]*r²[2] + q[3], fz², atol=1e-4) - @assert isapprox(q[1]*r³[1] + q[2]*r³[2] + q[3], fz³, atol=1e-4) - JuMP.@constraint(m, ẑ[t] == q[1]*x̂₁[t] + q[2]*x̂₂[t] + q[3]*y[t]) - end - elseif method in (:DisaggLogarithmic,:DLog) - T = pwl.T - X = pwl.x - Z = pwl.z - n = length(X) - γ = JuMP.@variable(m, [t=T,v=t], lower_bound=0, upper_bound=1, base_name="γ_$counter") - Tv = Dict(v => Any[] for v in 1:n) - for t in T, v in t - push!(Tv[v], t) - end - JuMP.@constraint(m, sum(γ) == 1) - JuMP.@constraint(m, sum(sum(γ[t,i] for t in Tv[i]) * X[i][1] for i in 1:n) == x₁) - JuMP.@constraint(m, sum(sum(γ[t,i] for t in Tv[i]) * X[i][2] for i in 1:n) == x₂) - JuMP.@constraint(m, sum(sum(γ[t,i] for t in Tv[i]) * Z[i] for i in 1:n) == z) - r = ceil(Int, log2(length(T))) - H = reflected_gray_codes(r) - y = JuMP.@variable(m, [1:r], Bin, base_name="y_$counter") - for j in 1:r - JuMP.@constraint(m, sum(sum(γ[T[i],v] for v in T[i])*H[i][j] for i in 1:length(T)) == y[j]) - end - else - # V-formulation methods - λ = JuMP.@variable(m, [1:nˣ,1:nʸ], lower_bound=0, upper_bound=1, base_name="λ_$counter") - JuMP.@constraint(m, sum(λ) == 1) - JuMP.@constraint(m, sum(λ[i,j]*uˣ[i] for i in 1:nˣ, j in 1:nʸ) == x₁) - JuMP.@constraint(m, sum(λ[i,j]*uʸ[j] for i in 1:nˣ, j in 1:nʸ) == x₂) - JuMP.@constraint(m, sum(λ[i,j]*fd[i,j] for i in 1:nˣ, j in 1:nʸ) == z) - - if method == :CC - T = pwl.T - y = JuMP.@variable(m, [T], Bin, base_name="y_$counter") - JuMP.@constraint(m, sum(y) == 1) - Ts = Dict((i,j) => Vector{Int}[] for i in 1:nˣ, j in 1:nʸ) - for t in T, ind in t - rˣ, rʸ = pwl.x[ind] - i, j = ˣtoⁱ[rˣ], ʸtoʲ[rʸ] - push!(Ts[(i,j)], t) - end - for i in 1:nˣ, j in 1:nʸ - JuMP.@constraint(m, λ[i,j] ≤ sum(y[t] for t in Ts[(i,j)])) - end - elseif method == :Incremental - error("Incremental formulation for bivariate functions is not currently implemented.") - # TODO: implement algorithm of Geissler et al. (2012) - elseif method == :OptimalIB - error("Optimal IB formulation has not yet been updated for JuMP v0.19.") - optimal_IB_scheme!(m, λ, pwl, subsolver) - else - # formulations with SOS2 along each dimension - Tx = [sum(λ[tˣ,tʸ] for tˣ in 1:nˣ) for tʸ in 1:nʸ] - Ty = [sum(λ[tˣ,tʸ] for tʸ in 1:nʸ) for tˣ in 1:nˣ] - - if method in (:Logarithmic,:Log) - sos2_logarithmic_formulation!(m, Tx) - sos2_logarithmic_formulation!(m, Ty) - elseif method in (:LogarithmicIB,:LogIB) - sos2_logarithmic_IB_formulation!(m, Tx) - sos2_logarithmic_IB_formulation!(m, Ty) - elseif method in (:ZigZag,:ZZB) - sos2_zigzag_formulation!(m, Tx) - sos2_zigzag_formulation!(m, Ty) - elseif method in (:ZigZagInteger,:ZZI) - sos2_zigzag_general_integer_formulation!(m, Tx) - sos2_zigzag_general_integer_formulation!(m, Ty) - elseif method == :GeneralizedCelaya - sos2_generalized_celaya_formulation!(m, Tx) - sos2_generalized_celaya_formulation!(m, Ty) - elseif method == :SymmetricCelaya - sos2_symmetric_celaya_formulation!(m, Tx) - sos2_symmetric_celaya_formulation!(m, Ty) - elseif method == :SOS2 - γˣ = JuMP.@variable(m, [1:nˣ], lower_bound=0, upper_bound=1, base_name="γˣ_$counter") - γʸ = JuMP.@variable(m, [1:nʸ], lower_bound=0, upper_bound=1, base_name="γʸ_$counter") - JuMP.@constraint(m, [tˣ in 1:nˣ], γˣ[tˣ] == sum(λ[tˣ,tʸ] for tʸ in 1:nʸ)) - JuMP.@constraint(m, [tʸ in 1:nʸ], γʸ[tʸ] == sum(λ[tˣ,tʸ] for tˣ in 1:nˣ)) - JuMP.@constraint(m, γˣ in MOI.SOS2([k for k in 1:nˣ])) - JuMP.@constraint(m, γʸ in MOI.SOS2([k for k in 1:nʸ])) - else - error("Unrecognized method $method") - end - - pattern = pwl.meta[:structure] - if pattern == :UnionJack - numT = 0 - minˣ, minʸ = uˣ[1], uʸ[1] - # find the index of the bottom-left point - idx = findfirst(pwl.x) do w; w == (minˣ, minʸ); end - for t in pwl.T - if idx in t - numT += 1 - end - end - @assert 1 <= numT <= 2 - - w = JuMP.@variable(m, binary=true, base_name="w_$counter") - # if numT==1, then bottom-left is contained in only one point, and so needs separating; otherwise numT==2, and need to offset by one - JuMP.@constraints(m, begin - sum(λ[tx,ty] for tx in 1:2:nˣ, ty in numT :2:nʸ) ≤ w - sum(λ[tx,ty] for tx in 2:2:nˣ, ty in (3-numT):2:nʸ) ≤ 1 - w - end) - elseif pattern == :K1 - # assumption is that the triangulation is uniform, as defined in types.jl - w = JuMP.@variable(m, [1:2], Bin, base_name="w_$counter") - JuMP.@constraints(m, begin - sum(λ[tx,ty] for tx in 1:nˣ, ty in 1:nʸ if mod(tx,2) == mod(ty,2) && (tx+ty) in 2:4:(nˣ+nʸ)) ≤ w[1] - sum(λ[tx,ty] for tx in 1:nˣ, ty in 1:nʸ if mod(tx,2) == mod(ty,2) && (tx+ty) in 4:4:(nˣ+nʸ)) ≤ 1 - w[1] - sum(λ[tx,ty] for tx in 1:nˣ, ty in 1:nʸ if mod(tx,2) != mod(ty,2) && (tx+ty) in 3:4:(nˣ+nʸ)) ≤ w[2] - sum(λ[tx,ty] for tx in 1:nˣ, ty in 1:nʸ if mod(tx,2) != mod(ty,2) && (tx+ty) in 5:4:(nˣ+nʸ)) ≤ 1 - w[2] - end) - elseif pattern == :OptimalTriangleSelection - error("Optimal triangle selection formulation has not yet been updated for JuMP v0.19.") - m.ext[:OptimalTriSelect] = Int[] - - if !haskey(m.ext, :OptimalTriSelectCache) - m.ext[:OptimalTriSelectCache] = Dict() - end - - J = [(i,j) for i in 1:nˣ, j in 1:nʸ] - E = Set{Tuple{Tuple{Int,Int},Tuple{Int,Int}}}() - for t in T - @assert length(t) == 3 - IJ = [(ˣtoⁱ[pwl.x[i][1]],ʸtoʲ[pwl.x[i][2]]) for i in t] - im = minimum(ij[1] for ij in IJ) - iM = maximum(ij[1] for ij in IJ) - jm = minimum(ij[2] for ij in IJ) - jM = maximum(ij[2] for ij in IJ) - @assert im < iM - @assert im < iM - if ((im,jm) in IJ) && ((iM,jM) in IJ) - push!(E, ((im,jM),(iM,jm))) - elseif ((im,jM) in IJ) && ((iM,jm) in IJ) - push!(E, ((im,jm),(iM,jM))) - else - error() - end - end - - if haskey(m.ext[:OptimalTriSelectCache], E) - xx, yy = m.ext[:OptimalTriSelectCache][E] - t = JuMP.size(xx,1) - else - if subsolver === nothing - error("No MIP solver provided to construct optimal triangle selection. Pass a solver object to the piecewiselinear function, e.g. piecewiselinear(m, x₁, x₂, bivariatefunc, method=:Logarithmic, subsolver=GurobiSolver())") - end - t = 1 - xx, yy = Array(Float64,0,0), Array(Float64,0,0) - while true - subm = JuMP.Model(solver=subsolver) - JuMP.@variable(subm, xˢᵘᵇ[1:t,J], Bin) - JuMP.@variable(subm, yˢᵘᵇ[1:t,J], Bin) - JuMP.@variable(subm, zˢᵘᵇ[1:t,J,J], Bin) - - for j in 1:t - for r in J, s in J - # lexicographic ordering on points on grid - if r[1] > s[1] || (r[1] == s[1] && r[2] >= s[2]) - continue - end - JuMP.@constraints(subm, begin - zˢᵘᵇ[j,r,s] <= xˢᵘᵇ[j,r] + xˢᵘᵇ[j,s] - zˢᵘᵇ[j,r,s] <= xˢᵘᵇ[j,r] + yˢᵘᵇ[j,r] - zˢᵘᵇ[j,r,s] <= xˢᵘᵇ[j,s] + yˢᵘᵇ[j,s] - zˢᵘᵇ[j,r,s] <= yˢᵘᵇ[j,r] + yˢᵘᵇ[j,s] - zˢᵘᵇ[j,r,s] >= xˢᵘᵇ[j,r] + yˢᵘᵇ[j,s] - 1 - zˢᵘᵇ[j,r,s] >= xˢᵘᵇ[j,s] + yˢᵘᵇ[j,r] - 1 - end) - end - for r in J - JuMP.@constraint(subm, xˢᵘᵇ[j,r] + yˢᵘᵇ[j,r] <= 1) - end - end - - for r in J, s in J - # lexicographic ordering on points on grid - (r[1] > s[1] || (r[1] == s[1] && r[2] >= s[2])) && continue - if (r,s) in E - JuMP.@constraint(subm, sum(zˢᵘᵇ[j,r,s] for j in 1:t) >= 1) - elseif max(abs(r[1]-s[1]), abs(r[2]-s[2])) == 1 - JuMP.@constraint(subm, sum(zˢᵘᵇ[j,r,s] for j in 1:t) == 0) - end - end - - JuMP.@objective(subm, Min, sum(xˢᵘᵇ) + sum(yˢᵘᵇ)) - stat = JuMP.solve(subm) - if any(isnan, subm.colVal) - t += 1 - else - xx = JuMP.getvalue(xˢᵘᵇ) - yy = JuMP.getvalue(yˢᵘᵇ) - m.ext[:OptimalTriSelectCache][E] = (xx,yy) - break - end - end - end - y = JuMP.@variable(m, [1:t], Bin, base_name="Δselect_$counter") - - for i in 1:t - JuMP.@constraints(m, begin - sum(λ[v[1],v[2]] for v in J if xx[i,v] ≈ 1) ≤ y[i] - sum(λ[v[1],v[2]] for v in J if yy[i,v] ≈ 1) ≤ 1 - y[i] - end) - end - push!(m.ext[:OptimalTriSelect], t) - elseif pattern in (:Stencil,:Stencil9) - w = JuMP.@variable(m, [1:3,1:3], Bin, base_name="w_$counter") - for oˣ in 1:3, oʸ in 1:3 - innoT = fill(true, nˣ, nʸ) - for (i,j,k) in pwl.T - xⁱ, xʲ, xᵏ = pwl.x[i], pwl.x[j], pwl.x[k] - iiˣ, iiʸ = ˣtoⁱ[xⁱ[1]], ʸtoʲ[xⁱ[2]] - jjˣ, jjʸ = ˣtoⁱ[xʲ[1]], ʸtoʲ[xʲ[2]] - kkˣ, kkʸ = ˣtoⁱ[xᵏ[1]], ʸtoʲ[xᵏ[2]] - # check to see if one of the points in the triangle falls on the grid - if (mod1(iiˣ,3) == oˣ && mod1(iiʸ,3) == oʸ) || (mod1(jjˣ,3) == oˣ && mod1(jjʸ,3) == oʸ) || (mod1(kkˣ,3) == oˣ && mod1(kkʸ,3) == oʸ) - innoT[iiˣ,iiʸ] = false - innoT[jjˣ,jjʸ] = false - innoT[kkˣ,kkʸ] = false - end - end - JuMP.@constraints(m, begin - sum(λ[i,j] for i in oˣ:3:nˣ, j in oʸ:3:nʸ) ≤ 1 - w[oˣ,oʸ] - sum(λ[i,j] for i in 1:nˣ, j in 1:nʸ if innoT[i,j]) ≤ w[oˣ,oʸ] - end) - end - else - @assert pattern in (:Upper, :Lower, :BestFit, :Random) - # Eⁿᵉ[i,j] = true means that we must cover the edge {(i,j),(i+1,j+1)} - Eⁿᵉ = fill(false, nˣ-1, nʸ-1) - for (i,j,k) in pwl.T - xⁱ, xʲ, xᵏ = pwl.x[i], pwl.x[j], pwl.x[k] - iiˣ, iiʸ = ˣtoⁱ[xⁱ[1]], ʸtoʲ[xⁱ[2]] - jjˣ, jjʸ = ˣtoⁱ[xʲ[1]], ʸtoʲ[xʲ[2]] - kkˣ, kkʸ = ˣtoⁱ[xᵏ[1]], ʸtoʲ[xᵏ[2]] - IJ = [(iiˣ,iiʸ), (jjˣ,jjʸ), (kkˣ,kkʸ)] - im = min(iiˣ, jjˣ, kkˣ) - iM = max(iiˣ, jjˣ, kkˣ) - jm = min(iiʸ, jjʸ, kkʸ) - jM = max(iiʸ, jjʸ, kkʸ) - if ((im,jM) in IJ) && ((iM,jm) in IJ) - Eⁿᵉ[im,jm] = true - else - @assert (im,jm) in IJ && (iM,jM) in IJ - end - end - - # diagonal lines running from SW to NE. Grouped with an offset of 3. - wⁿᵉ = JuMP.@variable(m, [0:2], Bin, base_name="wⁿᵉ_$counter") - for o in 0:2 - Aᵒ = Set{Tuple{Int,Int}}() - Bᵒ = Set{Tuple{Int,Int}}() - for offˣ in o:3:(nˣ-2) - SWinA = true # whether we put the SW corner of the next triangle to cover in set A - for i in (1+offˣ):(nˣ-1) - j = i - offˣ - if !(1 ≤ i ≤ nˣ-1) - continue - end - if !(1 ≤ j ≤ nʸ-1) - continue # should never happen - end - if Eⁿᵉ[i,j] # if we need to cover the edge... - if SWinA # figure out which set we need to put it in; this depends on previous triangle in our current line - push!(Aᵒ, (i ,j )) - push!(Bᵒ, (i+1,j+1)) - else - push!(Aᵒ, (i+1,j+1)) - push!(Bᵒ, (i ,j )) - end - SWinA = !SWinA - end - end - end - for offʸ in (3-o):3:(nʸ-1) - SWinA = true - for j in (offʸ+1):(nʸ-1) - i = j - offʸ - if !(1 ≤ i ≤ nˣ-1) - continue - end - if Eⁿᵉ[i,j] - if SWinA - push!(Aᵒ, (i ,j )) - push!(Bᵒ, (i+1,j+1)) - else - push!(Aᵒ, (i+1,j+1)) - push!(Bᵒ, (i ,j )) - end - SWinA = !SWinA - end - end - end - JuMP.@constraints(m, begin - sum(λ[i,j] for (i,j) in Aᵒ) ≤ wⁿᵉ[o] - sum(λ[i,j] for (i,j) in Bᵒ) ≤ 1 - wⁿᵉ[o] - end) - end - - wˢᵉ = JuMP.@variable(m, [0:2], Bin, base_name="wˢᵉ_$counter") - for o in 0:2 - Aᵒ = Set{Tuple{Int,Int}}() - Bᵒ = Set{Tuple{Int,Int}}() - for offˣ in o:3:(nˣ-2) - SEinA = true - # for i in (1+offˣ):-1:1 - # j = offˣ - i + 2 - for j in 1:(nʸ-1) - i = nˣ - j - offˣ - if !(1 ≤ i ≤ nˣ-1) - continue - end - if !Eⁿᵉ[i,j] - if SEinA - push!(Aᵒ, (i+1,j )) - push!(Bᵒ, (i ,j+1)) - else - push!(Aᵒ, (i ,j+1)) - push!(Bᵒ, (i+1,j )) - end - SEinA = !SEinA - end - end - end - for offʸ in (3-o):3:(nʸ-1) - SEinA = true - for j in (offʸ+1):(nʸ-1) - i = nˣ - j + offʸ - if !(1 ≤ i ≤ nˣ-1) - continue - end - if !Eⁿᵉ[i,j] - if SEinA - push!(Aᵒ, (i+1,j )) - push!(Bᵒ, (i ,j+1)) - else - push!(Aᵒ, (i ,j+1)) - push!(Bᵒ, (i+1,j )) - end - SEinA = !SEinA - end - end - end - JuMP.@constraints(m, begin - sum(λ[i,j] for (i,j) in Aᵒ) ≤ wˢᵉ[o] - sum(λ[i,j] for (i,j) in Bᵒ) ≤ 1 - wˢᵉ[o] - end) - end - end - end - end - - return z -end diff --git a/src/methods/disaggregated_logarithmic.jl b/src/methods/disaggregated_logarithmic.jl new file mode 100644 index 0000000..1879ad6 --- /dev/null +++ b/src/methods/disaggregated_logarithmic.jl @@ -0,0 +1,28 @@ +struct DisaggregatedLogarithmic <: Method end + +function formulate_pwl!(model::JuMP.Model, input_vars::NTuple{D, VarOrAff}, output_vars::NTuple{F, VarOrAff}, pwl::PWLFunctionPointRep{D, F}, method::DisaggregatedLogarithmic, direction::DIRECTION) where {D, F} + counter = model.ext[:PWL].counter + + segments = pwl.segments + num_bps = Dict(seg => length(seg.input_vals) for seg in segments) + + γ = JuMP.@variable(model, [seg in segments, i in 1:num_bps[seg]], lower_bound = 0, upper_bound = 1, base_name = "γ_$counter") + JuMP.@constraint(model, sum(γ) == 1) + + for j in 1:D + JuMP.@constraint(model, input_vars[j] == sum(sum(γ[seg, i] * seg.input_vals[i][j] for i in 1:num_bps[seg]) for seg in segments)) + end + for j in 1:F + rhs = sum(sum(γ[seg, i] * seg.output_vals[i][j] for i in 1:num_bps[seg]) for seg in segments) + _constrain_output_var(model, output_vars[j], rhs, direction) + end + + r = ceil(Int, log2(length(segments))) + _H = _reflected_gray_codes(r) + H = Dict(segments[i] => _H[i] for i in 1:length(segments)) + z = JuMP.@variable(model, [1:r], Bin, base_name = "z_$counter") + for j in 1:r + JuMP.@constraint(model, sum(sum(γ[seg, i] * H[seg][j] for i in 1:num_bps[seg]) for seg in segments) == z[j]) + end + return +end diff --git a/src/methods/logarithmic.jl b/src/methods/logarithmic.jl index 54b6b29..e71c754 100644 --- a/src/methods/logarithmic.jl +++ b/src/methods/logarithmic.jl @@ -1,17 +1,5 @@ struct Logarithmic <: Method end -function _reflected_gray_codes(k::Int) - if k == 0 - return Vector{Float64}[] - elseif k == 1 - return [[0.0], [1.0]] - else - codes′ = _reflected_gray_codes(k-1) - return vcat([vcat(code, 0.0) for code in codes′], - [vcat(code, 1.0) for code in reverse(codes′)]) - end -end - function formulate_pwl!(model::JuMP.Model, input_vars::Tuple{VarOrAff}, output_vars::NTuple{F,VarOrAff}, pwl::UnivariatePWLFunction{F}, method::Logarithmic, direction::DIRECTION) where {F} grid = _continuous_gridpoints_or_die(pwl) diff --git a/src/methods/six_stencil.jl b/src/methods/six_stencil.jl index d1ff3f3..d81c78d 100644 --- a/src/methods/six_stencil.jl +++ b/src/methods/six_stencil.jl @@ -1,5 +1,5 @@ struct SixStencil <: Method - axis_method::Method + axis_method::SOS2Method end # Logarithmic is default method for x_1 and x_2 axis sos2 constraints. diff --git a/src/methods/util.jl b/src/methods/util.jl index d810c07..e712472 100644 --- a/src/methods/util.jl +++ b/src/methods/util.jl @@ -1,29 +1,3 @@ -# function _continuous_gridpoints_or_die(pwl::UnivariatePWLFunction{F}) where {F} -# xs = Set{Tuple{Float64}}() -# for segment in pwl.segments -# for val in segment.input_vals -# push!(xs, val) -# end -# end -# ys = Dict{Tuple{Float64},NTuple{F,Float64}}() -# for segment in pwl.segments -# for i in 1:length(segment.input_vals) -# x = segment.input_vals[i] -# y = segment.output_vals[i] -# if haskey(ys, x) -# if y != ys[x] -# error("Expected piecewise linear function to be continuous.") -# end -# else -# ys[x] = y -# end -# end -# end -# X = sort!(collect(xs)) -# Y = [ys[x] for x in X] -# return X, Y -# end - function _continuous_gridpoints_or_die(pwl:: PWLFunction{D, F, SegmentPointRep{D, F}}) where {D, F} # Step 1: Collect all input points xs = Set{NTuple{D, Float64}}() @@ -138,6 +112,18 @@ function _sos2_encoding_constraints!(m::JuMP.Model, λ::Vector{T}, y::Vector{JuM return nothing end +function _reflected_gray_codes(k::Int) + if k == 0 + return Vector{Float64}[] + elseif k == 1 + return [[0.0], [1.0]] + else + codes′ = _reflected_gray_codes(k-1) + return vcat([vcat(code, 0.0) for code in codes′], + [vcat(code, 1.0) for code in reverse(codes′)]) + end +end + function _zigzag_codes(k::Int) if k <= 0 error("Invalid code length $k") diff --git a/src/types.jl b/src/types.jl index 79eb69a..d2422b3 100644 --- a/src/types.jl +++ b/src/types.jl @@ -33,112 +33,8 @@ struct PWLFunction{D, F, T <: Segment{D, F}} end end -const UnivariatePWLFunction{F} = PWLFunction{1, F, SegmentPointRep{1,F}} -const BivariatePWLFunction{F} = PWLFunction{2, F, SegmentPointRep{2,F}} +const PWLFunctionPointRep{D, F} = PWLFunction{D, F, SegmentPointRep{D, F}} +const PWLFunctionSegmentRep{D, F} = PWLFunction{D, F, SegmentHyperplaneRep{D, F}} -# -# struct -# -# function PWLFunction{D}(x::Vector{NTuple{D}}, z::Vector, T::Vector{Vector}, meta::Dict) where {D} -# @assert length(x) == length(z) -# for t in T -# @assert minimum(t) > 0 && maximum(t) <= length(x) -# end -# return PWLFunction{D}(x, z, T, meta) -# end -# -# PWLFunction(inputs) = PWLFunction(x, z, T, Dict()) -# -# const UnivariatePWLFunction = PWLFunction{1} -# -# function UnivariatePWLFunction(x, z) -# @assert issorted(x) -# return PWLFunction(Tuple{Float64}[(xx,) for xx in x], convert(Vector{Float64}, z), [[i,i+1] for i in 1:length(x)-1]) -# end -# -# function UnivariatePWLFunction(x, fz::Function) -# @assert issorted(x) -# return PWLFunction(Tuple{Float64}[(xx,) for xx in x], map(t->convert(Float64,fz(t)), x), [[i,i+1] for i in 1:length(x)-1]) -# end -# -# const BivariatePWLFunction = PWLFunction{2} -# -# function BivariatePWLFunction(x, y, fz::Function; pattern=:BestFit, seed=hash((length(x),length(y)))) -# @assert issorted(x) -# @assert issorted(y) -# X = vec(collect(Base.product(x,y))) -# # X = vec(Tuple{Float64,Float64}[(_x,_y) for _x in x, _y in y]) -# Z = map(t -> convert(Float64,fz(t...)), X) -# T = Vector{Vector{Int}}() -# m = length(x) -# n = length(y) -# -# mt = MersenneTwister(seed) -# # run for each square on [x[i],x[i+1]] × [y[i],y[i+1]] -# for i in 1:length(x)-1, j in 1:length(y)-1 -# SWt, NWt, NEt, SEt = LinearIndices((m,n))[i,j], LinearIndices((m,n))[i,j+1], LinearIndices((m,n))[i+1,j+1], LinearIndices((m,n))[i+1,j] -# xL, xU, yL, yU = x[i], x[i+1], y[j], y[j+1] -# @assert xL == X[SWt][1] == X[NWt][1] -# @assert xU == X[SEt][1] == X[NEt][1] -# @assert yL == X[SWt][2] == X[SEt][2] -# @assert yU == X[NWt][2] == X[NEt][2] -# SW, NW, NE, SE = fz(xL,yL), fz(xL,yU), fz(xU,yU), fz(xU,yL) -# mid1 = 0.5*(SW+NE) -# mid2 = 0.5*(NW+SE) -# -# if pattern == :Upper -# if mid1 > mid2 -# t1 = [SWt,NWt,NEt] -# t2 = [SWt,NEt,SEt] -# else -# t1 = [SWt,NWt,SEt] -# t2 = [SEt,NWt,NEt] -# end -# elseif pattern == :Lower -# if mid1 > mid2 -# t1 = [SWt,NWt,SEt] -# t2 = [SEt,NWt,NEt] -# else -# t1 = [SWt,NWt,NEt] -# t2 = [SWt,NEt,SEt] -# end -# elseif pattern == :BestFit -# mid3 = fz(0.5*(xL+xU), 0.5*(yL+yU)) -# if abs(mid1-mid3) < abs(mid2-mid3) -# t1 = [SWt,NWt,NEt] -# t2 = [SWt,NEt,SEt] -# else -# t1 = [SWt,NWt,SEt] -# t2 = [SEt,NWt,NEt] -# end -# elseif pattern == :UnionJack -# t1 = [SWt,SEt] -# t2 = [NWt,NEt] -# if iseven(i+j) -# push!(t1, NWt) -# push!(t2, SEt) -# else -# push!(t1, NEt) -# push!(t2, SWt) -# end -# elseif pattern == :K1 -# t1 = [SEt,SWt,NWt] -# t2 = [NWt,NEt,SEt] -# elseif pattern == :Random -# if rand(mt, Bool) -# t1 = [NWt,NEt,SEt] -# t2 = [SEt,SWt,NWt] -# else -# t1 = [SWt,NWt,NEt] -# t2 = [NEt,SEt,SWt] -# end -# else -# error("pattern $pattern not currently supported") -# end -# -# push!(T, t1) -# push!(T, t2) -# end -# -# return PWLFunction{2}(X, Z, T, Dict(:structure=>pattern)) -# end +const UnivariatePWLFunction{F} = PWLFunctionPointRep{1, F} +const BivariatePWLFunction{F} = PWLFunctionPointRep{2, F} diff --git a/test/1D-pwl-instances.h5 b/test/1D-pwl-instances.h5 deleted file mode 100644 index 248ab639fceb25532de1d79e7c23eba44f2d5cbe..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 24859632 zcmeFa4~*ScdG~odb-j1J-smPZVMtxL9j56tb<-QiNrot*KTtwP$m%;v-E>s>4L9y2 zoq|a(i4%rk!Y>n(4q(zLb?G!U>18ls2!7f7A`8t{5xPPa8dYBQ3PorZS?IpVszxYc zM^#jfkOk|R^ZA_O6OF>AtA)b7QT+Hk=Q+>$KL5@+zuz6t`RLf4@AzMLUbi!Bd@7Z& zJybXU>K{Miv-XD{+_u59ZGVHmY<6D$`z-Cnf%ungVdK9L2H{_g{#@?h-FMv;w*7L_ 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