Embedding Formulation

[jac0320]

@kaarthiksundar

File addition:

• Added new file embedding.jl for handling formulation
• separating out bin.jl

Data structure changes:

• Added embedding, embedding_encode, embedding_ibs, embedding_link for options with embedding formulations

Algorithm changes and Function additions:

• Add logs associated with embedding formulation
• Let multi.jl fit with embedding formulations, i.e., divert from sos-2 formulation if embedding is true
• Update function build_constr_block()
• Introducing Binary Product MultiLinear (bpml) for more complex multilinear terms that ha binary variables in them
• separating several term storage by using the modularized function
• Some refactoring in operators.jl

Error schemes and default changes:

Test changes:

• Added tests for bpml terms
• Added tests for embedding
• Cleaned up several test instances code

---------- OLD Comments ------------- @harshangrjn Please see this PR for some consideration on what should be left out.

This is the all the development for POD.jl on the embedding formulation side #64 . It contains three main aspects,

• Basic Embedding Formulation (Gray code Encoding)
• Independent Branching Scheme for Compact Embedding
• Binary Variable - Continuous Variable Bound restriction constraints reconstruction with embedding

The options introduced in this PR here are:

embedding::Bool -> Control the to use embedding formulation or not embedding_encode::Any -> Direct which encoding will be used (compatibility will be checked) embedding_ibs::Bool -> Whether to exploit the compactness of the formulation or not embedding_link::Bool -> Add bound restriction constraints to regulate variable bounds based on active partition

Test cases are added to verify the encoding mapping and algorithm. Note that embedding formulation, regardless what additional options to choose, should yield the same results as SOS-2 formulation.

!!! This PR branch off #72.

[codecov[bot]]

Codecov Report

Merging #73 into master will increase coverage by 0.79%. The diff coverage is 95.41%.

@@           Coverage Diff            @@
##           master    #73      +/-   ##
========================================
+ Coverage   78.21%    79%   +0.79%     
========================================
  Files          27     28       +1     
  Lines        5696   5898     +202     
========================================
+ Hits         4455   4660     +205     
+ Misses       1241   1238       -3

Impacted Files	Coverage Δ
src/POD.jl	100% <ø> (ø)	:arrow_up:
src/utility.jl	78.46% <ø> (ø)	:arrow_up:
src/algorithm.jl	85.55% <100%> (+0.16%)	:arrow_up:
src/solver.jl	61.02% <100%> (+0.87%)	:arrow_up:
src/log.jl	75.45% <100%> (+0.92%)	:arrow_up:
test/algorithm.jl	100% <100%> (ø)	:arrow_up:
test/solver.jl	100% <100%> (ø)	:arrow_up:
src/multi.jl	74.77% <89.36%> (+6.02%)	:arrow_up:
src/embedding.jl	92.94% <92.94%> (ø)

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[jac0320]

The "embedding" will be later refactored as "ebd". The rest of the string will be the same. This is the final stage of such options.