Convex generalized disjunctive programming (GDP)

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Edited By: Nicholas Schafhauser, Blerand Qeriqi, Ryan Cuppernull

Introduction

[ Insert picture from google doc of GDP branching to Logic Based Methods and Reformulation MI(N)LP ]

Theory

Methodology

The two most common ways of reformulating a GDP problem into an MINLP are through Big-M (BM) and Hull Reformulation (HR). BM is the simpler of the two, while HR results in tighter relaxation (smaller feasible region) and faster solution times. (https://kilthub.cmu.edu/articles/A_hierarchy_of_relaxations_for_nonlinear_convex_generalized_disjunctive_programming/6466535)

Below is an example of the reformulation of the GDP problem from the Theory section reformulated into an MINLP by using the Big-M method.


Notice that the boolean term from the original GDP has been converted into a numerical {0,1}. The logic relations have also been converted into linear integer constraints (Hy).

(https://kilthub.cmu.edu/articles/journal_contribution/Improved_Big-M_Reformulation_for_Generalized_Disjunctive_Programs/6467063)

This MINLP reformulation can now be used in well-known solvers (list them here) to calculate a solution.

Numerical Example

The following example was taken from: http://egon.cheme.cmu.edu/Papers/IMAGrossmannRuiz.pdf

GDP numeric example 1.png

GDP numeric example 3.png

http://egon.cheme.cmu.edu/Papers/IMAGrossmannRuiz.pdf

http://egon.cheme.cmu.edu/Papers/IMAGrossmannRuiz.pdf

Applications

Conclusion

References