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Using functional programming to recognize named structure in an optimization problem: Application to pooling
Author(s) -
Ceccon Francesco,
Kouyialis Georgia,
Misener Ruth
Publication year - 2016
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.15308
Subject(s) - heuristics , solver , pooling , mathematical optimization , computer science , nonlinear programming , preprocessor , optimization problem , set (abstract data type) , integer programming , algorithm , nonlinear system , mathematics , artificial intelligence , physics , quantum mechanics , programming language
Branch‐and‐cut optimization solvers typically apply generic algorithms, e.g., cutting planes or primal heuristics, to expedite performance for many mathematical optimization problems. But solver software receives an input optimization problem as vectors of equations and constraints containing no structural information. This article proposes automatically detecting named special structure using the pattern matching features of functional programming. Specifically, we deduce the industrially‐relevant nonconvex nonlinear Pooling Problem within a mixed‐integer nonlinear optimization problem and show that we can uncover pooling structure in optimization problems which are not pooling problems. Previous work has shown that preprocessing heuristics can find network structures; we show that we can additionally detect nonlinear pooling patterns. Finding named structures allows us to apply, to generic optimization problems, cutting planes or primal heuristics developed for the named structure. To demonstrate the recognition algorithm, we use the recognized structure to apply primal heuristics to a test set of standard pooling problems. © 2016 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J , 62: 3085–3095, 2016