Solving linear optimization over arithmetic constraint formula

Li Chen (), Yinrun Lyu (), Chong Wang (), Jingzheng Wu (), Changyou Zhang (), Nasro Min-Allah (), Jamal Alhiyafi () and Yongji Wang ()
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Li Chen: Chinese Academy of Sciences
Yinrun Lyu: Chinese Academy of Sciences
Chong Wang: Chinese Academy of Sciences
Jingzheng Wu: Chinese Academy of Sciences
Changyou Zhang: Chinese Academy of Sciences
Nasro Min-Allah: University of Dammam
Jamal Alhiyafi: University of Dammam
Yongji Wang: Chinese Academy of Sciences

Journal of Global Optimization, 2017, vol. 69, issue 1, No 4, 69-102

Abstract: Abstract Since Balas extended the classical linear programming problem to the disjunctive programming (DP) problem where the constraints are combinations of both logic AND and OR, many researchers explored this optimization problem under various theoretical or application scenarios such as generalized disjunctive programming (GDP), optimization modulo theories (OMT), robot path planning, real-time systems, etc. However, the possibility of combining these differently-described but form-equivalent problems into a single expression remains overlooked. The contribution of this paper is two folded. First, we convert the linear DP/GDP model, linear-arithmetic OMT problem and related application problems into an equivalent form, referred to as the linear optimization over arithmetic constraint formula (LOACF). Second, a tree-search-based algorithm named RS-LPT is proposed to solve LOACF. RS-LPT exploits the techniques of interval analysis and nonparametric estimation for reducing the search tree and lowering the number of visited nodes. Also, RS-LPT alleviates bad construction of search tree by backtracking and pruning dynamically. We evaluate RS-LPT against two most common DP/GDP methods, three state-of-the-art OMT solvers and the disjunctive transformation based method on optimization benchmarks with different types and scales. Our results favor RS-LPT as compared to existing competing methods, especially for large scale cases.

Keywords: Linear programming; Disjunctive programming; Optimization modulo theories; Search algorithm (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10898-017-0499-8

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