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Efficient Separation of RLT Cuts for Implicit and Explicit Bilinear Products

  • The reformulation-linearization technique (RLT) is a prominent approach to constructing tight linear relaxations of non-convex continuous and mixed-integer optimization problems. The goal of this paper is to extend the applicability and improve the performance of RLT for bilinear product relations. First, a method for detecting bilinear product relations implicitly contained in mixed-integer linear programs is developed based on analyzing linear constraints with binary variables, thus enabling the application of bilinear RLT to a new class of problems. Our second contribution addresses the high computational cost of RLT cut separation, which presents one of the major difficulties in applying RLT efficiently in practice. We propose a new RLT cutting plane separation algorithm which identifies combinations of linear constraints and bound factors that are expected to yield an inequality that is violated by the current relaxation solution. A detailed computational study based on implementations in two solvers evaluates the performance impact of the proposed methods.

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Author:Ksenia BestuzhevaORCiD, Ambros GleixnerORCiD, Tobias AchterbergORCiD
Document Type:In Proceedings
Parent Title (English):Integer Programming and Combinatorial Optimization. IPCO 2023.
First Page:14
Last Page:28
Series:Lecture Notes in Computer Science
Publisher:Springer, Cham
Year of first publication:2023
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