PSO-based and SA-based metaheuristics for bilinear programming problems: an application to the pooling problem

Abstract

Bilinear programming problems (BLP) are subsets of nonconvex quadratic programs and can be classified as strongly NP-Hard. The exact methods to solve the BLPs are inefficient for large instances and only a few heuristic methods exist. In this study, we propose two metaheuristic methods, one is based on particle swarm optimization (PSO) and the other is based on simulated annealing (SA). Both of the proposed approaches take advantage of the bilinear structure of the problem. For the PSO-based method, a search variable, which is selected among the variable sets causing bilinearity, is subjected to particle swarm optimization. The SA-based procedure incorporates a variable neighborhood scheme. The pooling problem, which has several application areas in chemical industry and formulated as a BLP, is selected as a test bed to analyze the performances. Extensive experiments are conducted and they indicate the success of the proposed solution methods.