epsilon-OA for the solution of bi-objective generalized disjunctive programming problems in the synthesis of nonlinear process networks

There has been an increasing interest in multicriteria optimization (MCO) of nonlinear process network problems in recent years. Several mathematical models have been developed and solved using MCO methodologies including e-constraint, weighted sum, and minimum distance. In this paper, we investigate the bi-objective nonlinear network synthesis problem and propose an effective algorithm, epsilon-OA, based on augmented epsilon-constraint and logic-based outer approximation (OA). We provide theoretical characterization of the proposed algorithm and show that the solutions generated are efficient. We illustrate the effectiveness of our novel algorithm on two benchmark problems. The epsilon-OA is compared to the straightforward use of OA with augmented epsilon-constraint algorithm (epsilon-con + OA), the augmented epsilon-constraint without OA (E-MINLP), and the traditional epsilon-constraint (T-epsilon-con). Based on the results, our novel algorithm is very effective in solving the bi-objective generalized disjunctive programming problems in the synthesis of process networks. (C) 2014 Elsevier Ltd. All rights reserved.