A Decomposition Approach for Bi-Objective Mixed-Integer Linear Programming Problems
Abstract
In this study, we analyze solution methods for approximating the Pareto front of bi-objective mixed-integer linear programming problems. First of all, we discuss a two-stage evolutionary algorithm. Given the values for the integer variables, the second stage of the two-stage evolution algorithm generates the values for the continuous variables of the corresponding Pareto efficient solutions. Then, the corresponding Pareto efficient solutions of integer variables are compared in the first-stage of the two-stage evolutionary algorithm to determine the Pareto efficient integer solutions. These stages are repeated within an evolutionary heuristic structure to approximate the Pareto front. Secondly, we propose a decomposition approach to separate the integral part of the feasible region of the problem. The decomposition approach separates the problem into sub-problems, each of which has an additional constraint, and approximates the Pareto fronts of the sub-problems using the two-stage evolutionary algorithm discussed. Then, using the sub-problem Pareto fronts, the Pareto front of the main problem is approximated. A numerical study is conducted to compare the two-stage evolutionary algorithm with the decomposition approach, which uses the two-stage evolutionary algorithm.
Recommended Citation
H. Farhangi et al., "A Decomposition Approach for Bi-Objective Mixed-Integer Linear Programming Problems," Procedings of the 67th Annual Conference and Expo of the Institute of Industrial Engineers (2017, Pittsburgh, PA), pp. 1229 - 1234, Institute of Industrial Engineers (IIE), May 2017.
Meeting Name
67th Annual Conference and Expo of the Institute of Industrial Engineers 2017 (2017: May 20-23, Pittsburgh, PA)
Department(s)
Engineering Management and Systems Engineering
Research Center/Lab(s)
Intelligent Systems Center
Keywords and Phrases
Decomposition; Engineers; Integer programming; Pareto principle; Continuous variables; Decomposition approach; Evolution algorithms; Integer variables; Mixed integer linear programming; Mixed integer linear programming problems; Pareto efficient solutions; Pivoting; Evolutionary algorithms; Bi-objective mixed-integer linear programming; Decomposition; Pivoting
International Standard Book Number (ISBN)
978-1-5108-4802-3
Document Type
Article - Conference proceedings
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2017 Institute of Industrial Engineers (IIE), All rights reserved.
Publication Date
01 May 2017
Comments
This work is partially supported by the US Department of Defense through the Systems Engineering Research Center (SERC) under Contract HQ0034-13-D-0004. SERC is a federally funded University Affiliated Research Center managed by Stevens Institute of Technology.