Multi-objective Branch and Bound based on Decomposition

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Abstract

<p>Traditional multi-objective branch-and-bound approaches to multi-objective mixed-integer linear programming (MOMILP) problems are very expensive to search due to the huge number of Pareto-optimal solutions. In this research, we propose a practical method of dividing a multi-objective problem into multiple single-objective problems by weight vectors and applying the branch-and-bound method (BB) to each subproblem. The proposed method is named multi-objective branch-and-bound based on decomposition (MOBB/D) because it is a combination of the concept of multi-objective evolutionary algorithm based on decomposition (MOEA/D) and BB. The most important feature of MOBB/D is to obtain many Pareto solutions efficiently by sharing information between nearby subproblems in MOMILP problems. In this paper, we describe an approach to share tables in the simplex method as an example of information. Moreover, MOBB/D can control computation cost for solving MOMILP problems by adjusting the number of obtained Pareto solutions. To verify the effectiveness of the proposed method, we compared the search performance of MOBB/D with and without the use of neighborhood information.</p>

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