Abstract
In multiobjective optimization, the result of an optimization algorithm is a set of efficient solutions from which the decision maker selects one. It is common that not all the efficient solutions can be computed in a short time and the search algorithm has to be stopped prematurely to analyze the solutions found so far. A set of efficient solutions that are well-spread in the objective space is preferred to provide the decision maker with a great variety of solutions. However, just a few exact algorithms in the literature exist with the ability to provide such a well-spread set of solutions at any moment: we call them anytime algorithms. We propose a new exact anytime algorithm for multiobjective combinatorial optimization combining three novel ideas to enhance the anytime behavior. We compare the proposed algorithm with those in the state-of-the-art for anytime multiobjective combinatorial optimization using a set of 480 instances from different well-known benchmarks and four different performance measures: the overall non-dominated vector generation ratio, the hypervolume, the general spread and the additive epsilon indicator. A comprehensive experimental study reveals that our proposal outperforms the previous algorithms in most of the instances.
Highlights
MultiObjective Optimization (MOO) is a field of research with many applications in different areas, such as biology, computer science, scheduling, and finances
A MultiObjective Program (MOP) is an optimization problem characterized by multiple and conflicting objective functions that are to be optimized over a feasible set of decisions
In this paper we propose a new exact algorithm to solve MultiObjective Combinatorial Optimization (MOCO) problems, which is valid for MultiObjective Discrete Optimization (MODO) problems with finite feasible sets
Summary
MultiObjective Optimization (MOO) is a field of research with many applications in different areas, such as biology, computer science, scheduling, and finances. The proposed algorithm is based on a general framework by Dächert and Klamroth [2] Speaking, it consists in analyzing a search region in the objective space and looking for new non-dominated points at each iteration. The contribution of this paper is to present new designing criteria and an innovative way of splitting the objective space so that the solutions obtained are well-spread over the objective space These are detailed in the following three novel proposals:. A new way of partitioning the search space after finding a new non-dominated point This partition reorders the selection of the future boxes to explore and has an influence in the spread of solutions. The last section is dedicated to the conclusions and future work
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