Abstract
In a multi-objective combinatorial optimization (MOCO) problem, multiple objectives must be optimized simultaneously. In past years, several constraint-based algorithms have been proposed for finding Pareto-optimal solutions to MOCO problems that rely on repeated calls to a constraint solver. Understanding the properties of these algorithms and analyzing their performance is an important problem. Previous work has focused on empirical evaluations on benchmark instances. Such evaluations, while important, have their limitations. Our paper adopts a different, purely theoretical approach, which is based on characterizing the search space into subspaces and analyzing the worst-case performance of a MOCO algorithm in terms of the expected number of calls to the underlying constraint solver. We apply the approach to two important constraint-based MOCO algorithms. Our analysis reveals a deep connection between the search mechanism of a constraint solver and the exploration of the search space of a MOCO problem.
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Notes
- 1.
From here after, we use solution unqualified to refer to a feasible solution and Pareto-optimal solution to refer to an optimal solution to a MOCO instance.
- 2.
Without loss of generality, we consider minimization problems.
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Acknowledgments
This work has been partially supported by Shanghai Municipal Natural Science Foundation (No. 17ZR1406900) and NSERC Discovery Grant.
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Guo, J., Blais, E., Czarnecki, K., van Beek, P. (2017). A Worst-Case Analysis of Constraint-Based Algorithms for Exact Multi-objective Combinatorial Optimization. In: Mouhoub, M., Langlais, P. (eds) Advances in Artificial Intelligence. Canadian AI 2017. Lecture Notes in Computer Science(), vol 10233. Springer, Cham. https://doi.org/10.1007/978-3-319-57351-9_16
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