Proven Runtime Guarantees for How the MOEA/D: Computes the Pareto Front from the Subproblem Solutions
Pages 197 - 212
Abstract
The decomposition-based multi-objective evolutionary algorithm (MOEA/D) does not directly optimize a given multi-objective function f, but instead optimizes single-objective subproblems of f in a co-evolutionary manner. It maintains an archive of all non-dominated solutions found and outputs it as approximation to the Pareto front. Once the MOEA/D found all optima of the subproblems (the g-optima), it may still miss Pareto optima of f. The algorithm is then tasked to find the remaining Pareto optima directly by mutating the g-optima.
In this work, we analyze for the first time how the MOEA/D with only standard mutation operators computes the whole Pareto front of the OneMinMax benchmark when the g-optima are a strict subset of the Pareto front. For standard bit mutation, we prove an expected runtime of function evaluations. Especially for the second, more interesting phase when the algorithm start with all g-optima, we prove an expected runtime. This runtime is super-polynomial if , since this leaves large gaps between the g-optima, which require costly mutations to cover.
For power-law mutation with exponent , we prove an expected runtime of function evaluations. The term stems from the second phase of starting with all g-optima, and it is independent of the number of subproblems N. This leads to a huge speedup compared to the lower bound for standard bit mutation. In general, our overall bound for power-law suggests that the MOEA/D performs best for , resulting in an bound. In contrast to standard bit mutation, smaller values of N are better for power-law mutation, as it is capable of easily creating missing solutions.
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Published In
Sep 2024
435 pages
ISBN:978-3-031-70070-5
DOI:10.1007/978-3-031-70071-2
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
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Springer-Verlag
Berlin, Heidelberg
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Published: 14 September 2024
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