Communication Dans Un Congrès Année : 2024

Proven Runtime Guarantees for How the MOEA/D Computes the Pareto Front from the Subproblem Solutions

Résumé

The decomposition-based multi-objective evolutionary algorithm (MOEA/D) does not directly optimize a given multi-objective function f , but instead optimizes N + 1 single-objective subproblems of f in a co-evolutionary manner. It maintains an archive of all nondominated solutions found and outputs it as approximation to the Pareto front. Once the MOEA/D found all optima of the subproblems (the goptima), 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 O(nN log n+n n/(2N) N log n) function evaluations. Especially for the second, more interesting phase when the algorithm start with all g-optima, we prove an Ω(n (1/2)(n/N+1) √ N 2 -n/N ) expected runtime. This runtime is super-polynomial if N = o(n), since this leaves large gaps between the g-optima, which require costly mutations to cover. For power-law mutation with exponent β ∈ (1, 2), we prove an expected runtime of O nN log n + n β log n function evaluations. The O n β log n 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 N = O(n β-1 ), resulting in an O(n β log n) 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.

Fichier principal
Vignette du fichier
Doerr_Krejca_Weeks__MOEAD_from_Subproblems__PPSN__2024_arxiv.pdf (313.59 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-04721295 , version 1 (04-10-2024)

Licence

Identifiants

Citer

Benjamin Doerr, Martin Krejca, Noé Weeks. Proven Runtime Guarantees for How the MOEA/D Computes the Pareto Front from the Subproblem Solutions. Parallel Problem Solving from Nature, PPSN 2024, 2024, Hagenberg, Austria. pp.197-212, ⟨10.1007/978-3-031-70071-2_13⟩. ⟨hal-04721295⟩
130 Consultations
213 Téléchargements

Altmetric

Partager

  • More