Dominance, epsilon, and hypervolume local optimal sets in multi-objective optimization, and how to tell the difference - Archive ouverte HAL
Communication Dans Un Congrès Année : 2018

Dominance, epsilon, and hypervolume local optimal sets in multi-objective optimization, and how to tell the difference

Résumé

Local search algorithms have shown good performance for several multi-objective combinatorial optimization problems. These approaches naturally stop at a local optimal set (LO-set) under given definitions of neighborhood and preference relation among subsets of solutions, such as set-based dominance relation, hypervolume or epsilon indicator. It is an open question how LO-sets under different set preference relations relate to each other. This paper reports an in-depth experimental analysis on multi-objective nk-landscapes. Our results reveal that, whatever the preference relation, the number of LO-sets typically increases with the problem non-linearity, and decreases with the number of objectives. We observe that strict LO-sets of bounded cardinality under set-dominance are LO-sets under both epsilon and hypervolume, and that LO-sets under hypervolume are LO-sets under set-dominance, whereas LO-sets under epsilon are not. Nonetheless, LO-sets under set-dominance are more similar to LO-sets under epsilon than under hypervolume. These findings have important implications for multi-objective local search. For instance, a dominance-based approach with bounded archive gets more easily trapped and might experience difficulty to identify an LO-set under epsilon or hypervolume. On the contrary, a hypervolume-based approach is expected to perform more steps before converging to better approximations.
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Dates et versions

hal-01823666 , version 1 (13-11-2018)

Identifiants

Citer

Arnaud Liefooghe, Manuel López-Ibáñez, Luís Paquete, Sébastien Verel. Dominance, epsilon, and hypervolume local optimal sets in multi-objective optimization, and how to tell the difference. GECCO 2018 - Genetic and Evolutionary Computation Conference, Jul 2018, Kyoto, Japan. pp.324-331, ⟨10.1145/3205455.3205572⟩. ⟨hal-01823666⟩
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