A Multiobjective Evolutionary Algorithm That Diversifies Population by Its Density

Abstract

Most existing multiobjective evolutionary algorithms (MOEAs) assume the existence of Pareto-optimal solutions/Pareto-optimal objective vectors in a neighborhood of an obtained Pareto-optimal set (PS)/Pareto-optimal front (PF). Obviously, this assumption does not work well on the multiobjective problem (MOP) whose true PF and true PS are in the form of multiple segments-truly disconnected MOP (TYD-MOP). Moreover, these MOEAs commonly involve more than three control parameters; and some of them even involve nine control parameters. The stabilities of their performance against parameter settings are generally unknown. In this paper, we propose a MOEA, namely multiobjective density driven evolutionary algorithm (MODdEA), which can handle TYD-MOP. MODdEA stores all evaluated solutions by a binary space partitioning (BSP) tree. Benefiting from the BSP scheme, a fast solution density estimation by the archive is naturally obtained. MODdEA uses this estimated density together with the nondominated rank to probabilistically select mating individuals, which relaxes the neighborhood assumption on PF in a parameter-less manner. Moreover, two genetic operators, extended arithmetic crossover and diversified mutation, are proposed to enhance the explorative search ability of the algorithm. MODdEA is examined on two test problem sets. The first test set consists of six TYD-MOPs; the second test set consists of 17 benchmark MOPs which are commonly examined by the existing MOEAs. Comparing to 14 test MOEAs, MODdEA has superior performance on TYD-MOP and is competitive on MOP whose true PF and PS are one single connected segment.