In the evolutionary multi-objective optimization (EMO) field, evolutionary algorithms have a population to store a well-converged and well-distributed solution set. In the literature, the population size is usually specified in the range of 100–300 to approximate the entire Pareto front. Recently, a new framework with an external archive has been actively studied where a solution set selected from the archive is used to approximate the Pareto front. In this framework, a small population size can be better than a standard population size since a smaller population size means a larger number of generations under the termination condition specified by the same number of evaluated solutions. In this paper, we numerically examine whether better results are obtained from a smaller population size specification than a standard specification when the algorithm performance is evaluated using a solution set selected from an external archive. In our experiments, we examine the performance of four representative EMO algorithms (NSGA-II, NSGA-III, MOEA/D, and SMS-EMOA) with four specifications of the population size (36, 66, 120, and 210) on two frequently-used artificial test suites (DTLZ and WFG) and three real-world test suites (RWA, DDMOP, and RE). Our experimental results show that better results are obtained from a smaller population size specification in many cases when we cannot evaluate many solutions (i.e., when solution evaluation is expensive).

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Small Population Size is Enough in Many Cases with External Archives

  • Yang Nan,
  • Hisao Ishibuchi,
  • Lie Meng Pang

摘要

In the evolutionary multi-objective optimization (EMO) field, evolutionary algorithms have a population to store a well-converged and well-distributed solution set. In the literature, the population size is usually specified in the range of 100–300 to approximate the entire Pareto front. Recently, a new framework with an external archive has been actively studied where a solution set selected from the archive is used to approximate the Pareto front. In this framework, a small population size can be better than a standard population size since a smaller population size means a larger number of generations under the termination condition specified by the same number of evaluated solutions. In this paper, we numerically examine whether better results are obtained from a smaller population size specification than a standard specification when the algorithm performance is evaluated using a solution set selected from an external archive. In our experiments, we examine the performance of four representative EMO algorithms (NSGA-II, NSGA-III, MOEA/D, and SMS-EMOA) with four specifications of the population size (36, 66, 120, and 210) on two frequently-used artificial test suites (DTLZ and WFG) and three real-world test suites (RWA, DDMOP, and RE). Our experimental results show that better results are obtained from a smaller population size specification in many cases when we cannot evaluate many solutions (i.e., when solution evaluation is expensive).