Quality-Time Analysis of Multi-Objective Evolutionary Algorithms


A quality-time analysis of multi-objective evolutionary algorithms (MOEAs) based on schema theorem and building blocks hypothesis is developed. A bicriteria OneMax problem, a hypothesis of niche and species, and a definition of dissimilar schemata are introduced for the analysis. In this paper, the convergence time, the first and last hitting time models are constructed for analyzing the performance of MOEAs. Population sizing model is constructed for determining appropriate population sizes. The models are verified using the bicriteria OneMax problem. The theoretical results indicate how the convergence time and population size of a MOEA scale up with the problem size, the dissimilarity of Pareto-optimal solutions, and the number of Pareto-optimal solutions of a multi-objective optimization problem.