Running time analysis of multi-objective evolutionary algorithms on a simple discrete optimization problem

Abstract

For the first time, a running time analysis of populationbased multi-objective evolutionary algorithms for a discrete optimization problem is given. To this end, we define a simple pseudo-Boolean bi-objective problem (Lotz: leading ones-trailing zeroes) and investigate time required to find the entire set of Pareto-optimal solutions. It is shown that different multi-objective generalizations of a (1+1) evolutionary algorithm (EA) as well as a simple population-based evolutionary multi-objective optimizer (SEMO) need on average at least θ(n³) steps to optimize this function. We propose the fair evolutionary multi-objective optimizer (FEMO) and prove that this algorithm performs a black box optimization in θ(n² log n) function evaluations where n is the number of binary decision variables.