Expected running time analysis of a multiobjective evolutionary algorithm on pseudo-boolean functions

Abstract

In this paper we suggest a multiobjective evolutionary algorithm based on a restricted mating pool (REMO) with a separate archive for storing the remaining population. Such archive based algorithms have been used for solving real-world applications, however, no theoretical results are available. In this paper, we present a rigorous expected running time complexity analysis for the algorithm on two discrete pseudo boolean functions. We use the well known linear function LOTZ (Leading Zeros : Trailing Ones) and a continuous multiobjective quadratic function which is adapted to the discrete boolean space, for the analysis. The analysis shows that the algorithm runs with an expected time of O(n2) on LOTZ. Moreover, we prove that the bound holds with an overwhelming probability. For an unary encoding of the multiobjective quadratic function ((χ -a)2, (χ -b)2) in the boolean space, the expected running time of REMO is found to be O(nlogn). A simple strategy based on partitioning of the decision space into fitness layers is used for the analysis. © Springer-Verlag Berlin Heidelberg 2004.