Empirical Analysis of Locality, Heritability and Heuristic Bias in Evolutionary Algorithms: A Case Study for the Multidimensional Knapsack Problem

Abstract

Our main aim is to provide guidelines and practical help for the design of appropriate representations and operators for evolutionary algorithms (EAs). For this purpose, we propose techniques to obtain a better understanding of various effects in the interplay of the representation and the operators. We study six different representations and associated variation operators in the context of a steady-state evolutionary algorithm for the multidimensional knapsack problem. Four of them are indirect decoder-based techniques, and two are direct encodings combined with different initialization, repair, and local improvement strategies. The complex decoders and the local improvement and repair strategies make it practically impossible to completely analyze such EAs in a fully theoretical way. After comparing the general performance of the chosen EA variants for the multidimensional knapsack problem on two benchmark suites, we present a hands-on approach for empirically analyzing important aspects of initialization, mutation, and crossover in an isolated fashion. Static, inexpensive measurements based on randomly created solutions are performed in order to quantify and visualize specific properties with respect to heuristic bias, locality, and heritability. These tests shed light onto the complex behavior of such EAs and point out reasons for good or bad performance. In addition, the proposed measures are also examined during actual EA runs, which gives further insight into dynamic aspects of evolutionary search and verifies the validity of the isolated static measurements. All measurements are described in a general way, allowing for an easy adaption to other representations and problems.