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.

Proactive selection of metaheuristics based on knowledge of previous results

“…As FDC needs the fitness values of all the solutions, it has been normally used to do postmortem study of the performance of metaheuristics in certain controlled type of problems. Other measures of problem difficulty can be found in [3,[5][6][7][8].…”

The Role of Representations in Dynamic Knapsack Problems

“…For the MKP, several different genetic representations and genetic operators have been proposed. A detailed analysis and comparison for static environments can be found in [6] and more recently in [15]. In the following, we describe the representations selected for our study in dynamic environments.…”

“…The representation together with the genetic operators and the fitness function define the fitness landscape, and it is generally agreed upon that a proper choice of representation and operators is crucial for the success of an EA, see e.g. [15,16].…”

“…The MKP is a well studied problem, and different representations have been proposed and compared e.g. in [6,9,14,15]. For our study, the binary representation with a penalty for constraint handling is selected as an example of a direct representation.…”

Solving the Multidimensional Knapsack Problem Using an Evolutionary Algorithm Hybridized with Branch and Bound

“…EAs have been used in several works for solving the MKP, e.g., [9,10,11,12,13] among others. To the best of our knowledge, the EA developed by Chu and Beasley in [11] represents the state-of-the-art in solving the MKP with EAs.…”