A Modification of the PBIL Algorithm Inspired by the CMA-ES Algorithm in Discrete Knapsack Problem

• Published in: Applied sciences Vol. 11; no. 19; p. 9136
• Main Authors: Konieczka, Maria, Poturała, Alicja, Arabas, Jarosław, Kozdrowski, Stanisław
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.10.2021
• Subjects: Adaptation; Algorithms; Chromosomes; Covariance Matrix Adaptation Evolution Strategy; Covariance Matrix Adaptation Population-Based Incremental Learning; data correlation; Experiments; Integer programming; Knapsack problem; Population; Population-Based Incremental Learning; Probability; Probability distribution; Variables
• ISSN: 2076-3417; 2076-3417
• DOI: 10.3390/app11199136

The subject of this paper is the comparison of two algorithms belonging to the class of evolutionary algorithms. The first one is the well-known Population-Based Incremental Learning (PBIL) algorithm, while the second one, proposed by us, is a modification of it and based on the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm. In the proposed Covariance Matrix Adaptation Population-Based Incremental Learning (CMA-PBIL) algorithm, the probability distribution of population is described by two parameters: the covariance matrix and the probability vector. The comparison of algorithms was performed in the discrete domain of the solution space, where we used the well-known knapsack problem in a variety of data correlations. The results obtained show that the proposed CMA-PBIL algorithm can perform better than standard PBIL in some cases. Therefore, the proposed algorithm can be a reasonable alternative to the PBIL algorithm in the discrete space domain.