The influence of linkage-learning in the linkage-tree GA when solving multidimensional knapsack problems

Abstract

Linkage Learning (LL) is an important issue concerning the development of more effective genetic algorithms (GA). It is from the identification of strongly dependent variables that crossover can be effective and an efficient search can be implemented. In the last decade many algorithms have confirmed the beneficial influence of LL when solving nearly decomposable problems. As it is a well-known fact from the no free-lunch theorem, LL can not be the best tool for all optimization problems, therefore, methods to identify those problems which could be efficiently solved by LL have become necessary. This paper investigates that nearlydecomposable problems present characteristic linkage-trees, therefore, those trees can be used as reference to infer whether or not some black-box optimization problem is a good candidate to be solved by LL. In this context, we consider the linkage-tree model from the Linkage-Tree GA (LTGA) and use the silhouette measure to expose some problems' characteristics. The silhouette fingerprints (SF) are defined for overlapping deceptive trap functions and compared with the SFs obtained for Multidimensional Knapsack Problems (MKP). The comparison allowed us to conclude that MKPs do not present evident linkages. This result was confirmed by experiments comparing the performance of the LTGA and the Randomized LTGA, in which both algorithms had very similar results.

Pairwise independence and its impact on Estimation of Distribution Algorithms

“…Liaw and Ting [32], for example, showed that univariate and bivariate EDAs could outperform more complex algorithms in some instances of the NK-model. Martins et al [33,34], on the other hand, investigated the accuracy of the linkage-tree models produced by the Linkage-Tree Genetic Algorithm (LTGA) and the performance of other EDAs on the Multidimensional Knapsack Problem (MKP). The authors also compared the LTGA performance when employing linkage-trees and random linkage-trees, with no evidence indicating that linkage-tree learning helped to solve the MKP [35].…”

A differential evolution algorithm with variable neighborhood search for multidimensional knapsack problem

“…Considering the new GA operators and fitness landscapes analysis, CBGA algorithms was used in series of studies in [23][24][25][26][27]. Most recently, estimation distribution algorithms (EDAs) are used in [28][29][30][31]. Furthermore, some other metaheuristic algorithms were developed for MKP such as particle swarm optimization (PSO) in [32][33][34][35], differential evaluation in [36] and other heuristic algorithms in [37].…”