Abstract
The design of each agent composing a Memetic Algorithm (MA) is a delicate task which often requires prior knowledge of the problem to be effective. This paper proposes a method to analyse one feature of the fitness landscape, that is the epistasis, with the aim of designing efficient local search algorithms for Memetic Frameworks. The proposed Analysis of Epistasis performs a sampling of points within the basin of attraction and builds a data set containing those candidate solutions whose objective function value falls below a threshold.The covariance matrix associated with this data set is then calculated. The eigenvectors of this covariance matrix are then computed and used as the reference system for the local search: a change of variables is performed and then the local search is performed on the new variables. The Analysis of Epistasis has been implemented on the three local search algorithms composing a popular MA called Multiple Trajectory Search (MTS). Numerical results show that the three modified local search algorithms outperform their original counterparts.
Highlights
Local search is a fundamental element of Memetic Computing
In order to experimentally demonstrate the effectiveness of the proposed Analysis of Epistasis, we tested the performance of Covariance Local Search 1 (CLS1), Covariance Local Search 2 (CLS2), and Covariance Local Search 3 (CLS3) and compared it against their original versions, Local Search 1 (LS1), Local Search 2 (LS2), Local Search 3 (LS3), respectively
In order to guarantee a fair comparison, the budget of CLS1, CLS2, and CLS3 has been split into two parts: 2500 × n function calls have been used to build the covariance matrix C whilst 2500 × n function calls have been spent to execute the algorithm
Summary
Local search is a fundamental element of Memetic Computing. Within Memetic Algorithms (MAs), properly designed local search algorithms may have a major impact on the performance of the entire Memetic Framework [1]. In Memetic Computing, FLA provides precious pieces of information to design global and local search algorithms employed within its framework [9]–[11]. The present paper focuses on local search design based on the analysis of epistasis. In Optimisation and in Genetic Algorithms (GAs) epistasis has been reinterpreted by means of an analogy: epistasis refers to the degree of dependency between genes in a chromosome and its objective function/fitness value [15].
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