Continuous fitness landscape analysis using a chaos-based random walk algorithm

2020 IEEE Congress on Evolutionary Computation (CEC)

Zhou

2020

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.

Section: Numerical Resultsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Covariance Local Search for Memetic Frameworks: A Fitness Landscape Analysis Approach

2020 IEEE Congress on Evolutionary Computation (CEC)

Zhou

2020

“…This article focuses on pattern search and proposes a novel method belonging to this family of methods. The design of the proposed method is based on a fitness landscape analysis approach: in order to have a problem specific solver, the optimisation problem is analysed by an Artificial Intelligence tool and the results of the analysis are used to design the algorithm, see [7,25,32,33]. In the specific case, the proposed pattern search aims to detect a preferential pattern that suits the specific problems.…”

Section: Introductionmentioning

confidence: 99%

Generalised Pattern Search Based on Covariance Matrix Diagonalisation

Rostami²

2021

SN COMPUT. SCI.

Pattern Search is a family of gradient-free direct search methods for numerical optimisation problems. The characterising feature of pattern search methods is the use of multiple directions spanning the problem domain to sample new candidate solutions. These directions compose a matrix of potential search moves, that is the pattern. Although some fundamental studies theoretically indicate that various directions can be used, the selection of the search directions remains an unaddressed problem. The present article proposes a procedure for selecting the directions that guarantee high convergence/high performance of pattern search. The proposed procedure consists of a fitness landscape analysis to characterise the geometry of the problem by sampling points and selecting those whose objective function values are below a threshold. The eigenvectors of the covariance matrix of this distribution are then used as search directions for the pattern search. Numerical results show that the proposed method systematically outperforms its standard counterpart and is competitive with modern complex direct search and metaheuristic methods.

Adaptive Covariance Pattern Search

Applications of Evolutionary Computation

2021

Pattern search is a family of single solution deterministic optimisation algorithms for numerical optimisation. Pattern search algorithms generate a new candidate solution by means of an archive of potential moves, named pattern. This pattern is generated by a basis of vectors that span the domain where the function to optimise is defined. The present article proposes an adaptive implementation of pattern search that performs, at run-time, a fitness landscape analysis of the problem to determine the pattern and adapt it to the geometry of the problem. The proposed algorithm, called Adaptive Covariance Pattern Search (ACPS) uses at the beginning the fundamental orthonormal basis (directions of the variables) to build the pattern. Subsequently, ACPS saves the successful visited solutions, calculates the covariance matrix associated with these samples, and then uses the eigenvectors of this covariance matrix to build the pattern. ACPS is a restarting algorithm that at each restart recalculates the pattern that progressively adapts to the problem to optimise. Numerical results show that the proposed ACPS appears to be a promising approach on various problems and dimensions.