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

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.

[1]  Maoguo Gong,et al.  Detecting composite communities in multiplex networks: A multilevel memetic algorithm , 2017, Swarm Evol. Comput..

[2]  Roberto Solis-Oba,et al.  Local Search , 2007, Handbook of Approximation Algorithms and Metaheuristics.

[3]  Fabio Caraffini,et al.  Rotation Invariance and Rotated Problems: An Experimental Study on Differential Evolution , 2018, EvoApplications.

[4]  Sébastien Vérel,et al.  Negative Slope Coefficient: A Measure to Characterize Genetic Programming Fitness Landscapes , 2006, EuroGP.

[5]  Qingfu Zhang,et al.  On Tchebycheff Decomposition Approaches for Multiobjective Evolutionary Optimization , 2018, IEEE Transactions on Evolutionary Computation.

[6]  Jaya Sil,et al.  Continuous fitness landscape analysis using a chaos-based random walk algorithm , 2018, Soft Comput..

[7]  Andries Petrus Engelbrecht,et al.  Quantifying ruggedness of continuous landscapes using entropy , 2009, 2009 IEEE Congress on Evolutionary Computation.

[8]  O. SIAMJ.,et al.  ON THE CONVERGENCE OF PATTERN SEARCH ALGORITHMS , 1997 .

[9]  Sébastien Vérel,et al.  Fitness Clouds and Problem Hardness in Genetic Programming , 2004, GECCO.

[10]  Yiwen Sun,et al.  Three-dimensional Gabor feature extraction for hyperspectral imagery classification using a memetic framework , 2015, Inf. Sci..

[11]  Zexuan Zhu,et al.  Wrapper–Filter Feature Selection Algorithm Using a Memetic Framework , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[12]  Ferrante Neri,et al.  Linear Algebra for Computational Sciences and Engineering , 2016, Springer International Publishing.

[13]  William H. Press,et al.  Numerical recipes in C (2nd ed.): the art of scientific computing , 1992 .

[14]  Charles M. Grinstead,et al.  Introduction to probability , 1999, Statistics for the Behavioural Sciences.

[15]  Andries Petrus Engelbrecht,et al.  A progressive random walk algorithm for sampling continuous fitness landscapes , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[16]  L. Dworsky.  An Introduction to Probability , 2008 .

[17]  Colin R. Reeves,et al.  Genetic Algorithms—Principles and Perspectives , 2002, Operations Research/Computer Science Interfaces Series.

[18]  Carlos García-Martínez,et al.  Memetic Algorithms for Continuous Optimisation Based on Local Search Chains , 2010, Evolutionary Computation.

[19]  Peter Merz,et al.  Advanced Fitness Landscape Analysis and the Performance of Memetic Algorithms , 2004, Evolutionary Computation.

[20]  William H. Press,et al.  Numerical Recipes in C, 2nd Edition , 1992 .

[21]  Riccardo Poli,et al.  Information landscapes and problem hardness , 2005, GECCO '05.

[22]  Yuval Davidor,et al.  Epistasis Variance: A Viewpoint on GA-Hardness , 1990, FOGA.

[23]  Xiaodong Li,et al.  Cooperative Co-Evolution With Differential Grouping for Large Scale Optimization , 2014, IEEE Transactions on Evolutionary Computation.

[24]  Ponnuthurai Nagaratnam Suganthan,et al.  Benchmark Functions for the CEC'2013 Special Session and Competition on Large-Scale Global Optimization , 2008 .

[25]  Andries Petrus Engelbrecht,et al.  A survey of techniques for characterising fitness landscapes and some possible ways forward , 2013, Inf. Sci..

[26]  Maoguo Gong,et al.  Cost-Aware Robust Control of Signed Networks by Using a Memetic Algorithm , 2020, IEEE Transactions on Cybernetics.

[27]  Giovanni Iacca,et al.  Parallel memetic structures , 2013, Inf. Sci..

[28]  David B. Fogel,et al.  An Introduction to Evolutionary Computation , 2022 .

[29]  Michael G. Epitropakis,et al.  HyperSPAM: A study on hyper-heuristic coordination strategies in the continuous domain , 2019, Inf. Sci..

[30]  Fabio Caraffini,et al.  An analysis on separability for Memetic Computing automatic design , 2014, Inf. Sci..

[31]  Bernd Freisleben,et al.  Fitness landscape analysis and memetic algorithms for the quadratic assignment problem , 2000, IEEE Trans. Evol. Comput..

[32]  Fabio Caraffini,et al.  A study on rotation invariance in differential evolution , 2019, Swarm Evol. Comput..

[33]  F. Wilcoxon.  Individual Comparisons by Ranking Methods , 1945 .

[34]  Cheng Chen,et al.  Community Preserving Network Embedding Based on Memetic Algorithm , 2020, IEEE Transactions on Emerging Topics in Computational Intelligence.

[35]  Thomas Stützle,et al.  Frankenstein's PSO: A Composite Particle Swarm Optimization Algorithm , 2009, IEEE Transactions on Evolutionary Computation.

[36]  Francisco Herrera,et al.  A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability , 2009, Soft Comput..

[37]  M. El-Sharkawi,et al.  Introduction to Evolutionary Computation , 2008 .

[38]  Chien-Chih Liao,et al.  A Novel Integer-Coded Memetic Algorithm for the Set $k$ -Cover Problem in Wireless Sensor Networks , 2018, IEEE Transactions on Cybernetics.

[39]  Chun Chen,et al.  Multiple trajectory search for Large Scale Global Optimization , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[40]  Jing J. Liang,et al.  Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization , 2005 .

[41]  William E. Hart,et al.  Memetic Evolutionary Algorithms , 2005 .