Improving differential evolution through a unified approach

Only a few attempts in past have been made in adopting a unified outlook towards different paradigms in evolutionary computation (EC). The underlying motivation of these studies was aimed at gaining better understanding of evolutionary methods, both at the level of theory as well as application, in order to design efficient evolutionary algorithms for solving wide-range of complex problems. However, the past descriptions have either been too general or sometimes abstract in issuing a clear direction for improving an evolutionary paradigm for a task-specific. This paper recollects the ‘Unified Theory of Evolutionary Computation’ from past and investigates four steps—Initialization, Selection, Generation and Replacement, which are sufficient to describe traditional forms of Evolutionary Optimization Systems such as Genetic Algorithms, Evolutionary Strategies, Evolutionary Programming, Particle Swarm Optimization and differential evolution (DE). Then, a relatively new evolutionary paradigm, DE, is chosen and studied for its performance on a set of unimodal problems. Discovering DEs inability as an efficient solver, DE is reviewed under ‘Unified Framework’ and functional requirements of each step are evaluated. Targeted towards enhancing the DE’s performance, several modifications are proposed through borrowing of operations from a benchmark solver G3-PCX. Success of this exercise is demonstrated in a step-by-step fashion via simulation results. The Unified Approach is highly helpful in understanding the role and re-modeling of DE steps in order to efficiently solve unimodal problems. In an avalanching-age of new methods in EC, this study outlines a direction for advancing EC methods by undertaking a collective outlook and an approach of concept-sharing.

[1]  Panos M. Pardalos,et al.  Global optimization by continuous grasp , 2007, Optim. Lett..

[2]  M. Clerc,et al.  Particle Swarm Optimization , 2006 .

[3]  Ali Ahrari,et al.  On the utility of randomly generated functions for performance evaluation of evolutionary algorithms , 2010, Optim. Lett..

[4]  Nikolaus Hansen,et al.  Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[5]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[6]  Janez Brest,et al.  Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems , 2006, IEEE Transactions on Evolutionary Computation.

[7]  A. Ravindran,et al.  Engineering Optimization: Methods and Applications , 2006 .

[8]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[9]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[10]  Hans-Paul Schwefel,et al.  Evolution and Optimum Seeking: The Sixth Generation , 1993 .

[11]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[12]  Kalyanmoy Deb,et al.  A population-based algorithm-generator for real-parameter optimization , 2005, Soft Comput..

[13]  Panos M. Pardalos,et al.  Handbook of applied optimization , 2002 .

[14]  P. Pardalos,et al.  Handbook of global optimization , 1995 .

[15]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[16]  Kenneth de Jong,et al.  Evolutionary computation: a unified approach , 2007, GECCO.

[17]  Kalyanmoy Deb,et al.  A Computationally Efficient Evolutionary Algorithm for Real-Parameter Optimization , 2002, Evolutionary Computation.

[18]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[19]  Kalyanmoy Deb,et al.  Enhancing performance of particle swarm optimization through an algorithmic link with genetic algorithms , 2013, Comput. Optim. Appl..

[20]  Kalyanmoy Deb,et al.  Development of efficient particle swarm optimizers by using concepts from evolutionary algorithms , 2010, GECCO '10.

[21]  Jouni Lampinen,et al.  A Fuzzy Adaptive Differential Evolution Algorithm , 2005, Soft Comput..

[22]  M. Montaz Ali,et al.  Population set-based global optimization algorithms: some modifications and numerical studies , 2004, Comput. Oper. Res..

[23]  H. Abbass.  The self-adaptive Pareto differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[24]  Hans-Georg Beyer,et al.  Toward a Theory of Evolution Strategies: Self-Adaptation , 1995, Evolutionary Computation.

[25]  D. Fogel.  An evolutionary approach to the traveling salesman problem , 1988, Biological Cybernetics.

[26]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[27]  P. N. Suganthan,et al.  Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization , 2009, IEEE Transactions on Evolutionary Computation.