Understand behavior and performance of Real Coded Optimization Algorithms via NK-linkage model

Classical NK-landcape model was designed for analyzing optimization and evolution process in binary solution space, so it can not be used to analyze real coded optimization algorithms (RCOAs) directly, which work in continuous solution space directly. In this paper, the concept of NK-landscape model is extended to the continuous space, and a new NK-landscape model with continuous space is proposed. The new model is powerful and comprehensive with simple structure and flexible formula. Therefore, it can be used to construct test functions of various types of linkages for analyzing various performances of RCOAs. The feasibility of the proposed model is testified via experiments with 3 well-known RCOAs, ( i.e. covariance matrix adapting evolutionary strategy (CMA-ES), differential evolution (DE), neighborhood search differential evolution (NSDE)). The results show that the new model can reveal the merits and demerits of RCOAs effectively.

[1]  Xin Yao,et al.  From an individual to a population: an analysis of the first hitting time of population-based evolutionary algorithms , 2002, IEEE Trans. Evol. Comput..

[2]  Riccardo Poli,et al.  Evolving Problems to Learn About Particle Swarm Optimizers and Other Search Algorithms , 2006, IEEE Transactions on Evolutionary Computation.

[3]  Xin Yao,et al.  Making a Difference to Differential Evolution , 2008, Advances in Metaheuristics for Hard Optimization.

[4]  Leonardo Vanneschi,et al.  A Study of Fitness Distance Correlation as a Difficulty Measure in Genetic Programming , 2005, Evolutionary Computation.

[5]  XI FachbereichInformatik.  Finite Markov Chain Results in Evolutionary Computation: a Tour D'horizon , 1998 .

[6]  Qingfu Zhang,et al.  On the convergence of a class of estimation of distribution algorithms , 2004, IEEE Transactions on Evolutionary Computation.

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

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

[9]  P. Stadler.  Landscapes and their correlation functions , 1996 .

[10]  P. Stadler.  Fitness Landscapes , 1993 .

[11]  Stuart A. Kauffman,et al.  The origins of order , 1993 .

[12]  Kalyanmoy Deb,et al.  Multi-objective test problems, linkages, and evolutionary methodologies , 2006, GECCO.

[13]  E. Weinberger,et al.  Correlated and uncorrelated fitness landscapes and how to tell the difference , 1990, Biological Cybernetics.

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

[15]  Petros Koumoutsakos,et al.  Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) , 2003, Evolutionary Computation.

[16]  Tim Jones.  Evolutionary Algorithms, Fitness Landscapes and Search , 1995 .

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

[18]  P. Suganthan,et al.  Problem Definitions and Evaluation Criteria for the CEC 2010 Competition on Constrained Real- Parameter Optimization , 2010 .

[19]  Qingfu Zhang,et al.  This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 1 RM-MEDA: A Regularity Model-Based Multiobjective Estimation of , 2022 .

[20]  Qingfu Zhang,et al.  Errata to "RM-MEDA: A Regularity Model-Based Multiobjective Estimation of Distribution Algorithm" [Feb 08 41-63] , 2008, IEEE Trans. Evol. Comput..

[21]  Bart Naudts,et al.  A comparison of predictive measures of problem difficulty in evolutionary algorithms , 2000, IEEE Trans. Evol. Comput..