Adaptive Learning Rate Elitism Estimation of Distribution Algorithm Combining Chaos Perturbation for Large Scale Optimization

Estimation of distribution algorithm (EDA) is a kind of EAs, which is based on the technique of probabilistic model and sampling. Large scale optimization problems are a challenge for the conventional EAs. This paper presents an adaptive learning rate elitism EDA combining chaos perturbation (ALREEDA) to improve the performance of traditional EDA to solve high dimensional optimization problems. The famous elitism strategy is introduced to maintain a good convergent performance of this algorithm. The learning rate of σ (a parameter of probabilistic model) is adaptive in the optimization to enhance the algorithm’s global and local search ability, and the chaos perturbation strategy is used to improve the algorithm’s local search ability. Some simulation experiments are conducted to verify the performance of ALREEDA by seven benchmarks of CEC’08 large scale optimization with dimensions 100, 500 and 1000. The results of ALREEDA are promising on majority of the testing problems, and it is comparable with other EDAs and some other improved EAs.

[1]  Ye Xu,et al.  An effective hybrid EDA-based algorithm for solving multidimensional knapsack problem , 2012, Expert Syst. Appl..

[2]  Ying Liang,et al.  A novel chaos danger model immune algorithm , 2013, Commun. Nonlinear Sci. Numer. Simul..

[3]  Xin Yao,et al.  Large scale evolutionary optimization using cooperative coevolution , 2008, Inf. Sci..

[4]  Abdullah Al Mamun,et al.  Multi-Objective Optimization with Estimation of Distribution Algorithm in a Noisy Environment , 2013, Evolutionary Computation.

[5]  Xin Yao,et al.  Unified eigen analysis on multivariate Gaussian based estimation of distribution algorithms , 2008, Inf. Sci..

[6]  Janez Brest,et al.  High-dimensional real-parameter optimization using Self-Adaptive Differential Evolution algorithm with population size reduction , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[7]  S. G. Ponnambalam,et al.  An elitist strategy genetic algorithm for integrated layout design , 2012 .

[8]  Jesús García,et al.  MB-GNG: Addressing drawbacks in multi-objective optimization estimation of distribution algorithms , 2011, Oper. Res. Lett..

[9]  Concha Bielza,et al.  Regularized continuous estimation of distribution algorithms , 2013, Appl. Soft Comput..

[10]  S. Ivvan Valdez,et al.  A Boltzmann based estimation of distribution algorithm , 2013 .

[11]  Jiadong Yang,et al.  Effective search for Pittsburgh learning classifier systems via estimation of distribution algorithms , 2012, Inf. Sci..

[12]  Peter A. N. Bosman,et al.  Matching inductive search bias and problem structure in continuous Estimation-of-Distribution Algorithms , 2008, Eur. J. Oper. Res..

[13]  Yong Wang,et al.  A regularity model-based multiobjective estimation of distribution algorithm with reducing redundant cluster operator , 2012, Appl. Soft Comput..

[14]  Janez Brest,et al.  Large Scale Global Optimization using Differential Evolution with self-adaptation and cooperative co-evolution , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

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

[16]  A. Vannelli,et al.  Non-linear game models for large-scale network bandwidth management , 2006 .

[17]  Jing J. Liang,et al.  Dynamic multi-swarm particle swarm optimizer with local search for Large Scale Global Optimization , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[18]  Marcus Gallagher,et al.  Real-valued Evolutionary Optimization using a Flexible Probability Density Estimator , 1999, GECCO.

[19]  Stojan Kravanja,et al.  Efficient Multilevel MINLP Strategies for Solving Large Combinatorial Problems in Engineering , 2003 .

[20]  Bin Yu,et al.  An ant colony optimization model: The period vehicle routing problem with time windows , 2011 .

[21]  Mohammad Saleh Tavazoei,et al.  Comparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithms , 2007, Appl. Math. Comput..

[22]  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).

[23]  Kay Chen Tan,et al.  A Hybrid Estimation of Distribution Algorithm with Decomposition for Solving the Multiobjective Multiple Traveling Salesman Problem , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[24]  Michael Defoin-Platel,et al.  Quantum-Inspired Evolutionary Algorithm: A Multimodel EDA , 2009, IEEE Transactions on Evolutionary Computation.

[25]  Hella Tokos,et al.  Development of a MINLP model for the optimization of a large industrial water system , 2011 .

[26]  Bin Li,et al.  A restart univariate estimation of distribution algorithm: sampling under mixed Gaussian and Lévy probability distribution , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[27]  Qingfu Zhang,et al.  DE/EDA: A new evolutionary algorithm for global optimization , 2005, Inf. Sci..

[28]  Alexander Mendiburu,et al.  Distributed Estimation of Distribution Algorithms for continuous optimization: How does the exchanged information influence their behavior? , 2014, Inf. Sci..

[29]  Peter Tiño,et al.  Scaling Up Estimation of Distribution Algorithms for Continuous Optimization , 2011, IEEE Transactions on Evolutionary Computation.

[30]  Jesús García,et al.  Multi-objective optimization with an adaptive resonance theory-based estimation of distribution algorithm , 2012, Annals of Mathematics and Artificial Intelligence.

[31]  Mohammad R. Akbarzadeh-Totonchi,et al.  Continuous Gaussian Estimation of Distribution Algorithm , 2012, SMPS.

[32]  Uwe Aickelin,et al.  An estimation of distribution algorithm with intelligent local search for rule-based nurse rostering , 2007, J. Oper. Res. Soc..

[33]  Bo Liu,et al.  Controlling Chaos by an Improved Estimation of Distribution Algorithm , 2010 .

[34]  Tomoyuki Hiroyasu,et al.  Real-coded Estimation of Distribution Algorithm by Using Probabilistic Models with Multiple Learning Rates , 2011, ICCS.

[35]  Chang Wook Ahn,et al.  Elitism-based compact genetic algorithms , 2003, IEEE Trans. Evol. Comput..

[36]  Peter J. Fleming,et al.  Why Use Elitism And Sharing In A Multi-objective Genetic Algorithm? , 2002, GECCO.

[37]  Rawaa Dawoud Al-Dabbagh,et al.  Variants of Hybrid Genetic Algorithms for Optimizing Likelihood ARMA Model Function and Many of Problems , 2011 .

[38]  Bin Li,et al.  Estimation of distribution and differential evolution cooperation for large scale economic load dispatch optimization of power systems , 2010, Inf. Sci..

[39]  Baozhen Yao,et al.  Production , Manufacturing and Logistics An improved ant colony optimization for vehicle routing problem , 2008 .

[40]  H. Mühlenbein,et al.  From Recombination of Genes to the Estimation of Distributions I. Binary Parameters , 1996, PPSN.

[41]  Shang-Jeng Tsai,et al.  Solving large scale global optimization using improved Particle Swarm Optimizer , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[42]  Dirk Thierens,et al.  Numerical Optimization with Real-Valued Estimation-of-Distribution Algorithms , 2006, Scalable Optimization via Probabilistic Modeling.

[43]  Xin Yao,et al.  Multilevel cooperative coevolution for large scale optimization , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[44]  Jinung An,et al.  Estimation of particle swarm distribution algorithms: Combining the benefits of PSO and EDAs , 2012, Inf. Sci..

[45]  Roberto Santana,et al.  Univariate marginal distribution algorithm dynamics for a class of parametric functions with unitation constraints , 2011, Inf. Sci..