An Orthogonal Evolutionary Algorithm With Learning Automata for Multiobjective Optimization

Research on multiobjective optimization problems becomes one of the hottest topics of intelligent computation. In order to improve the search efficiency of an evolutionary algorithm and maintain the diversity of solutions, in this paper, the learning automata (LA) is first used for quantization orthogonal crossover (QOX), and a new fitness function based on decomposition is proposed to achieve these two purposes. Based on these, an orthogonal evolutionary algorithm with LA for complex multiobjective optimization problems with continuous variables is proposed. The experimental results show that in continuous states, the proposed algorithm is able to achieve accurate Pareto-optimal sets and wide Pareto-optimal fronts efficiently. Moreover, the comparison with the several existing well-known algorithms: nondominated sorting genetic algorithm II, decomposition-based multiobjective evolutionary algorithm, decomposition-based multiobjective evolutionary algorithm with an ensemble of neighborhood sizes, multiobjective optimization by LA, and multiobjective immune algorithm with nondominated neighbor-based selection, on 15 multiobjective benchmark problems, shows that the proposed algorithm is able to find more accurate and evenly distributed Pareto-optimal fronts than the compared ones.

[1]  Jun Zhang,et al.  An Evolutionary Algorithm with Double-Level Archives for Multiobjective Optimization , 2015, IEEE Transactions on Cybernetics.

[2]  Fang Liu,et al.  A Novel Immune Clonal Algorithm for MO Problems , 2012, IEEE Transactions on Evolutionary Computation.

[3]  Qingfu Zhang,et al.  Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II , 2009, IEEE Transactions on Evolutionary Computation.

[4]  B. John Oommen,et al.  Solving Multiconstraint Assignment Problems Using Learning Automata , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[5]  Minjie Zhang,et al.  Multi-Objective Service Composition Using Reinforcement Learning , 2013, ICSOC.

[6]  Seyed Hamid Zahiri,et al.  Data Mining Using Learning Automata , 2009 .

[7]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[8]  Thomas Stützle,et al.  Combining Two Search Paradigms for Multi-objective Optimization: Two-Phase and Pareto Local Search , 2013, Hybrid Metaheuristics.

[9]  Luis A. Sarabia,et al.  Selection of nearly orthogonal blocks in ‘ad-hoc’ experimental designs☆ , 2014 .

[10]  Marco Laumanns,et al.  Scalable multi-objective optimization test problems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[11]  Leonie Kohl,et al.  Fundamental Concepts in the Design of Experiments , 2000 .

[12]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[13]  R. Lyndon While,et al.  A review of multiobjective test problems and a scalable test problem toolkit , 2006, IEEE Transactions on Evolutionary Computation.

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

[15]  Lin Jiang,et al.  Economic emission dispatching with variations of wind power and loads using multi-objective optimization by learning automata , 2014 .

[16]  Fangxing Li,et al.  A new multi-objective optimization technique for generation dispatch , 2009, 41st North American Power Symposium.

[17]  Joel J. P. C. Rodrigues,et al.  Intelligent Mobile Video Surveillance System as a Bayesian Coalition Game in Vehicular Sensor Networks: Learning Automata Approach , 2015, IEEE Transactions on Intelligent Transportation Systems.

[18]  Qingfu Zhang,et al.  Decomposition-Based Multiobjective Evolutionary Algorithm With an Ensemble of Neighborhood Sizes , 2012, IEEE Transactions on Evolutionary Computation.

[19]  M. Thathachar,et al.  Networks of Learning Automata: Techniques for Online Stochastic Optimization , 2003 .

[20]  Q. Henry Wu,et al.  Function optimisation by learning automata , 2013, Inf. Sci..

[21]  G. J. Mitchell,et al.  Principles and procedures of statistics: A biometrical approach , 1981 .

[22]  Kumpati S. Narendra,et al.  Learning automata - an introduction , 1989 .

[23]  Nazish Hoda,et al.  Orthogonal simulated annealing for multiobjective optimization , 2010, Comput. Chem. Eng..

[24]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[25]  Mohammad Reza Meybodi,et al.  Sampling from complex networks using distributed learning automata , 2014 .

[26]  Jian Zhuang,et al.  Combining Crowding Estimation in Objective and Decision Space With Multiple Selection and Search Strategies for Multi-Objective Evolutionary Optimization , 2014, IEEE Transactions on Cybernetics.

[27]  Maryam Kiani,et al.  State estimation of nonlinear dynamic systems using weighted variance-based adaptive particle swarm optimization , 2015, Appl. Soft Comput..

[28]  Wen Jiang,et al.  A new Learning Automata based approach for online tracking of event patterns , 2014, Neurocomputing.

[29]  Seyed Hamid Zahiri,et al.  A New Method for Multiobjective Optimization Based on Learning Automata , 2009 .

[30]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[31]  Harley Bornbach,et al.  An introduction to mathematical learning theory , 1967 .

[32]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints , 2014, IEEE Transactions on Evolutionary Computation.

[33]  Mozafar Bag Mohammadi,et al.  Adaptive multi-flow opportunistic routing using learning automata , 2015, Ad Hoc Networks.

[34]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[35]  Thomas St.  Combining Two Search Paradigms for Multi-objective Optimization: Two-Phase and Pareto Local Search , 2012 .

[36]  Ozan Tekinalp,et al.  A new multiobjective simulated annealing algorithm , 2007, J. Glob. Optim..

[37]  Q. Henry Wu,et al.  Multi-objective optimization by learning automata , 2013, J. Glob. Optim..

[38]  Q. Henry Wu,et al.  Multi-objective optimisation by reinforcement learning , 2010, IEEE Congress on Evolutionary Computation.

[39]  Mohamed A. Khamis,et al.  Adaptive multi-objective reinforcement learning with hybrid exploration for traffic signal control based on cooperative multi-agent framework , 2014, Eng. Appl. Artif. Intell..

[40]  Yuping Wang,et al.  An orthogonal genetic algorithm with quantization for global numerical optimization , 2001, IEEE Trans. Evol. Comput..

[41]  Jiannong Cao,et al.  Multiple Populations for Multiple Objectives: A Coevolutionary Technique for Solving Multiobjective Optimization Problems , 2013, IEEE Transactions on Cybernetics.

[42]  Ke Tang,et al.  Improving Estimation of Distribution Algorithm on Multimodal Problems by Detecting Promising Areas , 2015, IEEE Transactions on Cybernetics.

[43]  Mohammad Reza Meybodi,et al.  Sleep-based topology control in the Ad Hoc networks by using fitness aware learning automata , 2012, Comput. Math. Appl..

[44]  Peter R. Nelson,et al.  Design and Analysis of Experiments, 3rd Ed. , 1991 .

[45]  Ali Akbar Gharaveisi,et al.  Opposition-based discrete action reinforcement learning automata algorithm case study: optimal design of a PID controller , 2013 .

[46]  Qiuzhen Lin,et al.  A novel hybrid multi-objective immune algorithm with adaptive differential evolution , 2015, Comput. Oper. Res..

[47]  Longquan Yong,et al.  Biogeography-Based Optimization with Orthogonal Crossover , 2013 .

[48]  Carlos A. Coello Coello,et al.  Solving Multiobjective Optimization Problems Using an Artificial Immune System , 2005, Genetic Programming and Evolvable Machines.

[49]  Amit Konar,et al.  An Adaptive Memetic Algorithm using a synergy of Differential Evolution and Learning Automata , 2012, 2012 IEEE Congress on Evolutionary Computation.

[50]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[51]  Qingfu Zhang,et al.  Multiobjective evolutionary algorithms: A survey of the state of the art , 2011, Swarm Evol. Comput..

[52]  Qingfu Zhang,et al.  Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition , 2009 .

[53]  M. L. Tsetlin,et al.  Automaton theory and modeling of biological systems , 1973 .

[54]  Hamid Beigy,et al.  A new real-coded Bayesian optimization algorithm based on a team of learning automata for continuous optimization , 2014, Genetic Programming and Evolvable Machines.

[55]  Abir Chaabani,et al.  An Efficient Chemical Reaction Optimization Algorithm for Multiobjective Optimization , 2015, IEEE Transactions on Cybernetics.

[56]  Mengjie Zhang,et al.  Particle Swarm Optimization for Feature Selection in Classification: A Multi-Objective Approach , 2013, IEEE Transactions on Cybernetics.

[57]  Qingfu Zhang,et al.  An orthogonal genetic algorithm for multimedia multicast routing , 1999, IEEE Trans. Evol. Comput..

[58]  Fangxing Li,et al.  Using learning automata for multi-objective generation dispatch considering cost, voltage stability and power losses , 2011 .