A Hybrid Estimation of Distribution Algorithm with Decomposition for Solving the Multiobjective Multiple Traveling Salesman Problem

Evolutionary multiobjective optimization with decomposition, in which the algorithm is not required to differentiate between the dominated and nondominated solutions, is one of the promising approaches in dealing with multiple conflicting objectives. In this paper, the estimation of distribution algorithm (EDA) is integrated into the decomposition framework. The search behavior of the algorithm is further enhanced by hybridizing local search metaheuristic approaches with the decomposition EDA. Three local search techniques, including hill climbing, simulated annealing, and evolutionary gradient search, are considered. A novel multiobjective formulation of the multiple traveling salesman problem is proposed. The hybrid algorithms are used to solve the formulated problem with different number of objective functions, salesmen, and problem sizes. The effectiveness and efficiency of the algorithms are tested and benchmarked against several state-of-the-art multiobjective evolutionary paradigms.

[1]  Jean-Michel Renders,et al.  Hybridizing genetic algorithms with hill-climbing methods for global optimization: two possible ways , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[2]  Paul J. Werbos,et al.  Computational Intelligence for the Smart Grid-History, Challenges, and Opportunities , 2011, IEEE Computational Intelligence Magazine.

[3]  Gu Guochang,et al.  An implementation of evolutionary computation for path planning of cooperative mobile robots , 2002, Proceedings of the 4th World Congress on Intelligent Control and Automation (Cat. No.02EX527).

[4]  Hisao Ishibuchi,et al.  Special issue on emerging trends in soft computing: memetic algorithms , 2009, Soft Comput..

[5]  Kay Chen Tan,et al.  Memetic informed evolutionary optimization via data mining , 2011, Memetic Comput..

[6]  Ralf Salomon,et al.  Evolutionary algorithms and gradient search: similarities and differences , 1998, IEEE Trans. Evol. Comput..

[7]  Kay Chen Tan,et al.  Restricted Boltzmann machine based algorithm for multi-objective optimization , 2010, IEEE Congress on Evolutionary Computation.

[8]  Yew-Soon Ong,et al.  Memetic Computation—Past, Present & Future [Research Frontier] , 2010, IEEE Computational Intelligence Magazine.

[9]  Pedro Larrañaga,et al.  Research topics in discrete estimation of distribution algorithms based on factorizations , 2009, Memetic Comput..

[10]  Hussain Aziz Saleh,et al.  The design of the global navigation satellite system surveying networks using genetic algorithms , 2004, Eng. Appl. Artif. Intell..

[11]  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 .

[12]  J. A. Lozano,et al.  Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation , 2001 .

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

[14]  Jesús García,et al.  Solving complex high-dimensional problems with the multi-objective neural estimation of distribution algorithm , 2009, GECCO.

[15]  Oscar Cordón,et al.  Medical Image Registration Using Evolutionary Computation: An Experimental Survey , 2011, IEEE Computational Intelligence Magazine.

[16]  Xiaoping Zhong,et al.  A Decision-Tree-Based Multi-objective Estimation of Distribution Algorithm , 2007, 2007 International Conference on Computational Intelligence and Security (CIS 2007).

[17]  Kay Chen Tan,et al.  A predictive gradient strategy for multiobjective evolutionary algorithms in a fast changing environment , 2010, Memetic Comput..

[18]  T. Bektaş.  The multiple traveling salesman problem: an overview of formulations and solution procedures , 2006 .

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

[20]  William A. Gruver,et al.  Team scheduling by genetic search , 1999, Proceedings of the Second International Conference on Intelligent Processing and Manufacturing of Materials. IPMM'99 (Cat. No.99EX296).

[21]  Yang-Byung Park,et al.  A hybrid genetic algorithm for the vehicle scheduling problem with due times and time deadlines , 2001 .

[22]  Lixin Tang,et al.  A multiple traveling salesman problem model for hot rolling scheduling in Shanghai Baoshan Iron & Steel Complex , 2000, Eur. J. Oper. Res..

[23]  Eckart Zitzler,et al.  Evolutionary algorithms for multiobjective optimization: methods and applications , 1999 .

[24]  Jing Tang,et al.  Adaptation for parallel memetic algorithm based on population entropy , 2006, GECCO '06.

[25]  Carlos A. Coello Coello,et al.  A proposal to use stripes to maintain diversity in a multi-objective particle swarm optimizer , 2005, Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005..

[26]  Hisao Ishibuchi,et al.  A multi-objective genetic local search algorithm and its application to flowshop scheduling , 1998, IEEE Trans. Syst. Man Cybern. Part C.

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

[28]  Jun Zhang,et al.  Evolutionary Computation Meets Machine Learning: A Survey , 2011, IEEE Computational Intelligence Magazine.

[29]  Ferrante Neri,et al.  Memetic Compact Differential Evolution for Cartesian Robot Control , 2010, IEEE Computational Intelligence Magazine.

[30]  J. A. Lozano,et al.  Towards a New Evolutionary Computation: Advances on Estimation of Distribution Algorithms (Studies in Fuzziness and Soft Computing) , 2006 .

[31]  Amit Agarwal,et al.  Hybrid ant colony algorithms for path planning in sparse graphs , 2008, Soft Comput..

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

[33]  Kay Chen Tan,et al.  An investigation on evolutionary gradient search for multi-objective optimization , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[34]  Ignacio Rojas,et al.  Blind source separation in post-nonlinear mixtures using competitive learning, Simulated annealing, and a genetic algorithm , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[35]  Qingfu Zhang,et al.  Comparison between MOEA/D and NSGA-II on the Multi-Objective Travelling Salesman Problem , 2009 .

[36]  P. Bosman,et al.  Continuous iterated density estimation evolutionary algorithms within the IDEA framework , 2000 .

[37]  Wei Zhou,et al.  An improved genetic algorithm for multiple traveling salesman problem , 2010, 2010 2nd International Asia Conference on Informatics in Control, Automation and Robotics (CAR 2010).

[38]  Ying Wang,et al.  A Tabu search algorithm for static routing and wavelength assignment problem , 2005, IEEE Communications Letters.

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

[40]  Andrew B. Whinston,et al.  Computer-Assisted School Bus Scheduling , 1972 .

[41]  Cliff T. Ragsdale,et al.  A new approach to solving the multiple traveling salesperson problem using genetic algorithms , 2006, Eur. J. Oper. Res..

[42]  Kenneth C. Gilbert,et al.  A New Multiperiod Multiple Traveling Salesman Problem with Heuristic and Application to a Scheduling Problem , 1992 .

[43]  Mícheál Ó Foghlú,et al.  Frequent Closed Informative Itemset Mining , 2007 .

[44]  Leonid I. Perlovsky,et al.  Computational Intelligence Applications for Defense [Research Frontier] , 2011, IEEE Computational Intelligence Magazine.

[45]  Kay Chen Tan,et al.  Probabilistic Based Evolutionary Optimizers in Bi-objective Travelling Salesman Problem , 2010, SEAL.

[46]  Alok Singh,et al.  A new grouping genetic algorithm approach to the multiple traveling salesperson problem , 2008, Soft Comput..

[47]  David E. Goldberg,et al.  Multiobjective Estimation of Distribution Algorithms , 2006, Scalable Optimization via Probabilistic Modeling.

[48]  C. Okonjo-Adigwe.  An effective method of balancing the workload amongst salesmen , 1988 .

[49]  Hisao Ishibuchi,et al.  Guest editorial: Memetic Algorithms for Evolutionary Multi-Objective Optimization , 2010, Memetic Comput..

[50]  János Abonyi,et al.  Optimization of Multiple Traveling Salesmen Problem by a Novel Representation Based Genetic Algorithm , 2011, Intelligent Computational Optimization in Engineering.