MOEA/D-ACO: A Multiobjective Evolutionary Algorithm Using Decomposition and AntColony

Combining ant colony optimization (ACO) and the multiobjective evolutionary algorithm (EA) based on decomposition (MOEA/D), this paper proposes a multiobjective EA, i.e., MOEA/D-ACO. Following other MOEA/D-like algorithms, MOEA/D-ACO decomposes a multiobjective optimization problem into a number of single-objective optimization problems. Each ant (i.e., agent) is responsible for solving one subproblem. All the ants are divided into a few groups, and each ant has several neighboring ants. An ant group maintains a pheromone matrix, and an individual ant has a heuristic information matrix. During the search, each ant also records the best solution found so far for its subproblem. To construct a new solution, an ant combines information from its group's pheromone matrix, its own heuristic information matrix, and its current solution. An ant checks the new solutions constructed by itself and its neighbors, and updates its current solution if it has found a better one in terms of its own objective. Extensive experiments have been conducted in this paper to study and compare MOEA/D-ACO with other algorithms on two sets of test problems. On the multiobjective 0-1 knapsack problem, MOEA/D-ACO outperforms the MOEA/D with conventional genetic operators and local search on all the nine test instances. We also demonstrate that the heuristic information matrices in MOEA/D-ACO are crucial to the good performance of MOEA/D-ACO for the knapsack problem. On the biobjective traveling salesman problem, MOEA/D-ACO performs much better than the BicriterionAnt on all the 12 test instances. We also evaluate the effects of grouping, neighborhood, and the location information of current solutions on the performance of MOEA/D-ACO. The work in this paper shows that reactive search optimization scheme, i.e., the “learning while optimizing” principle, is effective in improving multiobjective optimization algorithms.

[1]  Anthony A. Maciejewski,et al.  Multi-objective robust static mapping of independent tasks on grids , 2010, IEEE Congress on Evolutionary Computation.

[2]  Manuel López-Ibáñez,et al.  Ant colony optimization , 2010, GECCO '10.

[3]  Kalyanmoy Deb,et al.  A Hybrid Framework for Evolutionary Multi-Objective Optimization , 2013, IEEE Transactions on Evolutionary Computation.

[4]  Qguhm -DVNLHZLF,et al.  On the performance of multiple objective genetic local search on the 0 / 1 knapsack problem . A comparative experiment , 2000 .

[5]  Joshua D. Knowles,et al.  Memetic Algorithms for Multiobjective Optimization: Issues, Methods and Prospects , 2004 .

[6]  Francisco Herrera,et al.  Analysis of the Best-Worst Ant System and Its Variants on the QAP , 2002, Ant Algorithms.

[7]  G. Gielen,et al.  Decomposition-based multi-objective optimization of second-generation current conveyors , 2009, 2009 52nd IEEE International Midwest Symposium on Circuits and Systems.

[8]  Mauro Brunato,et al.  R-EVO: A Reactive Evolutionary Algorithm for the Maximum Clique Problem , 2011, IEEE Transactions on Evolutionary Computation.

[9]  B. Bullnheimer,et al.  A NEW RANK BASED VERSION OF THE ANT SYSTEM: A COMPUTATIONAL STUDY , 1997 .

[10]  Saúl Zapotecas Martínez,et al.  A direct local search mechanism for decomposition-based multi-objective evolutionary algorithms , 2012, 2012 IEEE Congress on Evolutionary Computation.

[11]  P. Serafini,et al.  Scalarizing vector optimization problems , 1984 .

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

[13]  R. Battiti,et al.  Brain-Computer Evolutionary Multi-Objective Optimization ( BC-EMO ) : a genetic algorithm adapting to the decision maker , 2009 .

[14]  Li-Chen Fu,et al.  A two-phase evolutionary algorithm for multiobjective mining of classification rules , 2010, IEEE Congress on Evolutionary Computation.

[15]  Antonio J. Nebro,et al.  A Study of the Parallelization of the Multi-Objective Metaheuristic MOEA/D , 2010, LION.

[16]  Richard F. Hartl,et al.  Pareto Ant Colony Optimization: A Metaheuristic Approach to Multiobjective Portfolio Selection , 2004, Ann. Oper. Res..

[17]  Gabriele Eichfelder,et al.  Adaptive Scalarization Methods in Multiobjective Optimization , 2008, Vector Optimization.

[18]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization by NSGA-II and MOEA/D with large populations , 2009, 2009 IEEE International Conference on Systems, Man and Cybernetics.

[19]  Swagatam Das,et al.  SYNTHESIS OF DIFFERENCE PATTERNS FOR MONOPULSE ANTENNAS WITH OPTIMAL COMBINATION OF ARRAY-SIZE AND NUMBER OF SUBARRAYS --- A MULTI-OBJECTIVE OPTIMIZATION APPROACH , 2010, Progress In Electromagnetics Research B.

[20]  Bernhard Sendhoff,et al.  Adapting Weighted Aggregation for Multiobjective Evolution Strategies , 2001, EMO.

[21]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[22]  Yuefeng Li,et al.  Granule Based Intertransaction Association Rule Mining , 2007 .

[23]  Thomas Stützle,et al.  Automatic Algorithm Configuration Based on Local Search , 2007, AAAI.

[24]  Hisao Ishibuchi,et al.  Simultaneous use of different scalarizing functions in MOEA/D , 2010, GECCO '10.

[25]  Martin Middendorf,et al.  A Population Based Approach for ACO , 2002, EvoWorkshops.

[26]  Xin Yao,et al.  Decomposition-Based Memetic Algorithm for Multiobjective Capacitated Arc Routing Problem , 2011, IEEE Transactions on Evolutionary Computation.

[27]  Jacques Teghem,et al.  Two-phase Pareto local search for the biobjective traveling salesman problem , 2010, J. Heuristics.

[28]  Hisao Ishibuchi,et al.  Adaptation of Scalarizing Functions in MOEA/D: An Adaptive Scalarizing Function-Based Multiobjective Evolutionary Algorithm , 2009, EMO.

[29]  Daniel Angus,et al.  Multiple objective ant colony optimisation , 2009, Swarm Intelligence.

[30]  Tong Heng Lee,et al.  Multiobjective Evolutionary Algorithms and Applications , 2005, Advanced Information and Knowledge Processing.

[31]  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).

[32]  Thomas Stützle,et al.  The impact of design choices of multiobjective antcolony optimization algorithms on performance: an experimental study on the biobjective TSP , 2010, GECCO '10.

[33]  John A. W. McCall,et al.  A Novel Smart Multi-Objective Particle Swarm Optimisation Using Decomposition , 2010, PPSN.

[34]  DebK.,et al.  A fast and elitist multiobjective genetic algorithm , 2002 .

[35]  E. Hughes Multiple single objective Pareto sampling , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[36]  Zuren Feng,et al.  An ant colony optimization approach for the multidimensional knapsack problem , 2010, J. Heuristics.

[37]  Christine Solnon,et al.  Ant Colony Optimization for Multi-Objective Optimization Problems , 2007 .

[38]  Daniel Merkle,et al.  Bi-Criterion Optimization with Multi Colony Ant Algorithms , 2001, EMO.

[39]  Qingfu Zhang,et al.  An evolutionary algorithm with guided mutation for the maximum clique problem , 2005, IEEE Transactions on Evolutionary Computation.

[40]  Hisao Ishibuchi,et al.  An Empirical Study on the Effect of Mating Restriction on the Search Ability of EMO Algorithms , 2003, EMO.

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

[42]  Luca Maria Gambardella,et al.  Ant colony system: a cooperative learning approach to the traveling salesman problem , 1997, IEEE Trans. Evol. Comput..

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

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

[45]  John E. Beasley,et al.  A Genetic Algorithm for the Multidimensional Knapsack Problem , 1998, J. Heuristics.

[46]  Qingfu Zhang,et al.  Multi-objective mobile agent-based Sensor Network Routing using MOEA/D , 2010, IEEE Congress on Evolutionary Computation.

[47]  Roberto Battiti,et al.  Brain-Computer Evolutionary Multiobjective Optimization: A Genetic Algorithm Adapting to the Decision Maker , 2010, IEEE Trans. Evol. Comput..

[48]  Thomas Stützle,et al.  MAX-MIN Ant System , 2000, Future Gener. Comput. Syst..

[49]  Peter J. Fleming,et al.  Generalized Decomposition , 2013, EMO.

[50]  Mauro Brunato,et al.  Reactive Search and Intelligent Optimization , 2008 .

[51]  Francisco Herrera,et al.  A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP , 2007, Eur. J. Oper. Res..

[52]  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 .

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

[54]  E. Polak,et al.  On Multicriteria Optimization , 1976 .

[55]  Roberto Battiti,et al.  The Reactive Tabu Search , 1994, INFORMS J. Comput..

[56]  Pei-Chann Chang,et al.  The development of a sub-population genetic algorithm II (SPGA II) for multi-objective combinatorial problems , 2009, Appl. Soft Comput..

[57]  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.

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

[59]  John K. Zao,et al.  Optimizing degree distributions in LT codes by using the multiobjective evolutionary algorithm based on decomposition , 2010, IEEE Congress on Evolutionary Computation.

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