A Comparative Analysis of MOEAs Considering Two Discrete Optimization Problems

Multiobjective optimization is a research area for which several evolutionary algorithms have been used. Multiobjective evolutionary algorithms (MOEAs) have successfully been used in a wide range of tasks from toy problems to realworld applications. Among several MOEAs, two categories are highlighted: the multiobjective approaches, which are able to deal with 2 and 3 objectives and, more recently, the manyobjective approaches, specially designed to deal with 4 or more objectives. In this paper, we investigate five MOEAs, two of them - SPEA2 and NSGA-II - are well-known multiobjective methods to deal with few objectives, while other two of them - NSGA-III and MEAMT - represent the class of many-objective approaches. The fifth algorithm is MOEA/D that can be seen as a transition between the multi and the many-objective approaches. The five MOEAs are applied here in two well-known discrete optimization problems: the multicast routing problem (MRP) and the multiobjective knapsack problem (MKP). The experimental results were used to analize the behavior of the MOEAs with respect to the number of objectives and the optimization problem.

[1]  G.M.B. Oliveira,et al.  Determining multicast routes with QoS and traffic engineering requirements based on genetic algorithm , 2004, IEEE Conference on Cybernetics and Intelligent Systems, 2004..

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

[3]  Erdun Zhao,et al.  Bandwidth-delay-constrained least-cost multicast routing based on heuristic genetic algorithm , 2001, Comput. Commun..

[4]  Gina Maira Barbosa de Oliveira,et al.  Many-Objective Evolutionary Algorithms for Multicast Routing with Quality of Service Problem , 2016, 2016 5th Brazilian Conference on Intelligent Systems (BRACIS).

[5]  Marco Laumanns,et al.  SPEA2: Improving the Strength Pareto Evolutionary Algorithm For Multiobjective Optimization , 2002 .

[6]  N. Bretas,et al.  Main chain representation for evolutionary algorithms applied to distribution system reconfiguration , 2005, IEEE Transactions on Power Systems.

[7]  Thomas Bäck,et al.  The zero/one multiple knapsack problem and genetic algorithms , 1994, SAC '94.

[8]  Eckart Zitzler,et al.  HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization , 2011, Evolutionary Computation.

[9]  Qingfu Zhang,et al.  An Evolutionary Many-Objective Optimization Algorithm Based on Dominance and Decomposition , 2015, IEEE Transactions on Evolutionary Computation.

[10]  Gina Maira Barbosa de Oliveira,et al.  Multicast flow routing: Evaluation of heuristics and multiobjective evolutionary algorithms , 2010, IEEE Congress on Evolutionary Computation.

[11]  J. D. Schaffer,et al.  Some experiments in machine learning using vector evaluated genetic algorithms (artificial intelligence, optimization, adaptation, pattern recognition) , 1984 .

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

[13]  Gina Maira Barbosa de Oliveira,et al.  Four-objective formulations of multicast flows via evolutionary algorithms with quality demands , 2014, Telecommun. Syst..

[14]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[15]  Hisao Ishibuchi,et al.  Behavior of Multiobjective Evolutionary Algorithms on Many-Objective Knapsack Problems , 2015, IEEE Transactions on Evolutionary Computation.

[16]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization , 2008, 2008 3rd International Workshop on Genetic and Evolving Systems.

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

[18]  Alexandre C. B. Delbem,et al.  Multiobjective evolutionary algorithm with many tables for purely ab initio protein structure prediction , 2013, J. Comput. Chem..

[19]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[20]  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.

[21]  C. P. Ravikumar,et al.  Source-based delay-bounded multicasting in multimedia networks , 1998, Comput. Commun..

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

[23]  Paolo Toth,et al.  Knapsack Problems: Algorithms and Computer Implementations , 1990 .

[24]  Hisao Ishibuchi,et al.  Behavior of EMO algorithms on many-objective optimization problems with correlated objectives , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[25]  Kiyoshi Tanaka,et al.  Adaptive ∈-ranking on MNK-Landscapes , 2009, 2009 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making(MCDM).