Evolutionary Many-Objective Optimization Based on Kuhn-Munkres' Algorithm

In this paper, we propose a new multi-objective evolutionary algorithm (MOEA), which transforms a multi-objective optimization problem into a linear assignment problem using a set of weight vectors uniformly scattered. Our approach adopts uniform design to obtain the set of weights and Kuhn-Munkres’ (Hungarian) algorithm to solve the assignment problem. Differential evolution is used as our search engine, giving rise to the so-called Hungarian Differential Evolution algorithm (HDE). Our proposed approach is compared with respect to a MOEA based on decomposition (MOEA/D) and with respect to an indicator-based MOEA (the S metric selection Evolutionary Multi-Objective Algorithm, SMS- EMOA) using several test problems (taken from the specialized literature) having from two to ten objective functions. Our preliminary experimental results indicate that our proposed HDE outperforms MOEA/D and is competitive with respect to SMS-EMOA, but at a significantly lower computational cost.

[1]  M. Fleischer,et al.  The Measure of Pareto Optima , 2003, EMO.

[2]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization: A short review , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[3]  Frank Neumann,et al.  Analyzing Hypervolume Indicator Based Algorithms , 2008, PPSN.

[4]  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.

[5]  Heike Trautmann,et al.  On the properties of the R2 indicator , 2012, GECCO '12.

[6]  François Bourgeois,et al.  An extension of the Munkres algorithm for the assignment problem to rectangular matrices , 1971, CACM.

[7]  Y Wang.  NUMBER THEORETIC METHOD IN APPLIED STATISTICS , 1990 .

[8]  H. Scheffé.  Experiments with Mixtures , 1958 .

[9]  Lakhmi C. Jain,et al.  Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

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

[11]  Mark Fleischer,et al.  The measure of pareto optima: Applications to multi-objective metaheuristics , 2003 .

[12]  王元,et al.  NUMBER THEORETIC METHOD IN APPLIED STATISTICS , 1990 .

[13]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[14]  Hong Li,et al.  MOEA/D + uniform design: A new version of MOEA/D for optimization problems with many objectives , 2013, Comput. Oper. Res..

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

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

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

[18]  Simon M. Lucas,et al.  Parallel Problem Solving from Nature - PPSN X, 10th International Conference Dortmund, Germany, September 13-17, 2008, Proceedings , 2008, PPSN.

[19]  Nicola Beume,et al.  SMS-EMOA: Multiobjective selection based on dominated hypervolume , 2007, Eur. J. Oper. Res..

[20]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[21]  Tobias Friedrich,et al.  Approximating the Least Hypervolume Contributor: NP-Hard in General, But Fast in Practice , 2009, EMO.

[22]  Arnold J. Stromberg,et al.  Number-theoretic Methods in Statistics , 1996 .

[23]  Junichi Suzuki,et al.  R2-IBEA: R2 indicator based evolutionary algorithm for multiobjective optimization , 2013, 2013 IEEE Congress on Evolutionary Computation.

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

[25]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

[26]  J. Hammersley.  MONTE CARLO METHODS FOR SOLVING MULTIVARIABLE PROBLEMS , 1960 .

[27]  J. Munkres.  ALGORITHMS FOR THE ASSIGNMENT AND TRANSIORTATION tROBLEMS* , 1957 .

[28]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[29]  H. Kuhn.  The Hungarian method for the assignment problem , 1955 .