Multi-objective test problems, linkages, and evolutionary methodologies

Existing test problems for multi-objective optimization are criticized for not having adequate linkages among variables. In most problems, the Pareto-optimal solutions correspond to a fixed value of certain variables and diversity of solutions comes mainly from a random variation of certain other variables. In this paper, we introduce explicit linkages among variables so as to develop difficult two and multi-objective test problems along the lines of ZDT and DTLZ problems. On a number of such test problems, this paper compares the performance of a number of EMO methodologies having (i) variable-wise versus vector-wise recombination operators and (ii) spatial versus unidirectional recombination operators. Interesting and useful conclusions on the use of above operators are made from the study.

[1]  Kalyanmoy Deb,et al.  A Computationally Efficient Evolutionary Algorithm for Real-Parameter Optimization , 2002, Evolutionary Computation.

[2]  Gary B. Lamont,et al.  Multiobjective evolutionary algorithms: classifications, analyses, and new innovations , 1999 .

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

[4]  Rajkumar Roy,et al.  Evolutionary-based techniques for real-life optimisation: development and testing , 2002, Appl. Soft Comput..

[5]  Kalyanmoy Deb,et al.  Multi-objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems , 1999, Evolutionary Computation.

[6]  David E. Goldberg,et al.  Linkage Identification by Non-monotonicity Detection for Overlapping Functions , 1999, Evolutionary Computation.

[7]  K. Deb,et al.  On Finding Pareto-Optimal Solutions Through Dimensionality Reduction for Certain Large-Dimensional Multi-Objective Optimization Problems , 2022 .

[8]  Peter J. Fleming,et al.  On the Performance Assessment and Comparison of Stochastic Multiobjective Optimizers , 1996, PPSN.

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

[10]  Bernhard Sendhoff,et al.  On Test Functions for Evolutionary Multi-objective Optimization , 2004, PPSN.

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

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

[13]  A. Messac,et al.  Normal Constraint Method with Guarantee of Even Representation of Complete Pareto Frontier , 2004 .

[14]  R. Lyndon While,et al.  A Scalable Multi-objective Test Problem Toolkit , 2005, EMO.

[15]  Jouni Lampinen,et al.  GDE3: the third evolution step of generalized differential evolution , 2005, 2005 IEEE Congress on Evolutionary Computation.

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