Multi-Objective Optimization by Using Evolutionary Algorithms: The $p$-Optimality Criteria

In this paper, a novel general class of optimality criteria is defined and proposed to solve multi-objective optimization problems by using evolutionary algorithms. These criteria, named p-optimality criteria, allow us to value (assess) the relative importance of those solutions with outstanding performance in very few objectives and poor performance in all others, regarding those solutions with an equilibrium (balance) among all the objectives. The optimality criteria avoid interrelating the relative values of the different objectives, respecting the integrity of each one in a rational way. As an example, a simple multi-objective approach based on the p-optimality criteria and genetic algorithms is designed, where solutions used to generate new solutions are selected according to the proposed optimality criteria. It is implemented and applied on several benchmark test problems, and its performance is compared to that of the nondominated sort genetic algorithm-II method, in order to analyze the contribution and potential of these new optimality criteria.

[1]  Qingfu Zhang,et al.  Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition , 2009 .

[2]  Kim Sterelny,et al.  The Major Transitions in Evolution Revisited , 2011 .

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

[4]  Heike Trautmann,et al.  Integration of Preferences in Hypervolume-Based Multiobjective Evolutionary Algorithms by Means of Desirability Functions , 2010, IEEE Transactions on Evolutionary Computation.

[5]  Michael E. Wall,et al.  Galib: a c++ library of genetic algorithm components , 1996 .

[6]  Zhijian Wu,et al.  Performance assessment of DMOEA-DD with CEC 2009 MOEA competition test instances , 2009, 2009 IEEE Congress on Evolutionary Computation.

[7]  Kalyanmoy Deb,et al.  Local search based evolutionary multi-objective optimization algorithm for constrained and unconstrained problems , 2009, 2009 IEEE Congress on Evolutionary Computation.

[8]  Kalyanmoy Deb,et al.  Reference point based multi-objective optimization using evolutionary algorithms , 2006, GECCO.

[9]  Qingfu Zhang,et al.  Enhancing MOEA/D with guided mutation and priority update for multi-objective optimization , 2009, 2009 IEEE Congress on Evolutionary Computation.

[10]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[11]  Kalyanmoy Deb,et al.  A Comparative Analysis of Selection Schemes Used in Genetic Algorithms , 1990, FOGA.

[12]  Kalyanmoy Deb,et al.  Interactive evolutionary multi-objective optimization and decision-making using reference direction method , 2007, GECCO '07.

[13]  Zbigniew Michalewicz,et al.  Evolutionary Computation 1 , 2018 .

[14]  Kaisa Miettinen,et al.  Introduction to Multiobjective Optimization: Noninteractive Approaches , 2008, Multiobjective Optimization.

[15]  Lihui Wang,et al.  Multi-objective Evolutionary Optimisation for Product Design and Manufacturing , 2011 .

[16]  Kalyanmoy Deb,et al.  Multi-objective test problems, linkages, and evolutionary methodologies , 2006, GECCO.

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

[18]  R. Michod,et al.  Evolution of individuality during the transition from unicellular to multicellular life , 2007, Proceedings of the National Academy of Sciences.

[19]  David W. Coit,et al.  Multi-objective optimization using genetic algorithms: A tutorial , 2006, Reliab. Eng. Syst. Saf..

[20]  Hai-Lin,et al.  The multiobjective evolutionary algorithm based on determined weight and sub-regional search , 2009, 2009 IEEE Congress on Evolutionary Computation.

[21]  Kalyanmoy Deb,et al.  Light beam search based multi-objective optimization using evolutionary algorithms , 2007, 2007 IEEE Congress on Evolutionary Computation.

[22]  Marc Despontin,et al.  Multiple Criteria Optimization: Theory, Computation, and Application, Ralph E. Steuer (Ed.). Wiley, Palo Alto, CA (1986) , 1987 .

[23]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[24]  Chun Chen,et al.  Multiple trajectory search for unconstrained/constrained multi-objective optimization , 2009, 2009 IEEE Congress on Evolutionary Computation.