Constrained Multi-Objective Optimization Using Differential Evolution

Most real-world optimization problems include multiple objective functions and several constraints. The Differential Evolution algorithm was initially developed for unconstrained single-objective problems and was shown to be a fast, simple algorithm. In order to utilize these advantages in real-world problems it was adapted for multi-objective optimization recently. In this work a multi-objective Differential Evolution algorithm is extended for handling constraints. Results from three test functions confirm that the extended algorithm is capable of successfully optimizing constrained problems. Four implementations are compared that differ in the selection scheme and in the assignment of the crowding distance.

[1]  K..  Multiobjective Optimization Using a Pareto Differential Evolution Approach , 2022 .

[2]  Kalyanmoy Deb,et al.  Constrained Test Problems for Multi-objective Evolutionary Optimization , 2001, EMO.

[3]  Bogdan Filipic,et al.  DEMO: Differential Evolution for Multiobjective Optimization , 2005, EMO.

[4]  Dimitris K. Tasoulis,et al.  Vector evaluated differential evolution for multiobjective optimization , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[5]  N. Madavan.  Multiobjective optimization using a Pareto differential evolution approach , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[6]  Ivan Zelinka,et al.  Mechanical engineering design optimization by differential evolution , 1999 .

[7]  Kenneth V. Price,et al.  An introduction to differential evolution , 1999 .

[8]  H. Abbass.  The self-adaptive Pareto differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[9]  Xiaodong Li,et al.  Solving Rotated Multi-objective Optimization Problems Using Differential Evolution , 2004, Australian Conference on Artificial Intelligence.

[10]  Arthur C. Sanderson,et al.  Pareto-based multi-objective differential evolution , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

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

[12]  Carlos A. Coello Coello,et al.  Handling multiple objectives with particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

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

[14]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .