Author(s)

El-Desouky Rahmo^1,2, Marcin Studniarski³

¹Department of Mathematics, Faculty of Science, Taif University, Khurma, KSA.
²Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt.
³Faculty of Mathematics and Computer Science, University of Ƚódź, Ƚódź, Poland.

We develop a new evolutionary method of generating epsilon-efficient solutions of a continuous multiobjective programming problem. This is achieved by discretizing the problem and then using a genetic algorithm with some derived probabilistic stopping criteria to obtain all minimal solutions for the discretized problem. We prove that these minimal solutions are the epsilon-optimal solutions to the original problem. We also present some computational examples illustrating the efficiency of our method.

Vector Optimization, Approximate Solutions, Genetic Algorithm, Stopping Criteria

Rahmo, E. and Studniarski, M. (2017) Generating Epsilon-Efficient Solutions in Multiobjective Optimization by Genetic Algorithm. Applied Mathematics, 8, 395-409. doi: 10.4236/am.2017.83032.