Studniarski, M. (2011) Finding All Minimal Elements of a Finite Partially Ordered Set by Genetic Algorithm with a Prescribed Probability. Numerical Algebra, Control and Optimization, 1, 389-398.
https://doi.org/10.3934/naco.2011.1.389

has been cited by the following article:

• TITLE: Generating Epsilon-Efficient Solutions in Multiobjective Optimization by Genetic Algorithm

  AUTHORS: El-Desouky Rahmo, Marcin Studniarski

  KEYWORDS: Vector Optimization, Approximate Solutions, Genetic Algorithm, Stopping Criteria

  JOURNAL NAME: Applied Mathematics, Vol.8 No.3, March 30, 2017

  ABSTRACT: 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.