Genetic Algorithm for Finding the Nucleolus of Assignment Games
This paper describes a heuristic approach to finding the nucleolus of assignment games using genetic algorithms. The method consists of three steps, as follow. The first step is to maintain a set of possible solutions of the core, called population. With the concept of nucleolus, the lexicographic order is the function of fitness. The second step is to improve the population by a cyclic three-stage process consisting of a reproduction (selection), recombination (mating), and evaluation (survival of the fittest). Each cycle is called a generation. Generation by generation, the selected population will be a set of vectors with the higher fitness values. A mutation operator changes individuals that may lead to a high fitness region by performing an alternative search path. The last step is to terminate the loop by setting an acceptable condition. The highest fitness individual presents the nucleolus. The discussion includes an outline of the processing pseudocode.
KeywordsGenetic Algorithm Assignment Problem Linear Programming Problem Lexicographic Order Assignment Game
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