Selection

Zhang and Kim [ZK00] a comparative study was carried out of the performance of four selection methods: proportional, ranking, tournament and Genitor. In contrast to other studies that are based on an asymptotic study under more or less ideal conditions, this paper is devoted to a practical case, the problem of machine layout. The paper analyzes the quality of the solutions obtained in a reasonable amount of time and using mutation and crossover operators. The study concludes that the methods of ranking and tournament selection obtain better results than the methods of proportional and Genitor selection.

We have chosen the binary tournament selection, against the ranking selection, used by Zhang and Kim [ZK00] for two reasons:

• The complexity of the tournament selection is lower than the complexity of the ranking selection [Bäc96].
• The selective pressure is higher. This feature allows us to measure whether each crossover is able to keep the population diversity [GD91].

Tournament selection runs a tournament between two individuals and selects the winner. In order to assure that the best individuals always survive to the next generation, we use elitism, the best individual of the population in generation $t$ is always included in the population in generation $t+1$. It has been proved, both theoretically [Rud94] and empirically [Bäc96,Mic92,ZK00], the convenience of the use of elitism.