The entropy-based measure has been used in previous works to compute the population diversity in solving the cell formation problem with the genetic algorithm. Population diversity is crucial to the genetic algorithm's ability to continue fruitful exploration as it may be used in choosing an initial population, in defining a stopping criterion, in evaluating the population convergence, and in making the search more efficient throughout the selection of crossover operators or the adjustment of various control parameters (e.g., crossover or mutation rate, population size). We show in this note that, when a non-ordinal chromosome representation corresponding to the allocation of machines to cells is used, the current way of measuring the population diversity is inaccurate. Consequently, it leads to wrong conclusions when, at various iterations, carrying out fruitful exploration or an efficient search of the solution space is guided by the perceived population diversity degree. An alternative approach based on computing the distance and the similarity between chromosomes is discussed.

Cell formation problem, Cellular manufacturing systems, Genetic algorithm, Population diversity, Population heterogeneity
European Journal of Operational Research
Sprott School of Business

Nsakanda, A, Price, W.L. (Wilson L.), Diaby, M. (Moustapha), & Gravel, M. (Marc). (2007). Ensuring population diversity in genetic algorithms: A technical note with application to the cell formation problem. European Journal of Operational Research, 178(2), 634–638. doi:10.1016/j.ejor.2006.02.012