Mapping the convergence of genetic algorithms

Hybrid genetic algorithms have recently become very popular metaheuristic methods (Beasley [6]). Most genetic algorithms produce offspring by mating parents and attempt to improve the population makeup by replacing existing population members with superior offspring. In contrast, hybrid genetic algorithms, sometimes called memetic algorithms (Moscato [28]), incorporate some heuristic improvement on every offspring before considering its inclusion into the population. For a plethora of introductory expositions published on the topic, see Salhi [33] or Beasley [6]. This paper examines the convergence of genetic algorithms using a cluster-analytictype technique called the “MD procedure” (Marcoulides and Drezner [26]). The proposed procedure is illustrated with a hybrid genetic algorithm applied to the solution of the quadratic assignment problem (QAP). For a review of the QAP, see Rendl [31]. Because population members form clusters as progress is made to a solution, the clustering structure can provide a better implementation of genetic algorithms. For example, clustering structure can be used to develop better stopping criteria, for instance when the population clusters become stagnant. In the next section we describe the MD procedure. In Section 3 we describe the quadratic assignment problem and the hybrid genetic algorithm used for its solution. In