Elitism-based compact genetic algorithms

This paper describes two elitism-based compact genetic algorithms (cGAs)—persistent elitist compact genetic algorithm (pe-cGA), and nonpersistent elitist compact genetic algorithm (ne-cGA). The aim is to design efficient compact-type GAs by treating them as estimation of distribution algorithms (EDAs) for solving difficult optimization problems without compromising on memory and computation costs. The idea is to deal with issues connected with lack of memory—inherent disadvantage of cGAs—by allowing a selection pressure that is high enough to offset the disruptive effect of uniform crossover. The point is to properly reconcile the cGA with elitism. The pe-cGA finds a near optimal solution (i.e., a winner) that is maintained as long as other solutions (i.e., competitors) generated from probability vectors are no better. It attempts to adaptively alter the selection pressure according to the degree of problem difficulty by employing only the pair-wise tournament selection strategy. Moreover, it incorporates the equivalent model of the (1 + 1) evolution strategy (ES) with self-adaptive mutation. The pe-cGA, apart from providing a high performance, also reveals the hidden connection between EDAs (e.g., cGA) and ESs (e.g., (1 + 1)-ES). On the other hand, the ne-cGA further improves the performance of the pe-cGA by avoiding strong elitism that may lead to premature convergence. The ne-cGA comes with all the benefits of the pe-cGA. In addition, it maintains genetic diversity as a bonus. This paper also proposes an analytic model for investigating convergence enhancement (i.e., speedup). Experimental results show that the proposed algorithms, ne-cGA in particular, generally exhibit a better quality of solution and a higher rate of convergence for most of the problems than do the existing cGA, sGA, and (1 + 1)-ES. The speedup model has been verified by experiments. The results also show that an adequate alleviation of elitism further improves the solution quality, as well as the convergence speed.