A gestalt genetic algorithm

Abstract

The basic idea to defend in this paper is that an adequate perception of the search space, sacrificing most of the precision, can paradoxically accelerate the discovery of the most promising solution zones. While any search space can be observed at any scale according to the level of details, there is nothing inherent to the classical metaheuristics to naturally account for this multi-scaling. Nevertheless, the wider the search space the longer the time needed by any metaheuristic to discover and exploit the "promising" zones. Any possibility to compress this time is welcome. Abstracting the search space during the search is one such possibility. For instance, a common Ordering Genetic Algorithm (o-GA) is not well suited to efficiently resolve very large instances of the Traveling Salesman Problem (TSP). The mechanism presented here (reminiscent of Gestalt psychology) aims at abstracting the search space by substituting the variables of the problems with macro-versions of them. This substitution allows any given metaheuristic to tackle the problem at various scales or through different multi-resolution lenses. In the TSP problem to be treated here, the towns will simply be aggregated into regions and the metaheuristics will apply on this new one-level-up search space. The whole problem becomes now how to discover the most appropriate regions and to merge this discovery with the running of the o-GA at the new level.