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.

Abstract not found

Many metaheuristics have difficulty exploring their search space comprehensively. Exploration time and efficiency are highly dependent on the size and the ruggedness of the search space. For instance, the Simple Genetic Algorithm (SGA) is not totally suited to traverse very large landscapes, especially deceptive ones. The approach introduced here aims at improving the exploration process of the SGA by adding a second search process through the way the solutions are coded. An “observer ” is defined as each possible encoding that aims at reducing the search space. Adequacy of one observer is computed by applying this specific encoding and evaluating how this observer is beneficial for the SGA run. The observers are trained for a specific time by a second evolutionary stage. During the evolution of the observers, the most suitable observer helps the SGA to find a solution to the tackled problem faster. These observers aim at collapsing the search space and smoothing its ruggedness through a simplification of the genotype. A first implementation of this general approach is proposed, tested on the Shuffled Hierarchical IF-and-only-iF (SHIFF) problem. Very good results are obtained and some explanations are provided about why our approach tackles SHIFF so easily.

Abstract. Most metaheuristics try to find a good balance between exploitation and exploration to achieve their goals. The exploration efficiency is highly dependent on the cardinality and ruggedness of the search space. A metaheuristic like the Simple Genetic Algorithm (SGA) can suffer a lot when traversing very large landscapes, especially deceptive ones. The approach proposed here improves the exploration of the SGA through the use of behavioural information of the SGA itself. Behavioural information on the SGA is obtained through a number of competitive processes which we refer to as “observers”. The new metaheuristic we investigate, trains the observers for a specific time and then decides which of them is the most suitable to solve the whole problem. Concretely, a second evolutionary stage has been added to evolve observers for the SGA. These observers transform the cardinality and ruggedness of the search space through a simplification of the genotype. To test the proposed approach, we chose some difficult problems such as