Symmetry in the search space

The presence or symmetry in the representation of an optimization problem can have a positive or a negative influence on the dynamics of a search algorithm. Symmetry can cause a genetic algorithm or simulated annealing to get stuck in a local optimum, but it can also help an algorithm to find the optima more quickly, as the dual genetic algorithm does in some cases. The first part of the paper describes three common types of symmetry and their effects on evolutionary algorithms. Next to obvious permutations on the string representation leaving the objective value invariant, the interaction structure of the problem can be a source of symmetry. Typical examples can be found in the class of aggregated problems, studied in the second part of the paper. An abstract model for aggregated problems is introduced together with a strategy to overcome their symmetry