The effect of elitist fitness-based selection on the escape from local optima
Stephen Y. Chen · Applied Soft Computing · 2025
The concept of escape from local optima is formally defined in continuous domains to mean that a previously found locally optimal solution is replaced by a search solution (i.e., it has survived selection) that is in a different attraction basin. Exploration that does not lead to an update is not considered to have achieved an escape from a local optimum. The search solutions (blue circles) are unable to update the previously found local optimum (red star) and thus allow the metaheuristic to escape from the local optimum. Random Search is the baseline that a metaheuristic must improve upon to be worth its added complexity. Random Search, in the form of Hill Climbing, cannot escape from local optima. A key claim of many metaheuristics is that they are able to escape from local optima. However, these claims are poorly tested and often based on imprecise definitions of what it means to escape from a local optimum in continuous domain search spaces. A practical and precise definition for an escape from a local optimum is developed. It is then shown how elitist fitness-based selection can lead to the rejection of exploratory search solutions, and this can cause many popular metaheuristics to degrade into (localized) Random Search in their attempts to escape from local optima. The explosion of new metaheuristics has often been just a repeated re-invention of localized Random Search for the key task of escaping from local optima. • A formal definition for escaping from local optima is developed for continuous domain search spaces. • The effect of elitist fitness-based selection is shown to hinder the ability of many metaheuristics to escape from local optima in continuous domains. • Key differences between combinatorial and continuous domains are presented.