Determining Metaheuristic Similarity Using Behavioral Analysis

Many nature-inspired metaheuristics have been published, with claims of originality based on the metaphor that inspired the algorithm. Rarely is empirical evidence given to show algorithmic originality. In order to provide an easy and computationally cheap approach to characterize algorithm search behavior, a suite of 20 behavioral characteristics is proposed. This behavioral characteristic suite allows for the search behavior of an algorithm to be quantified without manual inspection. By doing so, behavioral novelty of any given algorithm may be determined by comparing the behavioral characteristics to those of well-known metaheuristics. To illustrate this use, and to evaluate whether metaheuristics are behaviorally distinct, a host of metaheuristics is run on various benchmark functions. To evaluate behavioral similarity across all problems, while acknowledging behavior to be problem dependant, a novel method is proposed. In addition to this method, new behavioral characteristics are also proposed. The behavioral vectors generated for each benchmark function are clustered. The relationships and trends present in the different clusters are summarized by creating a pair-wise matrix for every metaheuristic pair, which tallies the number of times that the pair are found within the same cluster. The tallies are then analyzed in order to make inference regarding the distinctness of any metaheuristic’s behaviors, across many different benchmark functions. The analysis finds that the range of unique search behaviors is small and that most metaheuristics share their behaviors with most other metaheuristics. The analysis also identifies both unique algorithms, as well as algorithms which have no unique behaviors.