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Metaheuristics are general methods that guide application of concreteheuristic(s) to problems that are too hard to solve using exact algorithms.However, even though a growing body of literature has been devoted to theirstatistical evaluation, the approaches proposed so far are able to assess onlycoupled effects of metaheuristics and heuristics. They do not reveal usanything about how efficient the examined metaheuristic is at guiding itssubordinate heuristic(s), nor do they provide us information about how much theheuristic component of the combined algorithm contributes to the overallperformance. In this paper, we propose a simple yet effective methodology ofdoing so by deriving a naive, placebo metaheuristic from the one being studiedand comparing the distributions of chosen performance metrics for the twomethods. We propose three measures of difference between the two distributions.Those measures, which we call BER values (benefit, equivalence, risk) are basedon a preselected threshold of practical significance which represents theminimal difference between two performance scores required for them to beconsidered practically different. We illustrate usefulness of our methodologyon the example of Simulated Annealing, Boolean Satisfiability Problem, and theFlip heuristic.

How to Estimate the Ability of a Metaheuristic Algorithm to Guide Heuristics During Optimization