Comparison of acceptance criteria in randomized local searches

Abstract

One key component of stochastic local search algorithms is the acceptance criterion that determines whether a solution is accepted as the new current solution or it is discarded. One of the most studied local search algorithms is simulated annealing. It often uses the Metropolis condition as acceptance criterion, which always accepts equal or better quality solutions and worse ones with a probability that depends on the amount of worsening and a parameter called temperature. After the introduction of simulated annealing several other acceptance criteria have been introduced to replace the Metropolis condition, some being claimed to be simpler and better performing. In this article, we evaluate various such acceptance criteria from an experimental perspective. We first tune the numerical parameters of the algorithms using automatic algorithm configuration techniques for two test problems, the quadratic assignment problem and a permutation flowshop problem. Our experimental results show that, while results may differ depending on the specific problem, the Metropolis condition and the late acceptance hill climbing rule are among the choices that obtain the best results.