Modeling Local Search Metaheuristics Using Markov Decision Processes

Local search metaheuristics like tabu search or simulated annealing are popular heuristic optimization algorithms for finding near-optimal solutions for combinatorial optimization problems. However, it is still challenging for researchers and practitioners to analyze their behavior and systematically choose one over a vast set of possible metaheuristics for the particular problem at hand. In this paper, we introduce a theoretical framework based on Markov Decision Processes (MDPs) for analyzing local search metaheuristics. This framework not only helps in providing convergence results for individual algorithms but also provides an explicit characterization of the exploration–exploitation tradeoff and a theory-grounded guidance for practitioners for choosing an appropriate metaheuristic for the problem at hand. We present this framework in detail and show how to apply it in the case of hill climbing and the simulated annealing algorithm, including computational experiments.