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Meta-heuristics are powerful tools for solving optimization problems whosestructural properties are unknown or cannot be exploited algorithmically. Wepropose such a meta-heuristic for a large class of optimization problems overdiscrete domains based on the particle swarm optimization (PSO) paradigm. Weprovide a comprehensive formal analysis of the performance of this algorithm oncertain "easy" reference problems in a black-box setting, namely the sortingproblem and the problem OneMax. In our analysis we use a Markov model of theproposed algorithm to obtain upper and lower bounds on its expectedoptimization time. Our bounds are essentially tight with respect to the Markovmodel. We show that for a suitable choice of algorithm parameters the expectedoptimization time is comparable to that of known algorithms and, furthermore,for other parameter regimes, the algorithm behaves less greedy and moreexplorative, which can be desirable in practice in order to escape localoptima. Our analysis provides a precise insight on the tradeoff betweenoptimization time and exploration. To obtain our results we introduce thenotion of indistinguishability of states of a Markov chain and provide boundson the solution of a recurrence equation with non-constant coefficients byintegration.

Exact Markov Chain-based Runtime Analysis of a Discrete Particle Swarm Optimization Algorithm on Sorting and OneMax