1 research outputs found
Exact Markov Chain-based Runtime Analysis of a Discrete Particle Swarm Optimization Algorithm on Sorting and OneMax
Meta-heuristics are powerful tools for solving optimization problems whose
structural properties are unknown or cannot be exploited algorithmically. We
propose such a meta-heuristic for a large class of optimization problems over
discrete domains based on the particle swarm optimization (PSO) paradigm. We
provide a comprehensive formal analysis of the performance of this algorithm on
certain "easy" reference problems in a black-box setting, namely the sorting
problem and the problem OneMAX. In our analysis we use a Markov-model of the
proposed algorithm to obtain upper and lower bounds on its expected
optimization time. Our bounds are essentially tight with respect to the
Markov-model. We show that for a suitable choice of algorithm parameters the
expected optimization time is comparable to that of known algorithms and,
furthermore, for other parameter regimes, the algorithm behaves less greedy and
more explorative, which can be desirable in practice in order to escape local
optima. Our analysis provides a precise insight on the tradeoff between
optimization time and exploration. To obtain our results we introduce the
notion of indistinguishability of states of a Markov chain and provide bounds
on the solution of a recurrence equation with non-constant coefficients by
integration