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.

元启发式是解决结构特性未知或无法通过算法利用的优化问题的强大工具。我们针对基于粒子群优化(PSO) 范式的离散域上的一大类优化问题提出了这种元启发式方法。我们提供这种算法对黑盒设置一定的“易”引用问题，即排序的问题，这个问题澳绩效的全面正式分析NE中号斧头. 在我们的分析中，我们使用所提出算法的马尔可夫模型来获得其预期优化时间的上限和下限。相对于马尔可夫模型，我们的界限基本上是严格的。我们表明，对于算法参数的合适选择，预期优化时间与已知算法的预期优化时间相当，此外，对于其他参数机制，该算法的行为不那么贪婪，更具探索性，这在实践中是可取的，以逃避局部最优化。我们的分析为优化时间和探索之间的权衡提供了准确的见解。为了获得我们的结果，我们引入了马尔可夫链状态不可区分的概念，并通过积分提供了具有非常数系数的递推方程的解的界限。