On modification of population-based search algorithms for convergence in stochastic combinatorial optimization

Motivated by the work of Homem-De-Mello on modifying pure random search (PRS) into a convergent sample-based PRS for stochastic optimization, this paper considers two general methods of converting any given population-based algorithm into a convergent sample-based one for stochastic combinatorial optimization. The methods are based on controlling sampling process at time t by -switching and on including the current optimizer-estimate as a candidate in the selection process of -switching. Under appropriate conditions on the sequence and the given algorithm, we establish a probability one convergence of the resulting population-based algorithms.