Particle algorithms for optimization on binary spaces

We discuss a unified approach to stochastic optimization of pseudo-Boolean objective functions based on particle methods, including the cross-entropy method and simulated annealing as special cases. We point out the need for auxiliary sampling distributions, that is parametric families on binary spaces, which are able to reproduce complex dependency structures, and illustrate their usefulness in our numerical experiments. We provide numerical evidence that particle-driven optimization algorithms based on parametric families yield superior results on strongly multi-modal optimization problems while local search heuristics outperform them on easier problems

Ranking and Selection under Input Uncertainty: Fixed Confidence and Fixed Budget

In stochastic simulation, input uncertainty (IU) is caused by the error in estimating the input distributions using finite real-world data. When it comes to simulation-based Ranking and Selection (R&S), ignoring IU could lead to the failure of many existing selection procedures. In this paper, we study R&S under IU by allowing the possibility of acquiring additional data. Two classical R&S formulations are extended to account for IU: (i) for fixed confidence, we consider when data arrive sequentially so that IU can be reduced over time; (ii) for fixed budget, a joint budget is assumed to be available for both collecting input data and running simulations. New procedures are proposed for each formulation using the frameworks of Sequential Elimination and Optimal Computing Budget Allocation, with theoretical guarantees provided accordingly (e.g., upper bound on the expected running time and finite-sample bound on the probability of false selection). Numerical results demonstrate the effectiveness of our procedures through a multi-stage production-inventory problem