Finite Simulation Budget Allocation for Ranking and Selection

We consider a simulation-based ranking and selection (R&S) problem under a fixed budget setting. Existing budget allocation procedures focus either on asymptotic optimality or on one-step-ahead allocation efficiency. Neither of them depends on the fixed simulation budget, the ignorance of which could lead to an inefficient allocation, especially when the simulation budget is finite. In light of this, we develop a finite-budget allocation rule that is adaptive to the simulation budget. Theoretical results show that the budget allocation strategies are distinctively different between a finite budget and a sufficiently large budget. Our proposed allocation rule can dynamically determine the ratio of budget allocated to designs according to different simulation budget and is optimal when the simulation budget goes to infinity, indicating it not only possesses desirable finite-budget properties but also achieves asymptotic optimality. Based on the proposed allocation rule, two efficient finite simulation budget allocation algorithms are developed. In the numerical experiments, we use both synthetic examples and a case study to show the superior efficiency of our proposed allocation rule

Efficient multi-objective ranking and selection in the presence of uncertainty

We consider the problem of ranking and selection with multiple-objectives in the presence of uncertainty. Simulation optimisation offers great opportunities in the design and optimisation of complex systems. In the presence of multiple objectives there is usually no single solution that performs best on all the objectives. Instead, there are several Pareto-optimal (efficient) solutions with different trade-offs which cannot be improved in any objective without sacrificing performance in another objective. For the case where alternatives are evaluated on multiple stochastic criteria, and the performance of an alternative can only be estimated via simulation, we consider the problem of efficiently identifying the Pareto optimal designs out of a (small) given set of alternatives. We develop a simple myopic budget allocation algorithm and propose several variants for different settings. In particular, this myopic method only allocates one simulation sample to one alternative in each iteration. Empirical tests show that the proposed algorithm can significantly reduce the necessary simulation budget and perform better than some existing well known algorithms in certain settings

Continuous optimization via simulation using Golden Region search

Simulation Optimization (SO) is the use of mathematical optimization techniques in which the objective function (and/or constraints) could only be numerically evaluated through simulation. Many of the proposed SO methods in the literature are rooted in or originally developed for deterministic optimization problems with available objective function. We argue that since evaluating the objective function in SO requires a simulation run which is more computationally costly than evaluating an available closed form function, SO methods should be more conservative and careful in proposing new candidate solutions for objective function evaluation. Based on this principle, a new SO approach called Golden Region (GR) search is developed for continuous problems. GR divides the feasible region into a number of (sub) regions and selects one region in each iteration for further search based on the quality and distribution of simulated points in the feasible region and the result of scanning the response surface through a metamodel. The experiments show the GR method is efficient compared to three well-established approaches in the literature. We also prove the convergence in probability to global optimum for a large class of random search methods in general and GR in particular

Genetic Algorithms in Stochastic Optimization and Applications in Power Electronics

Genetic Algorithms (GAs) are widely used in multiple fields, ranging from mathematics, physics, to engineering fields, computational science, bioinformatics, manufacturing, economics, etc. The stochastic optimization problems are important in power electronics and control systems, and most designs require choosing optimum parameters to ensure maximum control effect or minimum noise impact; however, they are difficult to solve using the exhaustive searching method, especially when the search domain conveys a large area or is infinite. Instead, GAs can be applied to solve those problems. And efficient computing budget allocation technique for allocating the samples in GAs is necessary because the real-life problems with noise are often difficult to evaluate and require significant computation effort. A single objective GA is proposed in which computing budget allocation techniques are integrated directly into the selection operator rather than being used during fitness evaluation. This allows fitness evaluations to be allocated towards specific individuals for whom the algorithm requires more information, and this selection-integrated method is shown to be more accurate for the same computing budget than the existing evaluation-integrated methods on several test problems. A combination of studies is performed on a multi-objective GA that compares integration of different computing budget allocation methods into either the evaluation or the environmental selection steps. These comparisons are performed on stochastic problems derived from benchmark multi-objective optimization problems and consider varying levels of noise. The algorithms are compared regarding both proximity to and coverage of the true Pareto-optimal front, and sufficient studies are performed to allow statistically significant conclusions to be drawn. Finally, the multi-objective GA with selection integrated sampling technique is applied to solve a multi-objective stochastic optimization problem in a grid connected photovoltaic inverter system with noise injected from both the solar power input and the utility grid

SIMULATION OPTIMIZATION USING OPTIMAL COMPUTING BUDGET ALLOCATION

Ph.DDOCTOR OF PHILOSOPH

Sequential Design for Ranking Response Surfaces

We propose and analyze sequential design methods for the problem of ranking several response surfaces. Namely, given $L \ge 2$ response surfaces over a continuous input space $\cal X$, the aim is to efficiently find the index of the minimal response across the entire $\cal X$. The response surfaces are not known and have to be noisily sampled one-at-a-time. This setting is motivated by stochastic control applications and requires joint experimental design both in space and response-index dimensions. To generate sequential design heuristics we investigate stepwise uncertainty reduction approaches, as well as sampling based on posterior classification complexity. We also make connections between our continuous-input formulation and the discrete framework of pure regret in multi-armed bandits. To model the response surfaces we utilize kriging surrogates. Several numerical examples using both synthetic data and an epidemics control problem are provided to illustrate our approach and the efficacy of respective adaptive designs.Comment: 26 pages, 7 figures (updated several sections and figures