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

Optimization Models for Sustainable Design and Management of Biopower Supply Chains

This dissertation presents optimization models to aid with the sustainable design and management of biopower (biomass cofiring) supply chains. We address three main challenges associated with today’s biopower projects: i) high cost of biomass collection, storage and delivery, ii) inefficiency of the mechanisms used to incentivize biomass usage for generating electricity, and iii) lack of clear understanding about the trade-offs between economic and environmental impacts of biopower supply chains. In order to address the high cost of delivering biomass, we present a novel mixed integer nonlinear program that integrates production and transportation decisions at power plants. Proposed model captures the loss in process efficiencies from using biomass, in-vestment and operational costs associated with cofiring, and savings due to production tax credit (PTC), a major governmental incentive to support biopower. We develop a La-grangian relaxation approach to provide upper bounds, and two linear approximations to provide lower bounds for the problem. An important finding is that the one-size-fits-all approach of PTC is not effective in motivating plants to utilize biomass and there is a need for sophisticated incentive schemes. In order to address the second issue, we propose alter-natives for the existing PTC incentive. The proposed flexible alternatives are functions of plant capacity and biomass cofiring ratio. We use a resource allocation framework to model and analyze the profit-earning potentials and fairness of the proposed incentive schemes. Finally, in order to address the last challenge, we propose a stochastic biobjective optimiza-tion model to analyze the economic and environmental impacts of biopower supply chains. The economic objective function maximizes the potential profits in the supply chain and the environmental objective function minimizes the life cycle greenhouse gasses (GHG). We use a life cycle assessment (LCA) approach to derive the emission factors for this objective function. We capture uncertainties of biomass quality and supply via the use of chance constraints. The results of this dissertation work are useful for electric utility companies and policy makers. Utility companies can use the proposed models to identify ways to improve biopower production, have better environmental performance, and make use of the existing incentives. Policy makers would gain insights on designing incentive schemes for a more efficient utilization of biomass and a fairer distribution of tax-payers money

Adaptive sampling trust-region methods for derivative-based and derivative-free simulation optimization problems

We consider unconstrained optimization problems where only “stochastic” estimates of the objective function are observable as replicates from a Monte Carlo simulation oracle. In the first study we assume that the function gradients are directly observable through the Monte Carlo simulation. We propose ASTRO, which is an adaptive sampling based trust-region optimization method where a stochastic local model is constructed, optimized, and updated iteratively. ASTRO is a derivative-based algorithm and provides almost sure convergence to a first-order critical point with good practical performance. In the second study the Monte Carlo simulation is assumed to provide no direct observations of the function gradient. We present ASTRO-DF, which is a class of derivative-free trust-region algorithms, where the stochastic local model is obtained through interpolation. Function estimation (as well as gradient estimation) and model construction within ASTRO and ASTRO-DF are adaptive in the sense that the extent of Monte Carlo sampling is determined by continuously monitoring and balancing metrics of sampling and structural errors within ASTRO and ASTRO-DF. Such error balancing is designed to ensure that the Monte Carlo effort within ASTRO and ASTRO-DF is sensitive to algorithm trajectory, sampling more whenever an iterate is inferred to be close to a critical point and less when far away. We demonstrate the almost-sure convergence of ASTRO-DF\u27s iterates to a first-order critical point when using quadratic stochastic interpolation models. The question of using more complicated models, e.g., regression or stochastic kriging, in combination with adaptive sampling is worth further investigation and will benefit from the methods of proof we present. We investigate the implementation of ASTRO and ASTRO-DF along with the heuristics that enhance the implementation of ASTRO-DF, and report their finite-time performance on a series of low-to-moderate dimensional problems in the CUTEr framework. We speculate that the iterates of both ASTRO and ASTRO-DF achieve the canonical Monte Carlo convergence rate, although a proof remains elusive

The sample average approximation method for multi-objective stochastic optimization

10.1109/WSC.2011.6148092Proceedings - Winter Simulation Conference4021-4032WSCP