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We consider the problem of identifying solutions to a stochastic system under multiple constraints. The objective function and the constraints are expressed in terms of performance measures of the system that are observable only via a simulation model parameterized by a finite number of decision variables. In solving for such a system, one faces the much harder challenge of verifying the feasibility of a potential solution. Toward this, we present cgR-SPLINE, a multistart simulation optimization (SO) algorithm on integer spaces. cgR-SPLINE sequentially solves random restarts of a gradient-based local search routine with increasing precision. The local search routine in turn solves progressively stricter outer approximations of the underlying problem. The local solution estimator from a recently ended restart is probabilistically compared against an incumbent solution, thus generating a sequence of global solution estimators. The optimal convergence rate of the solution iterates is observed to be sub-exponential, slower than the exponential rate observed for SO problems on unconstrained discrete spaces. Additionally, efficiency for cgR-SPLINE dictates that the number of multistarts and the total simulation budget be sublinearly related, implying an increased emphasis on exploration than is prescribed in the continuous context. Heuristics for choosing constraint relaxations and solution reporting demonstrate good finite-time performance on three SO problems, of which two are nontrivial. The extension of cgR-SPLINE's framework to mixed spaces seems a natural next step. The presence of infeasible points arbitrarily close to the stochastic boundary, however pose challenges for consistency. We present a general framework for mixed spaces that is very much along the lines of cgR-SPLINE and propose ideas for specific algorithmic refinements and solution reporting. Strategically locating the restarts of a multistart SO algorithm appears to be a largely unexplored research topic. Toward achieving efficiency during the exploration phase, we present ideas for ``antithetically" generating the restarts from probability measures constructed from the SO algorithm's performance trajectory. Asymptotic behavior of the proposed sampling strategy and policies for optimal parameter selection are presently conjectural, but appear promising based on the outcomes of preliminary experiments. / Ph. D.

We consider unconstrained Simulation Optimization (SO) problems, that is, optimization problems where the underlying objective function is unknown but can be estimated at any chosen point by repeatedly executing a Monte Carlo (stochastic) simulation. SO, introduced more than six decades ago through the seminal work of Robbins and Monro (and later by Kiefer and Wolfowitz), has recently generated much attention. Such interest is primarily because of SOs flexibility, allowing the implicit specification of functions within the optimization problem, thereby providing the ability to embed virtually any level of complexity. The result of such versatility has been evident in SOs ready adoption in fields as varied as finance, logistics, healthcare, and telecommunication systems. While SO has become popular over the years, Robbins and Monros original stochastic approximation algorithm and its numerous modern incarnations have seen only mixed success in solving SO problems. The primary reason for this is stochastic approximations explicit reliance on a sequence of algorithmic parameters to guarantee convergence. The theory for choosing such parameters is now well-established, but most such theory focuses on asymptotic performance. Automatically choosing parameters to ensure good finite-time performance has remained vexingly elusive, as evidenced by continuing efforts six decades after the introduction of stochastic approximation! The other popular paradigm to solve SO is what has been called sample-average approximation. Sample-average approximation, more a philosophy than an algorithm to solve SO, attempts to leverage advances in modern nonlinear programming by first constructing a deterministic approximation of the SO problem using a fixed sample size, and then applying an appropriate nonlinear programming method. Sample-average approximation is reasonable as a solution paradigm but again suffers from finite-time inefficiency because of the simplistic manner in which sample sizes are prescribed. It turns out that in many SO contexts, the effort expended to execute the Monte Carlo oracle is the single most computationally expensive operation. Sample-average approximation essentially ignores this issue since, irrespective of where in the search space an incumbent solution resides, prescriptions for sample sizes within sample-average approximation remain the same. Like stochastic approximation, notwithstanding beautiful asymptotic theory, sample-average approximation suffers from the lack of automatic implementations that guarantee good finite-time performance. In this dissertation, we ask: can advances in algorithmic nonlinear programming theory be combined with intelligent sampling to create solution paradigms for SO that perform well in finite-time while exhibiting asymptotically optimal convergence rates? We propose and study a general solution paradigm called Sampling Controlled Stochastic Recursion (SCSR). Two simple ideas are central to SCSR: (i) use any recursion, particularly one that you would use (e.g., Newton and quasi- Newton, fixed-point, trust-region, and derivative-free recursions) if the functions involved in the problem were known through a deterministic oracle; and (ii) estimate objects appearing within the recursions (e.g., function derivatives) using Monte Carlo sampling to the extent required. The idea in (i) exploits advances in algorithmic nonlinear programming. The idea in (ii), with the objective of ensuring good finite-time performance and optimal asymptotic rates, minimizes Monte Carlo sampling by attempting to balance the estimated proximity of an incumbent solution with the sampling error stemming from Monte Carlo. This dissertation studies the theoretical and practical underpinnings of SCSR, leading to implementable algorithms to solve SO. We first analyze SCSR in a general context, identifying various sufficient conditions that ensure convergence of SCSRs iterates to a solution. We then analyze the nature of such convergence. For instance, we demonstrate that in SCSRs which guarantee optimal convergence rates, the speed of the underlying (deterministic) recursion and the extent of Monte Carlo sampling are intimately linked, with faster recursions permitting a wider range of Monte Carlo effort. With the objective of translating such asymptotic results into usable algorithms, we formulate a family of SCSRs called Adaptive SCSR (A-SCSR) that adaptively determines how much to sample as a recursion evolves through the search space. A-SCSRs are dynamic algorithms that identify sample sizes to balance estimated squared bias and variance of an incumbent solution. This makes the sample size (at every iteration of A-SCSR) a stopping time, thereby substantially complicating the analysis of the behavior of A-SCSRs iterates. That A-SCSR works well in practice is not surprising" the use of an appropriate recursion and the careful sample size choice ensures this. Remarkably, however, we show that A-SCSRs are convergent to a solution and exhibit asymptotically optimal convergence rates under conditions that are no less general than what has been established for stochastic approximation algorithms. We end with the application of a certain A-SCSR to a parameter estimation problem arising in the context of brain-computer interfaces (BCI). Specifically, we formulate and reduce the problem of probabilistically deciphering the electroencephalograph (EEG) signals recorded from the brain of a paralyzed patient attempting to perform one of a specified set of tasks. Monte Carlo simulation in this context takes a more general view, as the act of drawing an observation from a large dataset accumulated from the recorded EEG signals. We apply A-SCSR to nine such datasets, showing that in most cases A-SCSR achieves correct prediction rates that are between 5 and 15 percent better than competing algorithms. More importantly, due to the incorporated adaptive sampling strategies, A-SCSR tends to exhibit dramatically better efficiency rates for comparable prediction accuracies. / Ph. D.

當產險公司需要同時兼顧競爭力並免於破產時，適當的資產配置就是一項相當重要的決策。然而採用均數-變異數分析(mean‐variance analysis)將受到許多限制，而動態控制理論則是難以實作，因此，我們提出一個新的解決方法。這個方法主要係應用模擬最佳化的演算法，例如基礎的基因演算法(basic genetic algorithm, GA)，多階層演化策略(multi-phase evolutionary strategies, MPES)及多階層基因演算法(multi-phase genetic algorithm, MPGA)等並結合模擬模型，來求解保險公司之資產配置的問題。首先我們建立投資市場及保險業務市場的模擬模型，之後再利用本研究所發展出新的最佳化演算法來搜尋最佳的資產配置。在實務上無法實現的多期投資策略，在我們的研究架構下得以被採用，並且在比較求解結果下，多期投資策略(reallocation strategies)較定額投資策略(re‐balancing strategies)有顯著較佳的績效。在兼顧保險公司投資收益並避免破產的目標函數下，我們所提出的研究方法已證明可以用來協助保險公司建立較佳的資產配置。 / Proper asset allocations are vital for property‐casualty insurers to be competitive and remain solvent. However, popular mean‐variance analysis is limited while dynamic control theory is difficult to implement. We thus propose to apply simulation optimizations such as basic genetic algorithm (GA), multi‐phase evolutionary strategies (MPES) and multi‐phase genetic algorithm (MPGA) to the asset allocation problems of the insurers. We first construct a simulation model of the property‐casualty insurer and then develop simulation optimization techniques to search optimal investment strategies upon the simulation results. The resulted reallocation strategies perform better than re‐balancing strategies used in practice with significant margins. Therefore, our proposal researches can be used to assist insurers to construct better asset allocations.

An accurate model for RO process has significant importance in the simulation and optimization proposes. A steady state model of RO process is developed based on solution diffusion theory to describe the permeation through membrane and thin film approach is used to describe the concentration polarization. The model is validated against the operation data reported in the literature. For the sake of clear understanding of the interaction of feed temperature and salinity on the design and operation of RO based desalination systems, simultaneous optimization of design and operation of RO network is investigated based on two-stage RO superstructure via MINLP approach. Different cases with several feed concentrations and seasonal variation of seawater temperature are presented. Also, the possibility of flexible scheduling in terms of the number of membrane modules required in operation in high and low temperature seasons is investigated A simultaneous modelling and optimization method for RO system including boron removal is then presented. A superstructure of the RO network is developed based on double pass RO network (two-stage seawater pass and one-stage brackish water pass). The MINLP problem based on the superstructure is used to find out an optimal RO network which will minimize the total annualized cost while fulfilling a given boron content limit. The effect of pH on boron rejection is investigated at deferent seawater temperatures. The optimal operation policy of RO system is then studied in this work considering variations in freshwater demand and with changing seawater temperature throughout the day. A storage tank is added to the RO layout to provide additional operational flexibility and to ensure the availability of freshwater at all times. Two optimization problems are solved incorporating two seawater temperature profiles, representing summer and winter seasons. The possibility of flexible scheduling of cleaning and maintenance of membrane modules is investigated. Then, the optimal design and operation of RO process is studied in the presence of membrane fouling and including several operational variations such as variable seawater temperature. The cleaning schedule of single stage RO process is formulated as MINLP problem using spiral wound modules. NNs based correlation has been developed based on the actual fouling data which can be used for estimating the permeability decline factors. The correlation based on actual data to predict the annual seawater temperature profile is also incorporated in the model. The proposed optimization procedure identified simultaneously the optimal maintenance schedule of RO network including its design parameters and operating policy. The steady state model of RO process is used to study the sensitivity of different operating and design parameters on the plant performance. A non-linear optimization problem is formulated to minimize specific energy consumption at fixed product flow rate and quality while optimizing the design and operating parameters. Then the MINLP formulation is used to find the optimal designs of RO layout for brackish water desalination. A variable fouling profile along the membrane stages is introduced to see how the network design and operation of the RO system are to be adjusted Finally, a preliminary control strategy for RO process is developed based on PID control algorithm and a first order transfer function (presented in the Appendix).

Numerical simulations are often used in computer graphics to capture the effects of natural phenomena such as fire, water and smoke. However, simulating large-scale events in this way, with the details needed for feature film, poses serious problems. Grid-based simulations at resolutions sufficient to incorporate small-scale details would be costly and use large amounts of memory, and likewise for particle based techniques. To overcome these problems, a new framework for simulation and rendering of gaseous phenomena is presented in this thesis. It makes use of a combination of different existing concepts for such phenomena to resolve many of the issues in using them separately, and the result is a potent method for high-detailed simulation and rendering at low cost. The developed method utilizes a slice refinement technique, where a coarse particle input is transformed into a set of two-dimensional view-aligned slices, which are simulated at high resolution. These slices are subsequently used in a rendering framework accounting for light scattering behaviors in participating media to achieve a final highly detailed volume rendering outcome. However,the transformations from three to two dimensions and back easily introduces visible artifacts, so a number of techniques have been considered to overcome these problems, where e.g. a turbulence function is used in the final volume density function to break up possible interpolation artifacts.

Les ports maritimes se confrontent à des exigences rigoureuses imposées par l'évolution de la taille de la flotte mondiale des porte-conteneurs et des zones de stockage qui arrivent à des niveaux de saturation élevés. Pour répondre à ces défis, plusieurs ports ont décidé de créer des terminaux multimodaux qui jouent le rôle de méga-hubs pour les terminaux maritimes, en vue de libérer les zones de stockage de ces terminaux, de développer la part du transport massifié de conteneurs et de réduire les émissions des gaz à effet de serre en utilisant des modes alternatifs à la route. Néanmoins, la gestion de ces nouveaux schémas logistiques est laborieuse. Cela s’explique par plusieurs facteurs, entre autres, la nature dynamique et distribuée de ces systèmes, la diversité des opérations et le manque des informations nécessaires au contrôle de flux. La finalité de cette thèse est de développer des approches capables de répondre aux besoins des opérateurs portuaires dans un terminal multimodal, avec prise en compte des différentes sources d’incertitudes. Deux problèmes d'optimisation sont principalement considérés dans cette thèse, à savoir : l'optimisation de tournées de navettes ferroviaires (The Rail Shuttle Routing Problem) et l'ordonnancement de grues de quai (The Quay Crane Scheduling Problem). En vue d'aborder la complexité et l’aspect incertain de ces problèmes, nous proposerons des modélisations mathématiques, ainsi que des approches de résolution basées sur l’optimisation par colonies de fourmis, l’optimisation robuste et le couplage Simulation-Optimisation. Les différents tests numériques effectués ont prouvé l’efficacité des algorithmes proposés et leur robustesse. / Today, seaports face increasingly stringent requirements imposed by the considerable growth of goods transited by sea. Indeed, the organization of the port sector has evolved rapidly and has caused several negative impacts, including pollution and congestion of terminals, which constitute today the major concerns of port operators. To address those challenges, several ports have decided to build multimodal terminals that act as mega-hubs for maritime terminals, in order to free the storage areas on the maritime terminals, to promote the use of consolidated container modes of transfer and to reduce greenhouse gas emissions by using alternative modes to the road. Nevertheless, the management of these new logistic systems is laborious. This is due to several factors, including the dynamic and distributed nature of these systems, the variety of operations, and the lack of information needed to control flow. The aim of this thesis is to develop approaches capable of meeting the needs of port operators in a multimodal terminal, taking into account the different sources of uncertainty. Two optimization problems are mainly considered in this thesis, namely : the Rail Shuttle Routing Problem(RSRP) and the Quay Crane Scheduling Problem(QCSP). To address the complexity and uncertainties of these problems, we propose new mathematical models, as well as some heuristics approaches based on ant colony optimization, robust optimization and Simulation-Optimization. The various numerical tests carried out proved the effectiveness and the robustness of the proposed algorithms.

Seawater intrusion (SWI) is a widespread environmental problem, particularly in arid and semi-arid coastal areas. Unplanned prolonged over-pumping of groundwater is the most important factor in SWI that could result in severe deterioration of groundwater quality. Therefore, appropriate management strategies should be implemented in coastal aquifers to control SWI with acceptable limits of economic and environmental costs. This PhD project presents the development and application of a simulation-optimization (S/O) model to assess different management methods of controlling saltwater intrusion while satisfying water demands, and with acceptable limits of economic and environmental costs, in confined and unconfined coastal aquifers. The first S/O model (FE-GA) is developed by direct linking of an FE simulation model with a multi-objective Genetic Algorithm (GA) to optimize the efficiency of a wide range of SWI management scenarios. However, in this S/O framework, several multiple calls of the simulation model by the population-based optimization model, evaluating best individual candidate solutions resulted in a considerable computational burden. To solve this problem the numerical simulation model is replaced by an Evolutionary Polynomial Regression (EPR)-based surrogate model in the next S/O model (EPR-GA). Through these S/O approaches (FE-GA and EPR-GA) the optimal coordinates and rates of the both abstraction and recharge barriers are determined in the studied management scenarios. As a result, a new combined methodology, so far called ADRTWW, is proposed to control SWI. The ADRTWW model consists of deep Abstraction of saline water near the coast followed by Desalination of the abstracted water to a potable level for public uses and simultaneously Recharging the aquifer using a more economic source of water such as treated wastewater (TWW). In accordance to the available recharge options (injection through well or infiltration from surface pond), the general performance of ADRTWW is evaluated in different hydro-geological settings of the aquifers indicating that it offers the least cost and least salinity in comparison with other scenarios. The great capabilities of both developed S/O models in identification of the best management solutions and the optimal coordinates and rates of the abstraction well and recharge well/pond are discussed. Both FE-GA and EPR-GA can be successfully employed by a robust decision support system. In the next phase of the study, the general impacts of sea level rise (SLR), associated with its transgression nature along the coastline surface on the saltwater intrusion mechanism are investigated in different hypothetical and real case studies of coastal aquifer systems. The results show that the rate and the amount of SWI are considerably greater in aquifers with flat shoreline slopes compared with those with steep slopes. The SWI process is followed by a significant depletion in quantity of freshwater resources at the end of the century. The situation is exacerbated with combined action of SLR and groundwater withdrawals. This finding is also confirmed by 3D simulation of SWI in a regional coastal aquifer (Wadi Ham aquifer) in the UAE subjected to the coupled actions of SLR and pumping.

Traffic signal systems serve as one of the most powerful control tools in improving the efficiency of surface transportation travel. Traffic operations on arterial roads are particularly complex because of traffic interruptions caused by signalized intersections along the corridor. This dissertation research presents a systematic framework of integrated traffic control in an attempt to break down the complexities into several simpler sub-problems such as pattern recognition, environment-mobility relationships and multi-objective optimization for multi-criterial signal timing design. The overall goal of this dissertation is to develop signal timing plans, including a day plan schedule, cycle length parameters, splits and offsets, which are suitable for real traffic conditions with consideration of multi-criterial performance of the surface transportation system. To this end, the specific objectives are to: (1) identify appropriate time-of-day breakpoints and intervals to accommodate traffic pattern variations for day plan schedule of signal timing; (2) explore the relationship between environmental outcomes (e.g., emissions) from emission estimators and mobility measures (e.g., delay and stops) for different types of intersections; (3) optimize signal timing parameters for multi-criteria objectives (e.g., minimizing vehicular delay, number of stops, marginal costs of emissions and total costs), with the comparison of performance metrics for different objectives, at the intersection level; (4) optimize arterial offsets for different objectives at the arterial level and compare the performance metrics of different objectives to recommend suitable objectives for integrated multi-criteria signal timing design in arterial traffic operations. An extensive review of the literature, which covers existing tools, traffic patterns, traffic control with environmental concerns, and related optimization methods, shows that both opportunities and challenges have emerged for multi-criteria traffic signal timing design. These opportunities include large quantities of traffic condition data collected by system detectors or non-intrusive data collection platforms as well as powerful tools for microscopic traffic modeling and instantaneous emission estimation. The challenge is how to effectively deal with these big data, either from field collection or detailed simulation, and provide useful information for decision makers in practice. Methodologically, there's a tradeoff between the accuracy of objective function values and the computational efficiency of simulation and optimization. To address this need, in this dissertation, traffic signal timing design that systematically enables the use of integrated data and models are investigated and analyzed in the four steps/studies. The technology of identifying time-of-day breakpoints in the first study shows a mathematical way to classify dynamic traffic patterns by understanding dynamic traffic features and instabilities at a macroscopic level on arterials. Given the limitations of using built-in emissions modules within current traffic simulation and signal optimization tools, the metamodeling-based approach presented in the second study makes a methodological contribution. The findings of the second study on environment-mobility relationships set up the base for extensive application of two-stage optimization in the third and fourth studies for sustainable traffic operations and management. The comparison of outputs from an advanced estimator with those from the current tool also addresses improving the emissions module for more accurate analysis (e.g., benefit-cost analysis) in practical signal retiming projects. The third study shows that there are tradeoffs between minimizing delay and minimizing marginal costs of emissions. When total cost (including cost of delay, fuel consumption and emissions) is set as a single objective function, that objective clears the way for relatively reliable results for all the aspects. In the fourth study, the improvements in marginal cost of emissions and total cost by dynamic programming procedure are obvious, which indicates the effectiveness of using total link cost as an objective at the corridor level. In summary, this dissertation advocates a sustainable traffic control system by simultaneously considering travel time, fuel consumption and emissions. The outcomes of this integrated multi-criteria signal timing design can be easily implemented by traffic operators in their daily life of retiming signal timing.