Дисертації з теми "Chance Constraint Optimization"
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Koker, Ezgi. "Chance Constrained Optimization Of Booster Disinfection In Water Distribution Networks." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613640/index.pdf.
Повний текст джерелаSassi, Achille. "Numerical methods for hybrid control and chance-constrained optimization problems." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLY005/document.
Повний текст джерелаThis thesis is devoted to the analysis of numerical methods in the field of optimal control, and it is composed of two parts. The first part is dedicated to new results on the subject of numerical methods for the optimal control of hybrid systems, controlled by measurable functions and discontinuous jumps in the state variable simultaneously. The second part focuses on a particular application of trajectory optimization problems for space launchers. Here we use some nonlinear optimization methods combined with non-parametric statistics techniques. This kind of problems belongs to the family of stochastic optimization problems and it features the minimization of a cost function in the presence of a constraint which needs to be satisfied within a desired probability threshold
Helmberg, Christoph, Sebastian Richter, and Dominic Schupke. "A Chance Constraint Model for Multi-Failure Resilience in Communication Networks." Universitätsbibliothek Chemnitz, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-175454.
Повний текст джерелаCalfa, Bruno Abreu. "Data Analytics Methods for Enterprise-wide Optimization Under Uncertainty." Research Showcase @ CMU, 2015. http://repository.cmu.edu/dissertations/575.
Повний текст джерелаLiu, Jianzhe. "On Control and Optimization of DC Microgrids." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1512049527948171.
Повний текст джерелаDai, Siyu S. M. Massachusetts Institute of Technology. "Probabilistic motion planning and optimization incorporating chance constraints." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/120230.
Повний текст джерелаCataloged from PDF version of thesis.
Includes bibliographical references (pages 201-208).
For high-dimensional robots, motion planning is still a challenging problem, especially for manipulators mounted to underwater vehicles or human support robots where uncertainties and risks of plan failure can have severe impact. However, existing risk-aware planners mostly focus on low-dimensional planning tasks, meanwhile planners that can account for uncertainties and react fast in high degree-of-freedom (DOF) robot planning tasks are lacking. In this thesis, a risk-aware motion planning and execution system called Probabilistic Chekov (p-Chekov) is introduced, which includes a deterministic stage and a risk-aware stage. A systematic set of experiments on existing motion planners as well as p-Chekov is also presented. The deterministic stage of p-Chekov leverages the recent advances in obstacle-aware trajectory optimization to improve the original tube-based-roadmap Chekov planner. Through experiments in 4 common application scenarios with 5000 test cases each, we show that using sampling-based planners alone on high DOF robots can not achieve a high enough reaction speed, whereas the popular trajectory optimizer TrajOpt with naive straight-line seed trajectories has very high collision rate despite its high planning speed. To the best of our knowledge, this is the first work that presents such a systematic and comprehensive evaluation of state-of-the-art motion planners, which are based on a significant amount of experiments. We then combine different stand-alone planners with trajectory optimization. The results show that the deterministic planning part of p-Chekov, which combines a roadmap approach that caches the all pair shortest paths solutions and an online obstacle-aware trajectory optimizer, provides superior performance over other standard sampling-based planners' combinations. Simulation results show that, in typical real-life applications, this "roadmap + TrajOpt" approach takes about 1 s to plan and the failure rate of its solutions is under 1%. The risk-aware stage of p-Chekov accounts for chance constraints through state probability distribution and collision probability estimation. Based on the deterministic Chekov planner, p-Chekov incorporates a linear-quadratic Gaussian motion planning (LQG-MP) approach into robot state probability distribution estimation, applies quadrature-sampling theories to collision risk estimation, and adapts risk allocation approaches for chance constraint satisfaction. It overcomes existing risk-aware planners' limitation in real-time motion planning tasks with high-DOF robots in 3- dimensional non-convex environments. The experimental results in this thesis show that this new risk-aware motion planning and execution system can effectively reduce collision risk and satisfy chance constraints in typical real-world planning scenarios for high-DOF robots. This thesis makes the following three main contributions: (1) a systematic evaluation of several state-of-the-art motion planners in realistic planning scenarios, including popular sampling-based motion planners and trajectory optimization type motion planners, (2) the establishment of a "roadmap + TrajOpt" deterministic motion planning system that shows superior performance in many practical planning tasks in terms of solution feasibility, optimality and reaction time, and (3) the development of a risk-aware motion planning and execution system that can handle high-DOF robotic planning tasks in 3-dimensional non-convex environments.
by Siyu Dai.
S.M.
Sun, Yufei. "Chance-constrained optimization & optimal control problems." Thesis, Curtin University, 2015. http://hdl.handle.net/20.500.11937/183.
Повний текст джерелаYang, Yi. "Sequential convex approximations of chance constrained programming /." View abstract or full-text, 2008. http://library.ust.hk/cgi/db/thesis.pl?IELM%202008%20YANG.
Повний текст джерелаArellano-Garcia, Harvey. "Chance constrained optimization of process systems under uncertainty." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=982225652.
Повний текст джерелаLuedtke, James. "Integer Programming Approaches for Some Non-convex and Stochastic Optimization Problems." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19711.
Повний текст джерелаIbrahim, Sarmad Khaleel. "DISTRIBUTION SYSTEM OPTIMIZATION WITH INTEGRATED DISTRIBUTED GENERATION." UKnowledge, 2018. https://uknowledge.uky.edu/ece_etds/116.
Повний текст джерелаMrázková, Eva. "Approximations in Stochastic Optimization and Their Applications." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2010. http://www.nusl.cz/ntk/nusl-233932.
Повний текст джерелаPiprek, Patrick [Verfasser], Florian [Akademischer Betreuer] Holzapfel, Sébastien [Gutachter] Gros, and Florian [Gutachter] Holzapfel. "Robust Trajectory Optimization Applying Chance Constraints and Generalized Polynomial Chaos / Patrick Piprek ; Gutachter: Sébastien Gros, Florian Holzapfel ; Betreuer: Florian Holzapfel." München : Universitätsbibliothek der TU München, 2020. http://d-nb.info/1211086992/34.
Повний текст джерелаKubo, Seiji. "Topology optimization for the duct flow problems in laminar and turbulent flow regimes." Kyoto University, 2019. http://hdl.handle.net/2433/242491.
Повний текст джерелаQiu, Feng. "Probabilistic covering problems." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/47567.
Повний текст джерелаAmini, Mahraz. "Optimal dispatch of uncertain energy resources." ScholarWorks @ UVM, 2019. https://scholarworks.uvm.edu/graddis/1046.
Повний текст джерелаSerra, Romain. "Opérations de proximité en orbite : évaluation du risque de collision et calcul de manoeuvres optimales pour l'évitement et le rendez-vous." Thesis, Toulouse, INSA, 2015. http://www.theses.fr/2015ISAT0035/document.
Повний текст джерелаThis thesis is about collision avoidance for a pair of spherical orbiting objects. The primary object - the operational satellite - is active in the sense that it can use its thrusters to change its trajectory, while the secondary object is a space debris that cannot be controlled in any way. Onground radars or other means allow to foresee a conjunction involving an operational space craft,leading in the production of a collision alert. The latter contains statistical data on the position and velocity of the two objects, enabling for the construction of a probabilistic collision model.The work is divided in two parts : the computation of collision probabilities and the design of maneuvers to lower the collision risk. In the first part, two kinds of probabilities - that can be written as integrals of a Gaussian distribution over an Euclidean ball in 2 and 3 dimensions -are expanded in convergent power series with positive terms. It is done using the theories of Laplace transform and Definite functions. In the second part, the question of collision avoidance is formulated as a chance-constrained optimization problem. Depending on the collision model, namely short or long-term encounters, it is respectively tackled via the scenario approach or relaxed using polyhedral collision sets. For the latter, two methods are proposed. The first one directly tackles the joint chance constraints while the second uses another relaxation called risk selection to obtain a mixed-integer program. Additionaly, the solution to the problem of fixed-time fuel minimizing out-of-plane proximity maneuvers is derived. This optimal control problem is solved via the primer vector theory
Sadat, Sayed Abdullah. "Optimal Bidding Strategy for a Strategic Power Producer Using Mixed Integer Programming." Scholar Commons, 2017. http://scholarcommons.usf.edu/etd/6631.
Повний текст джерелаFleming, James. "Robust and stochastic MPC of uncertain-parameter systems." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:c19ff07c-0756-45f6-977b-9d54a5214310.
Повний текст джерелаExcoffier, Mathilde. "Chance-Constrained Programming Approaches for Staffing and Shift-Scheduling Problems with Uncertain Forecasts : application to Call Centers." Thesis, Paris 11, 2015. http://www.theses.fr/2015PA112244/document.
Повний текст джерелаThe staffing and shift-scheduling problems in call centers consist in deciding how many agents handling the calls should be assigned to work during a given period in order to reach the required Quality of Service and minimize the costs. These problems are subject to a growing interest, both for their interesting theoritical formulation and their possible applicative effects. This thesis aims at proposing chance-constrained approaches considering uncertainty on demand forecasts.First, this thesis proposes a model solving the problems in one step through a joint chance-constrained stochastic program, providing a cost-reducing solution. A continuous-based approach leading to an easily-tractable optimization program is formulated with random variables following continuous distributions, a new continuous relation between arrival rates and theoritical real agent numbers and constraint linearizations. The global risk level is dynamically shared among the periods during the optimization process, providing reduced-cost solution. The resulting solutions respect the targeted risk level while reducing the cost compared to other approaches.Moreover, this model is extended so that it provides a better representation of real situations. First, the queuing system model is improved and consider the limited patience of customers. Second, another formulation of uncertainty is proposed so that the period correlation is considered.Finally, another uncertainty representation is proposed. The distributionally robust approach provides a formulation while assuming that the correct probability distribution is unknown and belongs to a set of possible distributions defined by given mean and variance. The problem is formulated with a joint chance constraint. The risk at each period is a decision variable to be optimized. A deterministic equivalent problem is proposed. An easily-tractable mixed-integer linear formulation is obtained through piecewise linearizations
Baker, Kyri A. "Coordination of Resources Across Areas for the Integration of Renewable Generation: Operation, Sizing, and Siting of Storage Devices." Research Showcase @ CMU, 2014. http://repository.cmu.edu/dissertations/465.
Повний текст джерелаKlöppel, Michael [Verfasser], Armin [Akademischer Betreuer] Hoffmann, Pu [Gutachter] Li, and Oliver [Gutachter] Stein. "Efficient numerical solution of chance constrained optimization problems with engineering applications / Michael Klöppel ; Gutachter: Pu Li, Oliver Stein ; Betreuer: Armin Hoffmann." Ilmenau : TU Ilmenau, 2014. http://d-nb.info/1178182878/34.
Повний текст джерелаLourens, Spencer. "Bias in mixtures of normal distributions and joint modeling of longitudinal and time-to-event data with monotonic change curves." Diss., University of Iowa, 2015. https://ir.uiowa.edu/etd/1685.
Повний текст джерелаKůdela, Jakub. "Advanced Decomposition Methods in Stochastic Convex Optimization." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-403864.
Повний текст джерелаPrigent, Sylvain. "Approche novatrice pour la conception et l’exploitation d’avions écologiques." Thesis, Toulouse, ISAE, 2015. http://www.theses.fr/2015ESAE0014/document.
Повний текст джерелаThe objective of this PhD work is to pose, investigate, and solve the highly multidisciplinary and multiobjective problem of environmentally efficient aircraft design and operation. In this purpose, the main three drivers for optimizing the environmental performance of an aircraft are the airframe, the engine, and the mission profiles. The figures of merit, which will be considered for optimization, are fuel burn, local emissions, global emissions, and climate impact (noise excluded). The study will be focused on finding efficient compromise strategies and identifying the most powerful design architectures and design driver combinations for improvement of environmental performances. The modeling uncertainty will be considered thanks to rigorously selected methods. A hybrid aircraft configuration is proposed to reach the climatic impact reduction objective
Velay, Maxime. "Méthodes d’optimisation distribuée pour l’exploitation sécurisée des réseaux électriques interconnectés." Thesis, Université Grenoble Alpes (ComUE), 2018. http://www.theses.fr/2018GREAT063/document.
Повний текст джерелаOur societies are more dependent on electricity than ever, thus any disturbance in the power transmission and delivery has major economic and social impact. The reliability and security of power systems are then crucial to keep, for power system operators, in addition to minimizing the system operating cost. Moreover, transmission systems are interconnected to decrease the cost of operation and improve the system security. One of the main challenges for transmission system operators is therefore to coordinate with interconnected power systems, which raises scalability, interoperability and privacy issues. Hence, this thesis is concerned with how TSOs can operate their networks in a decentralized way but coordinating their operation with other neighboring TSOs to find a cost-effective scheduling that is globally secure.The main focus of this thesis is the security of power systems, this is why the evolution of the main characteristics of the blackouts that are failures in power system security, of the period 2005-2016 is studied. The approach consists in determining what the major characteristics of the incidents of the past 10 years are, to identify what should be taken into account to mitigate the risk of incidents. The evolution have been studied and compared with the characteristics of the blackouts before 2005. The study focuses on the pre-conditions that led to those blackouts and on the cascades, and especially the role of the cascade speed. Some important features are extracted and later integrated in our work.An algorithm that solve the preventive Security Constrained Optimal Power Flow (SCOPF) problem in a fully distributed manner, is thus developed. The preventive SCOPF problem consists in adding constraints that ensure that, after the loss of any major device of the system, the new steady-state reached, as a result of the primary frequency control, does not violate any constraint. The developed algorithm uses a fine-grained decomposition and is implemented under the multi-agent system paradigm based on two categories of agents: devices and buses. The agents are coordinated with the Alternating Direction method of multipliers in conjunction with a consensus problem. This decomposition provides the autonomy and privacy to the different actors of the system and the fine-grained decomposition allows to take the most of the decomposition and provides a good scalability regarding the size of the problem. This algorithm also have the advantage of being robust to any disturbance of the system, including the separation of the system into regions.Then, to account for the uncertainty of production brought by wind farms forecast error, a two-step distributed approach is developed to solve the Chance-Constrained Optimal Power Flow problem, in a fully distributed manner. The wind farms forecast errors are modeled by independent Gaussian distributions and the mismatches with the initials are assumed to be compensated by the primary frequency response of generators. The first step of this algorithm aims at determining the sensitivity factors of the system, needed to formulate the problem. The results of this first step are inputs of the second step that is the CCOPF. An extension of this formulation provides more flexibility to the problem and consists in including the possibility to curtail the wind farms. This algorithm relies on the same fine-grained decomposition where the agents are again coordinated by the ADMM and a consensus problem. In conclusion, this two-step algorithm ensures the privacy and autonomy of the different system actors and it is de facto parallel and adapted to high performance platforms
Alais, Jean-Christophe. "Risque et optimisation pour le management d'énergies : application à l'hydraulique." Thesis, Paris Est, 2013. http://www.theses.fr/2013PEST1071/document.
Повний текст джерелаHydropower is the main renewable energy produced in France. It brings both an energy reserve and a flexibility, of great interest in a contextof penetration of intermittent sources in the production of electricity. Its management raises difficulties stemming from the number of dams, from uncertainties in water inflows and prices and from multiple uses of water. This Phd thesis has been realized in partnership with Electricité de France and addresses two hydropower management issues, modeled as stochastic dynamic optimization problems. The manuscript is divided in two parts. In the first part, we consider the management of a hydroelectric dam subject to a so-called tourist constraint. This constraint assures the respect of a given minimum dam stock level in Summer months with a prescribed probability level. We propose different original modelings and we provide corresponding numerical algorithms. We present numerical results that highlight the problem under various angles useful for dam managers. In the second part, we focus on the management of a cascade of dams. We present the approximate decomposition-coordination algorithm called Dual Approximate Dynamic Programming (DADP). We show how to decompose an original (large scale) problem into smaller subproblems by dualizing the spatial coupling constraints. On a three dams instance, we are able to compare the results of DADP with the exact solution (obtained by dynamic programming); we obtain approximate gains that are only at a few percents of the optimum, with interesting running times. The conclusions we arrived at offer encouraging perspectives for the stochastic optimization of large scale problems
Wang, Chenghao. "Contribution à l’optimisation robuste de réseaux." Thesis, Compiègne, 2021. http://www.theses.fr/2021COMP2632.
Повний текст джерелаThis Ph.D. Thesis is focused on proposing new optimization modeling and algorithmic approaches for dealing with real-world network optimization problems arising in the transportation and telecommunications fields. Since the focus has been on real-world applications, a relevant aspect that has been taken into account is data uncertainty, i.e. the fact that the value of a subset of input data of the problem is not exactly known when the problem is solved. More precisely, in the context of transportation problems, it was considered the flight level assignment problem, which arises in air traffic management. It aims at establishing the flight levels of a set of aircraft in order to improve the total assignment revenue, to reduce the total number of flight conflicts and also the total en-route delay. In this context, we proposed a new chance-constrained optimization problem and iterative constraint-generation heuristic which is based on both analytical and sampling methods. Besides transportation problems, this Thesis has also focused on the optimal design of 5th generation of wireless networks (5G) considering Superfluid and virtual architectures. Specifically, the 5G Superfluid architecture is based on atomic virtual entities called Reusable Functional Block (RFB). We investigated the problem of minimizing the total installation costs of a 5G Superfluid network (composed of virtual entities and realized over a physical network) while guaranteeing constraint on user coverage, downlink traffic performance and technical constraints on RFBs of different nature. To solve this hard problem, we proposed a Benders decomposition approach. Concerning instead the design of general virtual networks, we adopted a green paradigm that pursues energy-efficiency and tackled a state-of-the-art robust mixed integer linear programming formulation of the problem, by means of a new matheuris tic based on combining a genetic algorithm with exact large neighborhood searches. Results of computational tests executed considering realistic problem instances have shown the validity of all the new optimization modeling and algorithmic approaches proposed in this Thesis for the transportation and telecommunications problems sketched above
Lorenz, Nicole. "Application of the Duality Theory." Doctoral thesis, Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-94108.
Повний текст джерелаKabalan, Bilal. "Systematic methodology for generation and design of hybrid vehicle powertrains." Thesis, Lyon, 2020. http://www.theses.fr/2020LYSE1048.
Повний текст джерелаTo meet the vehicle fleet-wide average CO2 targets, the stringent pollutant emissions standards, and the clients’ new demands, the automakers realized the inevitable need to offer more hybrid and electric powertrains. Designing a hybrid powertrain remains however a complex task. It is an intricate system involving numerous variables that are spread over different levels: architecture, component technologies, sizing, and control. The industry lacks frameworks or tools that help in exploring the entire design space and in finding the global optimal solution on all these levels. This thesis proposes a systematic methodology that tries to answer a part of this need. Starting from a set of chosen components, the methodology automatically generates all the possible graphs of architectures using constraint-programming techniques. A tailored representation is developed to picture these graphs. The gearbox elements (clutches, synchronizer units) are represented with a level of details appropriate to generate the new-trend dedicated hybrid gearboxes, without making the problem too complex. The graphs are then transformed into other types of representation: 0ABC Table (describing the mechanical connections between the components), Modes Table (describing the available modes in the architectures) and Modes Table + (describing for each available mode the global efficiency and ratio of the power flow between all the components). Based on these representations, the architectures are filtered and the most promising ones are selected. They are automatically assessed and optimized using a general hybrid model specifically developed to calculate the performance and fuel consumption of all the generated architectures. This model is inserted inside a bi-level optimization process: Genetic Algorithm GA is used on the sizing and components level, while Dynamic Programming DP is used on the control level. A case study is performed and the capability of the methodology is proven. It succeeded in automatically generating all the graphs of possible architectures, and filtering dismissed architectures that were then proven not efficient. It also selected the most promising architectures for optimization. The results show that the proposed methodology succeeded in finding an architecture better than the ones proposed without the methodology (consumption about 5% lower)
Lin, Chi-Ping, and 林奇平. "Solving Minimum Cost Redundancy Allocation Problem with Chance Constraint Using Simulation Optimization." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/btfs47.
Повний текст джерела國立清華大學
工業工程與工程管理學系所
105
Redundancy allocation problem (RAP), which aims to minimize the system total cost subject to some constraints on system reliability, represents an important problem in system design with many applications in areas such as electronic systems, power systems, telecommunication systems and manufacturing systems. In this paper, we extend RAP to a more generalized situation, First, the network topology is generalized, i.e., the components in the system can be of any logical relationship. Second, there exist chance constraints that the overall system reliability is required to exceed a prescribed value. We propose an efficient simulation optimization method. A numerical study shows that the proposed method can locate the optimal solution more efficiently compared to the existing methods.
Ta, Thuy Anh. "Stochastic optimization of staffing for multiskill call centers." Thèse, 2019. http://hdl.handle.net/1866/23441.
Повний текст джерелаIn this thesis, we study the staffing optimization problem in multiskill call centers, in which we aim at minimizing the operating cost while delivering a high quality of service (QoS) to customers. We also introduce the use of chance constraints which require that the QoSs are met with a given probability. These constraints are adequate in the case when the performance is measured over a short time interval as QoS measures are random variables in a given time period. The proposed staffing problems are challenging in the sense that the stochastic constraints have no-closed forms and need to be approximated by simulation. In addition, the QoS functions are typically non-linear and non-convex. We consider staffing optimization problems in different settings and study the proposed models in both theoretical and practical aspects. The methodologies developed are general, in the sense that they can be adapted and applied to other staffing/scheduling problems in queuing-based systems. The thesis consists of three articles dealing with different challenges in modeling and solving staffing optimization problems in multiskill call centers. The first and second articles concern a two-stage staffing optimization problem under uncertainty. While in the first one, we study a general two-stage discrete stochastic programming model to provide a theoretical guarantee for the consistency of the sample average approximation (SAA) when the sample sizes go to infinity, the second one applies the SAA approach to solve the two-stage staffing optimization problem under arrival rate uncertainty. Both papers indicate the viability of the SAA approach in our context, in both theoretical and practical aspects. To be more precise, in the first article, we consider a general two-stage discrete stochastic problem with expected value constraints. We formulate its SAA with nested sampling. We show that under some assumptions that hold in call center examples, one can obtain the optimal solutions of the original problem by solving its SAA with large enough sample sizes. Moreover, we show that the probability that the optimal solution of the sample problem is an optimal solution of the original problem, approaches one exponentially fast as we increase the sample sizes. These theoretical findings are important, not only for call center applications, but also for other decision-making problems with discrete decision variables. The second article concerns solution methods to solve a two-stage staffing problem under arrival rate uncertainty. It is motivated by the fact that the SAA version of the two-stage staffing problem becomes expensive to solve with a large number of scenarios, as for each scenario, one needs to use simulation to approximate the QoS constraints. We develop an algorithm that combines simulation, cut generation, cut strengthening and Benders decomposition to solve the SAA problem. We show the efficiency of the approach, especially when the number of scenarios is large. In the last article, we consider problems with chance constraints on the service level measures. Our methodology proposed in this article is motivated by the fact that the QoS functions generally display ``S-shape'' curves and might be well approximated by appropriate sigmoid functions. Based on this idea, we develop a novel approach that combines non-linear regression, simulation and trust region local search to efficiently solve large-scale staffing problems in a viable way. The main advantage of the approach is that the optimization procedure can be formulated as a sequence of steps of performing simulation and solving linear programming models. Numerical results based on real-life call center examples show the practical viability of our approach. The methodologies developed in this thesis can be applied in many other settings, e.g., staffing and scheduling problems in other queuing-based systems with other types of QoS constraints. These also raise several research directions that might be interesting to investigate. For examples, a clustering approach to mitigate the expensiveness of the two-stage staffing models, or a distributionally robust optimization version to better deal with data uncertainty.
Ta, Thuy Anh. "Staffing Optimization with Chance Constraints in Call Centers." Thèse, 2013. http://hdl.handle.net/1866/10687.
Повний текст джерелаCall centers are key components of almost any large organization. The problem of labor management has received a great deal of attention in the literature. A typical formulation of the staffing problem is in terms of infinite-horizon performance measures. The method of combining simulation and optimization is used to solve this staffing problem. In this thesis, we consider a problem of staffing call centers with respect to chance constraints. We introduce chance-constrained formulations of the scheduling problem which requires that the quality of service (QoS) constraints are met with high probability. We define a sample average approximation of this problem in a multiskill setting. We prove the convergence of the optimal solution of the sample-average problem to that of the original problem when the sample size increases. For the special case where we consider the staffing problem and all agents have all skills (a single group of agents), we design three simulation-based optimization methods for the sample problem. Given a starting solution, we increase the staffings in periods where the constraints are violated, and decrease the number of agents in several periods where decrease is acceptable, as much as possible, provided that the constraints are still satisfied. For the call center models in our numerical experiment, these algorithms give good solutions, i.e., most constraints are satisfied, and we cannot decrease any agent in any period to obtain better results. One advantage of these algorithms, compared with other methods, that they are very easy to implement.
"Chance-constrained optimization with stochastically dependent perturbations." 2012. http://library.cuhk.edu.hk/record=b5549428.
Повний текст джерела在这篇论文中我们主要研究机会约束下的线性矩阵不等式,并假设扰动分布不必相互独立,其仅有的相关性信息只由一系列子扰动的独立关系结构提供。通过推导矩阵值随机变量的大偏差上界,我们得出这一类条件约束的安全可解近似。我们随后考虑了基于条件风险价值度量的机会约束规划问题, 以及带多项式扰动的机会约束优化问题。另外,通过构造相应的鲁棒对等式的不确定集合,我们把机会约束规划转换成鲁棒优化问题。由于这种近似可以表示为一组线性矩阵不等式,因而可以使用现成的优化软件方便地求解。最后,我们把该安全可解近似方法运用到一个控制理论问题,以及一个带风险价值约束的投资组合优化问题中。
The wide applicability of chanceconstrained programming, together with advances in convex optimization and probability theory, has created a surge of interest in finding efficient methods for processing chance constraints in recent years. One of the successes is the development of so-called safe tractable approximations of chance-constrained programs, where a chance constraint is replaced by a deterministic and efficiently computable inner approximation. Currently, such an approach applies mainly to chance-constrained linear inequalities, in which the data perturbations are either independent or define a known covariance matrix. However, its applicability to the case of chanceconstrained conic inequalities with dependent perturbations--which arises in supply chain management, finance, control and signal processing applications--remains largely unexplored.
In this thesis, we consider the problem of processing chance-constrained affinely perturbed linear matrix inequalities, in which the perturbations are not necessarily independent, and the only information available about the dependence structure is a list of independence relations. Using large deviation bounds for matrix-valued random variables, we develop safe tractable approximations of those chance constraints. Extensions to the Matrix CVaR (Conditional Value-at-Risk) risk measure and general polynomials perturbations are also provided separately. Further more, we show that the chanceconstrained linear matrix inequalities optimization problem can be converted to a robust optimization problem by constructing the uncertainty set of the corresponding robust counterpart. A nice feature of our approximations is that they can be expressed as systems of linear matrix inequalities, thus allowing them to be solved easily and efficiently by off-the-shelf optimization solvers. We also provide a numerical illustration of our constructions through a problem in control theory and a portfolio VaR (Value-at-Risk) optimization problem.
Detailed summary in vernacular field only.
Detailed summary in vernacular field only.
Wang, Kuncheng.
Thesis (Ph.D.)--Chinese University of Hong Kong, 2012.
Includes bibliographical references (leaves 94-101).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstract also in Chinese.
Abstract --- p.i
Acknowledgement --- p.vi
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Motivations and Philosophy --- p.1
Chapter 1.2 --- Background --- p.2
Chapter 1.3 --- Literature Review --- p.4
Chapter 1.4 --- Contribution --- p.7
Chapter 2 --- Preliminaries --- p.10
Chapter 2.1 --- Probabilistic Inequalities --- p.10
Chapter 2.2 --- Exact Proper Fractional Covers --- p.12
Chapter 2.2.1 --- Exact Proper Fractional Cover of Quadratic Perturbations --- p.15
Chapter 3 --- Large Deviations of Sums of Dependent Random Matrices --- p.18
Chapter 3.1 --- The Matrix Exponential Function and Its Properties --- p.18
Chapter 3.2 --- Main Theorem --- p.19
Chapter 4 --- From Large Deviations to ChanceConstrained LMIs --- p.26
Chapter 4.1 --- General Results --- p.26
Chapter 4.2 --- Application to ChanceConstrained Quadratically Perturbed Linear Matrix Inequalities --- p.30
Chapter 4.3 --- Bounding the Matrix Moment Generating Functions --- p.31
Chapter 4.4 --- Iterative Improvement of the Proposed Approximations --- p.42
Chapter 5 --- Computational Studies --- p.49
Chapter 5.1 --- Application to Control Problems --- p.49
Chapter 5.2 --- Application to Value-at-Risk Portfolio Optimization --- p.57
Chapter 6 --- ChanceConstrained LMIs with CVaR Risk Measure --- p.64
Chapter 6.1 --- Matrix CVaR Risk Measure --- p.65
Chapter 6.2 --- Some Useful Inequalities --- p.68
Chapter 6.3 --- From Matrix CVaR to ChanceConstrained LMIs --- p.69
Chapter 6.3.1 --- Bound π¹(A₀, · · · ,A[subscript m]) --- p.70
Chapter 6.3.2 --- Bound π²(A₀, · · · ,A[subscript m]) --- p.71
Chapter 6.3.3 --- Bound π³(A₀, · · · ,A[subscript m]) --- p.72
Chapter 6.3.4 --- Convex Approximation of π[superscript i](A0, · · · ,Am) --- p.73
Chapter 7 --- Extension to Polynomials Perturbations --- p.75
Chapter 7.1 --- Decoupling Theory --- p.75
Chapter 7.2 --- Safe Tractable Approximation by SecondOrder Cone Programming --- p.77
Chapter 8 --- Construct Uncertainty Set for Chance Constraints --- p.81
Chapter 8.1 --- Problem Statement --- p.82
Chapter 8.2 --- Fractional Cover for Quartic Perturbations --- p.83
Chapter 8.3 --- Probabilistic Guarantees --- p.85
Chapter 8.3.1 --- Probabilistic Bound Based on Large Deviations --- p.85
Chapter 8.4 --- The Value of Ω for Bounds --- p.88
Chapter 8.5 --- Computational Study --- p.89
Chapter 8.5.1 --- Independent Standard Normal Perturbations --- p.89
Chapter 8.5.2 --- Independent Bounded Quadratic Perturbations --- p.91
Chapter 9 --- Conclusion --- p.93
Bibliography --- p.94
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