Download or read book Online Stochastic Combinatorial Optimization written by Pascal Van Hentenryck and published by MIT Press (MA). This book was released on 2006 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: A framework for online decision making under uncertainty and time constraints, with online stochastic algorithms for implementing the framework, performance guarantees, and demonstrations of a variety of applications.

Download or read book Online Stochastic Combinatorial Optimization written by Hentenryck & Bent and published by . This book was released on 2006 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Optimization written by Stanislav Uryasev and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic programming is the study of procedures for decision making under the presence of uncertainties and risks. Stochastic programming approaches have been successfully used in a number of areas such as energy and production planning, telecommunications, and transportation. Recently, the practical experience gained in stochastic programming has been expanded to a much larger spectrum of applications including financial modeling, risk management, and probabilistic risk analysis. Major topics in this volume include: (1) advances in theory and implementation of stochastic programming algorithms; (2) sensitivity analysis of stochastic systems; (3) stochastic programming applications and other related topics. Audience: Researchers and academies working in optimization, computer modeling, operations research and financial engineering. The book is appropriate as supplementary reading in courses on optimization and financial engineering.

Download or read book Combining Benders and Dantzig Wolfe Decompositions for Online Stochastic Combinatorial Optimization written by Antoine Legrain and published by . This book was released on 2016 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Local Search Algorithms for Multiobjective Combinatorial Optimization written by Luis F. Paquete and published by IOS Press. This book was released on 2006 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Local Search algorithms were shown to give state-of-the-art results for many other problems, but little is known on how to design and analyse them for Multiobjective Combinatorial Optimization Problems. This book aims to fill this gap. It defines two search models that correspond to two distinct ways of tackling MCOPs by SLS algorithms."

Download or read book Stochastic Combinatorial Optimization written by Jianqiang Cheng and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we studied three types of stochastic problems: chance constrained problems, distributionally robust problems as well as the simple recourse problems. For the stochastic programming problems, there are two main difficulties. One is that feasible sets of stochastic problems is not convex in general. The other main challenge arises from the need to calculate conditional expectation or probability both of which are involving multi-dimensional integrations. Due to the two major difficulties, for all three studied problems, we solved them with approximation approaches.We first study two types of chance constrained problems: linear program with joint chance constraints problem (LPPC) as well as maximum probability problem (MPP). For both problems, we assume that the random matrix is normally distributed and its vector rows are independent. We first dealt with LPPC which is generally not convex. We approximate it with two second-order cone programming (SOCP) problems. Furthermore under mild conditions, the optimal values of the two SOCP problems are a lower and upper bounds of the original problem respectively. For the second problem, we studied a variant of stochastic resource constrained shortest path problem (called SRCSP for short), which is to maximize probability of resource constraints. To solve the problem, we proposed to use a branch-and-bound framework to come up with the optimal solution. As its corresponding linear relaxation is generally not convex, we give a convex approximation. Finally, numerical tests on the random instances were conducted for both problems. With respect to LPPC, the numerical results showed that the approach we proposed outperforms Bonferroni and Jagannathan approximations. While for the MPP, the numerical results on generated instances substantiated that the convex approximation outperforms the individual approximation method.Then we study a distributionally robust stochastic quadratic knapsack problems, where we only know part of information about the random variables, such as its first and second moments. We proved that the single knapsack problem (SKP) is a semedefinite problem (SDP) after applying the SDP relaxation scheme to the binary constraints. Despite the fact that it is not the case for the multidimensional knapsack problem (MKP), two good approximations of the relaxed version of the problem are provided which obtain upper and lower bounds that appear numerically close to each other for a range of problem instances. Our numerical experiments also indicated that our proposed lower bounding approximation outperforms the approximations that are based on Bonferroni's inequality and the work by Zymler et al.. Besides, an extensive set of experiments were conducted to illustrate how the conservativeness of the robust solutions does pay off in terms of ensuring the chance constraint is satisfied (or nearly satisfied) under a wide range of distribution fluctuations. Moreover, our approach can be applied to a large number of stochastic optimization problems with binary variables.Finally, a stochastic version of the shortest path problem is studied. We proved that in some cases the stochastic shortest path problem can be greatly simplified by reformulating it as the classic shortest path problem, which can be solved in polynomial time. To solve the general problem, we proposed to use a branch-and-bound framework to search the set of feasible paths. Lower bounds are obtained by solving the corresponding linear relaxation which in turn is done using a Stochastic Projected Gradient algorithm involving an active set method. Meanwhile, numerical examples were conducted to illustrate the effectiveness of the obtained algorithm. Concerning the resolution of the continuous relaxation, our Stochastic Projected Gradient algorithm clearly outperforms Matlab optimization toolbox on large graphs.

Download or read book Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems written by Laurent Perron and published by Springer Science & Business Media. This book was released on 2008-05-08 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 5th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, CPAIOR 2008, held in Paris, France, in May 2008. The 18 revised long papers and 22 revised short papers presented together with 3 invited talks were carefully reviewed and selected from 130 submissions. The papers describe current research in the fields of constraint programming, artificial intelligence, and operations research to explore ways of solving large-scale, practical optimization problems through integration and hybridization of the fields' different techniques.

Download or read book Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems written by J. Christopher Beck and published by Springer Science & Business Media. This book was released on 2006-05-16 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, CPAIOR 2006, held in Cork, Ireland in May/June 2006. The 20 revised full papers presented together with 3 invited talks were carefully reviewed and selected from 67 submissions. The papers address methodological and foundational issues from AI, OR, and algorithmics and present applications to the solution of combinatorial optimization problems in various fields via constraint programming.

Download or read book Hybrid Offline Online Methods for Optimization Under Uncertainty written by A. De Filippo and published by IOS Press. This book was released on 2022-04-12 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Balancing the solution-quality/time trade-off and optimizing problems which feature offline and online phases can deliver significant improvements in efficiency and budget control. Offline/online integration yields benefits by achieving high quality solutions while reducing online computation time. This book considers multi-stage optimization problems under uncertainty and proposes various methods that have broad applicability. Due to the complexity of the task, the most popular approaches depend on the temporal granularity of the decisions to be made and are, in general, sampling-based methods and heuristics. Long-term strategic decisions that may have a major impact are typically solved using these more accurate, but expensive, sampling-based approaches. Short-term operational decisions often need to be made over multiple steps within a short time frame and are commonly addressed via polynomial-time heuristics, with the more advanced sampling-based methods only being applicable if their computational cost can be carefully managed. Despite being strongly interconnected, these 2 phases are typically solved in isolation. In the first part of the book, general methods based on a tighter integration between the two phases are proposed and their applicability explored, and these may lead to significant improvements. The second part of the book focuses on how to manage the cost/quality trade-off of online stochastic anticipatory algorithms, taking advantage of some offline information. All the methods proposed here provide multiple options to balance the quality/time trade-off in optimization problems that involve offline and online phases, and are suitable for a variety of practical application scenarios.

Download or read book Coping with Incomplete Information in Scheduling Stochastic and Online Models written by Nicole Megow and published by Cuvillier Verlag. This book was released on 2007-05-23 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Incomplete information is an omnipresent issue when dealing with real-world optimization problems. Typically, such limitations concern the uncertainty of given data or the complete lack of knowledge about future parts of a problem instance. This thesis is devoted to investigations on how to cope with incomplete information when solving scheduling problems. These problems involve the temporal allocation of limited resources for executing activities so as to optimize some objective. Scheduling problems are apparent in many applications including, for example, manufacturing and service industries but also compiler optimization and parallel computing. There are two major frameworks for modeling limited information in the theory of optimization. One deals with "stochastic information", the other with "online information". We design algorithms for NP-hard scheduling problems in both, the online and the stochastic scheduling models. Thereby, we provide first constant performance guarantees orimprove previously best known results. Both frameworks have their legitimacy depending on the actual application. Nevertheless, problem settings are conceivable that comprise both, uncertain information about the data set and the complete lack of knowledge about the future. This rouses the need for a generalized model that integrates both traditional information environments. Such a general model is designed as a natural extension that combines stochastic and online information. But the challenging question is whether there exists any algorithm that can perform well in such a restricted information environment. More precisely, is there an algorithm that yields a constant performance guarantee? We successfully treat this intriguing question and give a positive answer by providing such algorithms for machine scheduling problems. In fact, our results are competitive with the performance guarantees best known in the traditional settings of stochastic and online scheduling. Thus, they do not only justify the generalized model but also imply - at least in the considered problem settings - that optimization in the general model with incomplete information does not necessarily mean to give up performance.

Download or read book Stochastic Algorithms for Combinatorial Optimization written by Sifuei Ku and published by . This book was released on 1987 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Local Search Algorithms for Multiobjective Combinatorial Optimization written by Luís F. Paquete and published by . This book was released on 2006 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Boosting Stochastic Problem Solvers Through Online Self analysis of Performance written by Vincent A. Cicirello and published by . This book was released on 2003 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "In many combinatorial domains, simple stochastic algorithms often exhibit superior performance when compared to highly customized approaches. Many of these simple algorithms outperform more sophisticated approaches on difficult benchmark problems; and often lead to better solutions as the algorithms are taken out of the world of benchmarks and into the real-world. Simple stochastic algorithms are often robust, scalable problem solvers. This thesis explores methods for combining sets of heuristics within a single stochastic search. The ability of stochastic search to amplify heuristics is often a key factor in its success. Heuristics are not, however, infallible and in most domains no single heuristic dominates. It is therefore desirable to gain the collective power of a set of heuristics; and to design a search control framework capable of producing a hybrid algorithm from component heuristics with the ability to customize itself to a given problem instance. A primary goal is to explore what can be learned from quality distributions of iterative stochastic search in combinatorial optimization domains; and to exploit models of quality distributions to enhance the performance of stochastic problem solvers. We hypothesize that models of solution quality can lead to effective search control mechanisms, providing a general framework for combining multiple heuristics into an enhanced decision-making process. These goals lead to the development of a search control framework, called QD-BEACON, that uses online-generated statistical models of search performance to effectively combine search heuristics. A prerequisite goal is to develop a suitable stochastic sampling algorithm for combinatorial search problems. This goal leads to the development of an algorithm called VBSS that makes better use, in general, of the discriminatory power of a given search heuristic as compared to existing sampling approaches. The search frameworks of this thesis are evaluated on combinatorial optimization problems. Specifically, we show that: 1) VBSS is an effective method for amplifying heuristic performance for the weighted tardiness sequencing problem with sequence-dependent setups; 2) QD-BEACON can enhance the current best known algorithm for weighted tardiness sequencing; and 3) QD-BEACON and VBSS together provide the new best heuristic algorithm for the constrained optimization problem known as RCPSP/max."

Download or read book Approximation Techniques for Stochastic Combinatorial Optimization Problems written by Ravishankar Krishnaswamy and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Designing Reinforcement Learning Models for Combinatorial Optimization Problems written by Tao Li and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving combinatorial optimization problems, especially stochastic problems, could be complicated. Reinforcement learning (RL) algorithms train a machine learning model to make a sequence of decisions. Instead of learning the direct rewards, it learns the long-term effects on the actions based on the states and policy; such a method could efficiently solve stochastic combinatorial optimization problems. Thus using RL to learn the stochastic environment and solve the combinatorial optimization problems with randomness could have better performance than using operation research (OR) methods and heuristic algorithms directly. Thus we design RL structures to solve typical combinatorial optimization problems such as vehicle routing problem, job shop scheduling problem, and online knapsack problem; and compare the performance with the OR methods.RL algorithms have even more advantages on solving some specific stochastic combinatorial optimization problems. Assuming we are facing stochastic problems whose random parameters are related to some features. These kind of problems can be applied on a lot of situations in real life. For example, the ice cream factory distribute their products to the shops, and the demands of the customers are highly related to the features such as temperature and humidity. In operation research (OR), we can predict the random parameters based on the historical data, and then solve the problem as a discrete scenarios stochastic problem. However, the prediction error could lead us to an expensive cost policy. Thus we use the RL model, which can extract the information in the feature and learn the approach based on that. In this way, we can skip the prediction and learn the relationship between the policy and features directly to reach a better performance than the OR method.

Download or read book Stochastic Combinatorial Optimization with Applications in Graph Covering written by Hao-Hsiang Wu and published by . This book was released on 2018 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study stochastic combinatorial optimization models and propose methods for their solution. First, we consider a risk-neutral two-stage stochastic programming model for which the objective value function of the second-stage subproblems is submodular. Next, we consider risk-averse combinatorial optimization problems, where in one variant, the risk is measured with a chance constraint, and in another variant, conditional value-at-risk is used to quantify risk. We demonstrate the proposed models and methods on various graph covering problems. We provide our research scope and a review of fundamental models in Chapter 1. In Chapter 2, we introduce a new class of problems that we refer to as two-stage stochastic submodular optimization models. We propose a delayed constraint generation algorithm to find the optimal solution to this class of problems with a finite number of samples. We apply the generic model and method to stochastic influence maximization problems arising in social networks. Consider a covering problem on a random graph, where there is uncertainty on whether an arc appears in the graph. The problem aims to find a subset of nodes that reaches the largest expected number of nodes in the graph. In contrast to existing studies that involve greedy approximation algorithms with a 63% performance guarantee, our work focuses on solving the problem optimally. We show that the submodularity of the influence function can be exploited to develop strong optimality cuts that are more effective than the standard optimality cuts available in the literature. We report our computational experiments with large-scale real-world datasets for two fundamental influence maximization problems, independent cascade and linear threshold, and show that our proposed algorithm outperforms the basic greedy algorithm of Kempe et al. (2003). In Chapter 3, we investigate a class of chance-constrained combinatorial optimization problems. The chance-constrained program aims to find the minimum cost selection of a vector of binary decisions such that a desirable event occurs with a high probability. For a given decision, we assume that we have an oracle that computes the probability of a desirable event exactly. Using this oracle, we propose an exact general method for solving the chance-constrained problem. Furthermore, we show that if the chance-constrained program is solved approximately by a sampling-based approach, then the oracle can be used as a tool for checking and fixing the feasibility of the optimal solution given by this approach. We demonstrate the effectiveness of our proposed methods on a probabilistic partial set covering problem (PPSC). We give a compact mixed-integer program that solves PPSC optimally (without sampling) for a special case. For large-scale instances for which the exact methods exhibit slow convergence, we propose a sampling-based approach that exploits the submodular structure of PPSC. In particular, we introduce a new class of facet-defining inequalities for a submodular substructure of PPSC and show that a sampling-based algorithm coupled with the probability oracle solves the large-scale test instances effectively. In Chapter 4, we study a class of risk-averse submodular maximization problems that optimizes the conditional value-at-risk (CVaR) of a random objective function at a given risk level, where the random objective function is defined as a nondecreasing submodular set function. We assume that we have an oracle that computes the CVaR of the random objective function exactly. Using this oracle, we propose an exact general method for solving this problem. Furthermore, we show that the problem can be solved approximately by a sampling-based approach. We demonstrate the proposed methods on a variant of stochastic set covering problem.

Download or read book Nonlinear Combinatorial Optimization written by Ding-Zhu Du and published by Springer. This book was released on 2019-05-31 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate students and researchers in applied mathematics, optimization, engineering, computer science, and management science will find this book a useful reference which provides an introduction to applications and fundamental theories in nonlinear combinatorial optimization. Nonlinear combinatorial optimization is a new research area within combinatorial optimization and includes numerous applications to technological developments, such as wireless communication, cloud computing, data science, and social networks. Theoretical developments including discrete Newton methods, primal-dual methods with convex relaxation, submodular optimization, discrete DC program, along with several applications are discussed and explored in this book through articles by leading experts.