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Operations Research an Introduction

01 Jan 2007-
TL;DR: This chapter discusses Deterministic Dynamic Programming, a model for nonlinear programming, and nonlinear Programming Algorithms, a system for solving linear programming problems.
Abstract: 1. Overview of Operations Research. I. DETERMINISTIC MODELS. 2. Introduction to Linear Programming. 3. The Simplex Method. 4. Duality and Sensitivity Analysis. 5. Transportation Model and Its Variants. 6. Network Models. 7. Advanced Linear Programming. 8. Goal Programming. 9. Integer Linear Programming. 10. Deterministic Dynamic Programming. 11. Deterministic Inventory Models. II. PROBABILISTIC MODELS. 12. Review of Basic Probability. 13. Forecasting Models. 14. Decision Analysis and Games. 15. Probabilistic Dynamic Programming. 16. Probabilistic Inventory Models. 17. Queueing Systems. 18. Simulation Modeling. 19. Markovian Decision Process. III. NONLINEAR MODELS. 20. Classical Optimization Theory. 21. Nonlinear Programming Algorithms. Appendix A: Review of Matrix Algebra. Appendix B: Introduction to Simnet II. Appendix C: Tora and Simnet II Installation and Execution. Appendix D: Statistical Tables. Appendix E: Answers to Odd-Numbered Problems. Index.
Citations
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Journal Article
TL;DR: This work categorize and analyze two approaches of Safe Reinforcement Learning, based on the modification of the optimality criterion, the classic discounted finite/infinite horizon, with a safety factor and the incorporation of external knowledge or the guidance of a risk metric.
Abstract: Safe Reinforcement Learning can be defined as the process of learning policies that maximize the expectation of the return in problems in which it is important to ensure reasonable system performance and/or respect safety constraints during the learning and/or deployment processes. We categorize and analyze two approaches of Safe Reinforcement Learning. The first is based on the modification of the optimality criterion, the classic discounted finite/infinite horizon, with a safety factor. The second is based on the modification of the exploration process through the incorporation of external knowledge or the guidance of a risk metric. We use the proposed classification to survey the existing literature, as well as suggesting future directions for Safe Reinforcement Learning.

1,124 citations


Cites background from "Operations Research an Introduction..."

  • ...This criterion is also known in the literature as variancepenalized criterion (Gosavi, 2009), expected value-variance criterion (Taha, 1992; Heger, 1994b) and expected-value-minus-variance-criterion (Geibel and Wysotzki, 2005)....

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Journal ArticleDOI
TL;DR: It is demonstrated that this fails in general to solve the ‘label switching’ problem, and an alternative class of approaches, relabelling algorithms, which arise from attempting to minimize the posterior expected loss under a class of loss functions are described.
Abstract: Summary. In a Bayesian analysis of finite mixture models, parameter estimation and clustering are sometimes less straightforward than might be expected. In particular, the common practice of estimating parameters by their posterior mean, and summarizing joint posterior distributions by marginal distributions, often leads to nonsensical answers. This is due to the so-called 'label switching' problem, which is caused by symmetry in the likelihood of the model parameters. A frequent response to this problem is to remove the symmetry by using artificial identifiability constraints. We demonstrate that this fails in general to solve the problem, and we describe an alternative class of approaches, relabelling algorithms, which arise from attempting to minimize the posterior expected loss under a class of loss functions. We describe in detail one particularly simple and general relabelling algorithm and illustrate its success in dealing with the label switching problem on two examples.

1,060 citations

Journal ArticleDOI
TL;DR: In this paper, a mixed integer non-linear programming model is presented to solve the multiple sourcing problem, which takes into account the total cost of logistics, including net price, storage, transportation and ordering costs.

641 citations

Proceedings ArticleDOI
01 Jan 2001
TL;DR: A new approach to fuel-optimal path planning of multiple vehicles using a combination of linear and integer programming and the framework of mixed integer/linear programming is well suited for path planning and collision avoidance problems.
Abstract: This paper presents a new approach to fuel-optimal path planning of multiple vehicles using a combination of linear and integer programming. The basic problem formulation is to have the vehicles move from an initial dynamic state to a final state without colliding with each other, while at the same time avoiding other stationary and moving obstacles. It is shown that this problem can be rewritten as a linear program with mixed integer/linear constraints that account for the collision avoidance. A key benefit of this approach is that the path optimization can be readily solved using the CPLEX optimization software with an AMPL/Matlab interface. An example is worked out to show that the framework of mixed integer/linear programming is well suited for path planning and collision avoidance problems. Implementation issues are also considered. In particular, we compare receding horizon strategies with fixed arrival time approaches.

566 citations

Proceedings ArticleDOI
13 Jun 2005
TL;DR: This work presents the context-aware routing (CAR) algorithm, a novel approach to the provision of asynchronous communication in partially-connected mobile ad hoc networks, based on the intelligent placement of messages.
Abstract: The vast majority of mobile ad hoc networking research makes a very large assumption - that communication can only take place between nodes that are simultaneously accessible within the same connected cloud (i.e., that communication is synchronous). In reality, this assumption is likely to be a poor one, particularly for sparsely or irregularly populated environments. We present the context-aware routing (CAR) algorithm. CAR is a novel approach to the provision of asynchronous communication in partially-connected mobile ad hoc networks, based on the intelligent placement of messages. We discuss the details of the algorithm, and then present simulation results demonstrating that it is possible for nodes to exploit context information in making local decisions that lead to good delivery ratios and latencies with small overheads.

436 citations