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Stochastic programming

About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.


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TL;DR: A multistage, stochastic, mixed-integer programming model for planning capacity expansion of production facilities, and applies “variable splitting” to two model variants, and solves those variants using Dantzig-Wolfe decomposition.
Abstract: We describe a multistage, stochastic, mixed-integer programming model for planning capacity expansion of production facilities. A scenario tree represents uncertainty in the model; a general mixed-integer program defines the operational submodel at each scenario-tree node, and capacity-expansion decisions link the stages. We apply “variable splitting” to two model variants, and solve those variants using Dantzig-Wolfe decomposition. The Dantzig-Wolfe master problem can have a much stronger linear programming relaxation than is possible without variable splitting, over 700% stronger in one case. The master problem solves easily and tends to yield integer solutions, obviating the need for a full branch-and-price solution procedure. For each scenario-tree node, the decomposition defines a subproblem that may be viewed as a single-period, deterministic, capacity-planning problem. An effective solution procedure results as long as the subproblems solve efficiently, and the procedure incorporates a good “duals stabilization method.” We present computational results for a model to plan the capacity expansion of an electricity distribution network in New Zealand, given uncertain future demand. The largest problem we solve to optimality has six stages and 243 scenarios, and corresponds to a deterministic equivalent with a quarter of a million binary variables.

112 citations

Journal ArticleDOI
TL;DR: In this paper, a scenario aggregation-based approach is proposed to solve the problem of dynamic capacity allocation in a fleet composition problem. But the authors focus on the stochastic nature of passenger demand in the fleet composition.
Abstract: Recently, airlines and aircraft manufacturers have realized the benefits of the emerging concept of dynamic capacity allocation, and have initiated advanced decision support systems to assist them in this respect. Strategic airline fleet planning is one of the major issues addressed through such systems. We present background research connected with the dynamic allocation concept, which accounts explicitly for the stochastic nature of passenger demand in the fleet composition problem. We address this problem through a scenario aggregation-based approach and present results on representative case studies based on realistic data. Our investigations establish clear benefits of a stochastic approach as compared with deterministic formulations, as well as its implementation feasibility using state-of-the-art optimization software.

112 citations

Journal ArticleDOI
TL;DR: This paper proposed a network optimization model for hotel revenue management under an uncertain environment in a stochastic programming formulation so as to capture the randomness of the unknown demand and showed that the model can be modified to adopt these strategic considerations.

112 citations

Journal ArticleDOI
TL;DR: This work applies a mathematical programming technique called stochastic dynamic programming, which determines optimal management decisions for every possible management trajectory, to manage the translocation of the bridled nailtail wallaby from Queensland, Australia.
Abstract: Active adaptive management (AAM) is an approach to wildlife management that acknowledges our imperfect understanding of natural systems and allows for some resolution of our uncertainty. Such learning may be characterized by risky strategies in the short term. Experimentation is only considered acceptable if it is expected to be repaid by increased returns in the long term, generated by an improved understanding of the system. By setting AAM problems within a decision theory framework, we can find this optimal balance between achieving our objectives in the short term and learning for the long term. We apply this approach to managing the translocation of the bridled nailtail wallaby (Onychogalea fraenata), an endangered species from Queensland, Australia. Our task is to allocate captive-bred animals, between two sites or populations to maximize abundance at the end of the translocation project. One population, at the original site of occupancy, has a known growth rate. A population potentially could be established at a second site of suitable habitat, but we can only learn the growth rate of this new population by monitoring translocated animals. We use a mathematical programming technique called stochastic dynamic programming, which determines optimal management decisions for every possible management trajectory. We find optimal strategies under active and passive adaptive management, which enables us to examine the balance between learning and managing directly. Learning is more often optimal when we have less prior information about the uncertain population growth rate at the new site, when the growth rate at the original site is low, and when there is substantial time remaining in the translocation project. Few studies outside the area of optimal harvesting have framed AAM within a decision theory context. This is the first application to threatened species translocation.

112 citations

Journal ArticleDOI
TL;DR: A design technique based on a self-adaptive DE (SADE) algorithm is applied to real-valued antenna and microwave design problems, showing the advantages of the SADE strategy and the DE in general.
Abstract: Particle swarm optimization (PSO) is an evolutionary algorithm based on the bird fly. Differential evolution (DE) is a vector population based stochastic optimization method. The fact that both algorithms can handle efficiently arbitrary optimization problems has made them popular for solving problems in electromagnetics. In this paper, we apply a design technique based on a self-adaptive DE (SADE) algorithm to real-valued antenna and microwave design problems. These include linear-array synthesis, patch-antenna design and microstrip filter design. The number of unknowns for the design problems varies from 6 to 60. We compare the self-adaptive DE strategy with popular PSO and DE variants. We evaluate the algorithms' performance regarding statistical results and convergence speed. The results obtained for different problems show that the DE algorithms outperform the PSO variants in terms of finding best optima. Thus, our results show the advantages of the SADE strategy and the DE in general. However, these results are considered to be indicative and do not generally apply to all optimization problems in electromagnetics.

111 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023175
2022423
2021526
2020598
2019578
2018532