Networks · 2011 · 138 citations · 17 references
Natural SciencesIndustrial EngineeringOperations ManagementCapacity PlanningDesign OptimizationOptimizationCombinatorial OptimizationHeuristic OptimizationMetaheuristic OptimizationOptimization Under UncertaintyStochastic OptimizationStochastic ProgrammingMetaheuristic SearchMulti-commodity Flow ProblemMulti-stage Stochastic ProgrammingMultistage Stochastic OptimizationProgressive HedgingScenario-based OptimizationStochastic Network OptimizationStochastic Programming Decomposition
The stochastic fixed‑charge capacitated multicommodity network design problem addresses uncertain demand in network design. The authors seek to minimize the combined cost of first‑stage design decisions and expected second‑stage distribution costs. They employ a progressive‑hedging inspired metaheuristic that decomposes scenarios into deterministic CMND subproblems, solves them with specialized methods, and iteratively aligns design arcs through guided strategies. Numerical experiments show the parallel method is computationally efficient and yields high‑quality solutions across various problem sizes and demand correlations. © 2011 Wiley Periodicals, Inc., NETWORKS, 2011.
Abstract We consider the stochastic fixed‐charge capacitated multicommodity network design (S‐CMND) problem with uncertain demand. We propose a two‐stage stochastic programming formulation, where design decisions make up the first stage, while recourse decisions are made in the second stage to distribute the commodities according to observed demands. The overall objective is to optimize the cost of the first‐stage design decisions plus the total expected distribution cost incurred in the second stage. To solve this formulation, we propose a metaheuristic framework inspired by the progressive hedging algorithm of Rockafellar and Wets. Following this strategy, scenario decomposition is used to separate the stochastic problem following the possible outcomes, scenarios, of the random event. Each scenario subproblem then becomes a deterministic CMND problem to be solved, which may be addressed by efficient specialized methods. We also propose and compare different strategies to gradually guide scenario subproblems to agree on the status of design arcs and aim for a good global design. These strategies are embedded into a parallel solution method, which is numerically shown to be computationally efficient and to yield high‐quality solutions under various problem characteristics and demand correlations. © 2011 Wiley Periodicals, Inc. NETWORKS, 2011.
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Introduction to Stochastic Programming
J M Wilson · Journal of the Operational Research Society · 1998 · 1.7K citations