Progressive hedging-based metaheuristics for stochastic network design

  • Authors:

  • Teodor Gabriel Crainic;Xiaorui Fu;Michel Gendreau;Walter Rei;Stein W. Wallace

  • Affiliations:

  • Département de management et technologie, École des sciences de la gestion, Université du Québec à Montréal, Montréal, Canada and Interuniversity R ...;Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), Québec, Canada\' and Département d'informatique et de recherche opérationnelle, ...;Département de management et technologie, École des sciences de la gestion, Université du Québec à Montréal, Montréal, Canada and Interuniversity R ...;Département de management et technologie, École des sciences de la gestion, Université du Québec à Montréal, Montréal, Canada and Interuniversity R ...;Department of Management Science, Management School, Lancaster University, Lancaster, United Kingdom

  • Venue:
  • Networks
  • Year:
  • 2011

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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. © 2011 Wiley Periodicals, Inc.