CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Optimal Placement of Add/Drop Multiplexers: Heuristic and Exact Algorithms
Operations Research
Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems
INFORMS Journal on Computing
Improving Discrete Model Representations via Symmetry Considerations
Management Science
Uncertain convex programs: randomized solutions and confidence levels
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Computers and Operations Research
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
A Sample Approximation Approach for Optimization with Probabilistic Constraints
SIAM Journal on Optimization
Planning and Scheduling by Logic-Based Benders Decomposition
Operations Research
Symmetry and search in a network design problem
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
The integer L-shaped method for stochastic integer programs with complete recourse
Operations Research Letters
Dual decomposition in stochastic integer programming
Operations Research Letters
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We consider the edge-partition problem, which is a graph theoretic problem arising in the design of Synchronous Optical Networks. The deterministic edge-partition problem considers an undirected graph with weighted edges, and simultaneously assigns nodes and edges to subgraphs such that each edge appears in exactly one subgraph, and such that no edge is assigned to a subgraph unless both of its incident nodes are also assigned to that subgraph. Additionally, there are limitations on the number of nodes and on the sum of edge weights that can be assigned to each subgraph. In this paper, we consider a stochastic version of the edge-partition problem in which we assign nodes to subgraphs in a first stage, realize a set of edge weights from a finite set of alternatives, and then assign edges to subgraphs. We first prescribe a two-stage cutting plane approach with integer variables in both stages, and examine computational difficulties associated with the proposed cutting planes. As an alternative, we prescribe a hybrid integer programming/constraint programming algorithm capable of solving a suite of test instances within practical computational limits.