Scalable Heuristics for a Class of Chance-Constrained Stochastic Programs

We describe computational procedures for solving a wide-ranging class of stochastic programs with chance constraints where the random components of the problem are discretely distributed. Our procedures are based on a combination of Lagrangian relaxation and scenario decomposition, which we solve using a novel variant of Rockafellar and Wets' progressive hedging algorithm [Rockafellar, R. T., R. J.-B. Wets. 1991. Scenarios and policy aggregation in optimization under uncertainty. Math. Oper. Res.16(1) 119–147]. Experiments demonstrate the ability of the proposed algorithm to quickly find near-optimal solutions—where verifiable—to both difficult and very large chance-constrained stochastic programs, both with and without integer decision variables. The algorithm exhibits strong scalability in terms of both run time required and final solution quality on large-scale instances.

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