A multicut algorithm for two-stage stochastic linear programs

Abstract

Outer linearization methods, such as Van Slyke and Wets's L-shaped method for stochastic linear programs, generally apply a single cut on the nonlinear objective at each major iteration. The structure of stochastic programs allows for several cuts to be placed at once. This paper describes a multicut algorithm to carry out this procedure. It presents experimental and theoretical justification for reductions in major iterations.

A stochastic integer programming approach to solving a synchronous optical network ring design problem

“…Works by Birge and Louveaux (1988) and Gassmann (1990) conduct experiments on stochastic linear programs, suggesting that the multicut approach is usually preferable when the number of realizations |Ξ| is not significantly larger than the number of first-stage constraints. We are unaware of similar experiments on stochastic programs with first-stage integer variables.…”

An enhanced decomposition algorithm for multistage stochastic hydroelectric scheduling

“…In selecting an advanced start procedure, one must balance the computational benefit that the preliminary cuts yield with the cost of generating the cuts. Birge and Louveaux [4] introduced the multicut L-shaped algorithm for SLP-2 (1 Figure 2 for three strategies on test problem Moke4.45. Note (i) the faster convergence of the multicut algorithm, (ii) the additional computational effort but improved initial relative error of the advanced start procedure, and (iii) the effect of the warm start on the time per iteration as the algorithm proceeds.…”

“…We also described a streamlined advanced start procedure that generates preliminary cuts to help guide the early iterations of the decomposition algorithm; this enhancement provided additional speedup over naive implementations. We found the multicut method due to Birge and Louveaux [4] also yielded computational savings over its single cut counterpart. Consistent with earlier findings of Abrahamson [1] and Wittrock [15] (in the deterministic case) and Gassmann [7] (in the stochastic case) we found that the fastpass tree traversing strategy performed well.…”

Augmented Markov Chain Monte Carlo Simulation for Two-Stage Stochastic Programs with Recourse

“…The scalar variable provides an outer approximation to the expected recourse function, and the cuts represent the second-stage constraints in terms of first-stage decision variable. A variant is the multicut L-shaped algorithm of Birge and Louveaux (1988).…”