This paper presents a novel decomposition method for two-stage stochastic mixed-integer optimization problems. The algorithm builds upon the idea of similarity between finite sample sets to measure how similar the first-stage decisions are among the uncertainty realization scenarios. Using such a Similarity Index, the non-anticipative constraints are removed from the problem formulation so that the … Read more
\(\) Watson and Woodruff (2011) developed a heuristic for computing variable-dependent values of the penalty parameter $\rho$ from the model itself. We combine this heuristic with a gradient-based method, in order to obtain a new method for calculating $\rho$ values. We then introduce a method for iteratively computing variable-dependent $\rho$ values. This method is based … Read more
In transportation problems and in many other planning problems, there are important sources of uncertainty that must be addressed to find effective and efficient solutions. A common approach for solving these dynamic and stochastic problems is the Multiple Scenario Approach (MSA), that has been proved effective for transportation problems, but it does not provide flexibility … Read more
Efficient solution of stochastic programming problems generally requires the use of parallel computing resources. Here, we describe the open source package mpi-sppy, in which efficient and scalable parallelization is a central feature. We describe the overall architecture and provide computational examples and results showing scalability to the largest instances that we know of for the … Read more
We develop a stochastic optimization model for scheduling a hybrid solar-battery storage system. Solar power in excess of the promise can be used to charge the battery, while power short of the promise is met by discharging the battery. We ensure reliable operations by using a joint chance constraint. Models with a few hundred scenarios … Read more
We present a new primal-dual algorithm for computing the value of the Lagrangian dual of a stochastic mixed-integer program (SMIP) formed by relaxing its nonanticipativity constraints. The algorithm relies on the well-known progressive hedging method, but unlike previous progressive hedging approaches for SMIP, our algorithm can be shown to converge to the optimal Lagrangian dual … Read more
In this paper, we propose a new approach to reduce the total running time (RT) of the progressive hedging algorithm (PHA) for solving multistage stochastic programs (MSPs) defined on a scenario tree. Instead of using the conventional scenario decomposition scheme, we apply a multi-scenario decomposition scheme and partition the scenario set in order to minimize … Read more