David L. Woodruff \(\) 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 the context of optimization under uncertainty, we consider various combinations of distribution estimation and resampling (bootstrap and bagging) for obtaining samples used to acquire a solution and for computing a confidence interval for an optimality gap. This paper makes three experimental contributions to on-going research in data driven stochastic programming: a) most of the … Read more
In this paper we describe software for stochastic programming that uses only sampled data to obtain both a consistent sample-average solution and a consistent estimate of confidence intervals for the optimality gap using bootstrap and bagging. The underlying distribution whence the samples come is not required. Article Download View Software for data-based stochastic programming using … Read more
When the uncertainty is explicitly modeled in an optimization problem, it is often necessary to use samples to compute a solution, which gives rise to a need to compute confidence intervals around the objective function value that is obtained. In this paper we describe software that implements well-known methods for two stage problems and we … 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 propose a decomposition algorithm for multistage stochastic programming that resembles the progressive hedging method of Rockafellar and Wets, but is provably capable of several forms of asynchronous operation. We derive the method from a class of projective operator splitting methods fairly recently proposed by Combettes and Eckstein, significantly expanding the known applications of those … Read more
Building on the work of Gendreau, Laporte, and Seguin (1996), we review the past 20 years of scientific literature on stochastic vehicle routing problems (SVRP). The numerous variants of the problem that have been studied in the literature are described and categorized. Also a thorough review of solution methods applied to the SVRP is included … Read more
We present a method for computing lower bounds in the Progressive Hedging Algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using … Read more
Unit commitment decisions made in the day-ahead market and during subsequent reliability assessments are critically based on forecasts of load. Traditional, deterministic unit commitment is based on point or expectation-based load forecasts. In contrast, stochastic unit commitment relies on multiple load scenarios, with associated probabilities, that in aggregate capture the range of likely load time-series. … Read more
In this second portion of a two-part analysis of a scalable computational approach to stochastic unit commitment, we focus on solving stochastic mixed-integer programs in tractable run-times. Our solution technique is based on Rockafellar and Wets’ progressive hedging algorithm, a scenario-based decomposition strategy for solving stochastic programs. To achieve high-quality solutions in tractable run-times, we … Read more