Topic
Stochastic programming
About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: The proposed method is shown to outperform deterministic model predictive control in terms of average EV charging cost and an enhancement to the classical discrete stochastic dynamic programming method is proposed.
Abstract: This paper investigates the application of stochastic dynamic programming to the optimization of charging and frequency regulation capacity bids of an electric vehicle (EV) in a smart electric grid environment. We formulate a Markov decision problem to minimize an EV's expected cost over a fixed charging horizon. We account for both Markov random prices and a Markov random regulation signal. We also propose an enhancement to the classical discrete stochastic dynamic programming method. This enhancement allows optimization over a continuous space of decision variables via linear programming at each state. Simple stochastic process models are built from real data and used to simulate the implementation of the proposed method. The proposed method is shown to outperform deterministic model predictive control in terms of average EV charging cost.
141 citations
••
TL;DR: The stochastic MPC (SMPC) problem in the dual control paradigm is presented, where the control inputs to an uncertain system have a probing effect for active uncertainty learning and a directing effect for controlling the system dynamics.
141 citations
••
TL;DR: In this paper, the authors propose short-term decision-support models for aggregators that sell electricity to prosumers and buy back surplus electricity, where the aggregator can control flexible energy units at the prosumers.
141 citations
••
TL;DR: In this paper, a mixed-integer nonlinear stochastic programming model is proposed to hedge against the uncertainties in port operations, which include the uncertain wait time due to port congestion and uncertain container handling time.
Abstract: This paper examines the design of liner ship route schedules that can hedge against the uncertainties in port operations, which include the uncertain wait time due to port congestion and uncertain container handling time. The designed schedule is robust in that uncertainties in port operations and schedule recovery by fast steaming are captured endogenously. This problem is formulated as a mixed-integer nonlinear stochastic programming model. A solution algorithm which incorporates a sample average approximation method, linearization techniques, and a decomposition scheme, is proposed. Extensive numerical experiments demonstrate that the algorithm obtains near-optimal solutions with the stochastic optimality gap less 1.5% within reasonable time.
140 citations
••
TL;DR: In this paper, Monte Carlo sampling-based procedures for assessing solution quality in stochastic programs are developed. But the quality is defined via the optimality gap and the procedures' output is a confidence interval on this gap.
Abstract: Determining whether a solution is of high quality (optimal or near optimal) is fundamental in optimization theory and algorithms. In this paper, we develop Monte Carlo sampling-based procedures for assessing solution quality in stochastic programs. Quality is defined via the optimality gap and our procedures' output is a confidence interval on this gap. We review a multiple-replications procedure that requires solution of, say, 30 optimization problems and then, we present a result that justifies a computationally simplified single-replication procedure that only requires solving one optimization problem. Even though the single replication procedure is computationally significantly less demanding, the resulting confidence interval might have low coverage probability for small sample sizes for some problems. We provide variants of this procedure that require two replications instead of one and that perform better empirically. We present computational results for a newsvendor problem and for two-stage stochastic linear programs from the literature. We also discuss when the procedures perform well and when they fail, and we propose using ɛ-optimal solutions to strengthen the performance of our procedures.
140 citations