The Similarity Index to Decompose Two-Stage Stochastic Scheduling Problems

作     者：Daniel Montes José Luis Pitarch Cesar de Prada 

作者机构：Department of Systems Engineering and Automatic Control Universidad de Valladolid Spain Instituto U. de Automática e Informática Industrial (ai2) Universitat Politècnica de Valencia Spain Institute of Sustainable Processes Universidad de Valladolid Spain 

出 版 物：《IFAC-PapersOnLine》 

年 卷 期：2022年第55卷第7期

页      面：821-826页

主　　题：Decomposition Online Scheduling Uncertainty Mixed-Integer Optimization 

摘      要：Two-stage stochastic scheduling problems often involve a large number of continuous and discrete variables, so fnding solutions in short time periods is challenging and computationally expensive. However, for online or closed-loop scheduling implementations, optimal or near-optimal solutions are required in real-time. We propose a decomposition method based on the so-called Similarity Index (SI). An iterative procedure is set up so that each sub-problem (corresponding to a scenario) is solved independently, aiming to optimize the original cost function while maximizing the similarity of the frst-stage variables among the scenarios solutions. The SI is incorporated into each subproblem cost function, multiplied by a penalty parameter that is updated in each iteration until reaching complete similarity in the frst-stage variables among all subproblems. The method is applied to schedule production and maintenance tasks in an evaporation network. The tests show that signifcant benefts are expected in terms of computational demands as the number of scenarios increases.