Generating cluster submodels from two-stage stochastic mixed integer optimization models

Stochastic optimization problems of practical applications lead, in general, to some large models. The size of those models is linked to the number of scenarios that defines the scenario tree. This number of scenarios can be so large that decomposition strategies are required for problem solving in reasonable computing time. Methodologies such as Branch-and-Fix Coordination and Lagrangean Relaxation make use of these decomposition approaches, where independent scenario clusters are given. In this work, we present a technique to generate cluster submodel structures from the decomposition of a general two-stage stochastic mixed integer optimization model. Scenario cluster submodels are generated from the original stochastic problem by combining the compact and splitting variable representations in some of the variables related to the nodes that belong to the first stage. We consider a two-stage stochastic capacity expansion problem as illustrative example where several decompositions are provided.This research has been partially supported by the projects MTM2015-65317-P from the Spanish Ministry of Economy and Competitiveness, PPG17/32 and GIU 17/011 from the University of the Basque Country, UPV/EHU, and Grupo de Investigación IT-928-16 from the Basque Government

Managing Traffic Data through Clustering and Radial Basis Functions

Due to the importance of road transport an adequate identification of the various road network levels is necessary for an efficient and sustainable management of the road infrastructure. Additionally, traffic values are key data for any pavement management system. In this work traffic volume data of 2019 in the Basque Autonomous Community (Spain) were analyzed and modeled. Having a multidimensional sample, the average annual daily traffic (AADT) was considered as the main variable of interest, which is used in many areas of the road network management. First, an exploratory analysis was performed, from which descriptive statistical information was obtained continuing with the clustering by various variables in order to standardize its behavior by translation. In a second stage, the variable of interest was estimated in the entire road network of the studied country using linear-based radial basis functions (RBFs). The estimated model was compared with the sample statistically, evaluating the estimation using cross-validation and highest-traffic sectors are defined. From the analysis, it was observed that the clustering analysis is useful for identifying the real importance of each road segment, as a function of the real traffic volume and not based on other criteria. It was also observed that interpolation methods based on linear-type radial basis functions (RBF) can be used as a preliminary method to estimate the AADT.This research was funded by The University of the Basque Country (UPV/EHU), Call for Innovation Projects “IKD i3 Laborategia” (Call 1-2020, 2019/20)

Generating cluster submodels from two-stage stochastic mixed integer optimization models

Stochastic optimization problems of practical applications lead, in general, to some large models. The size of those models is linked to the number of scenarios that defines the scenario tree. This number of scenarios can be so large that decomposition strategies are required for problem solving in reasonable computing time. Methodologies such as Branch-and-Fix Coordination and Lagrangean Relaxation make use of these decomposition approaches, where independent scenario clusters are given. In this work, we present a technique to generate cluster submodel structures from the decomposition of a general two-stage stochastic mixed integer optimization model. Scenario cluster submodels are generated from the original stochastic problem by combining the compact and splitting variable representations in some of the variables related to the nodes that belong to the first stage. We consider a two-stage stochastic capacity expansion problem as illustrative example where several decompositions are provided.This research has been partially supported by the projects MTM2015-65317-P from the Spanish Ministry of Economy and Competitiveness, PPG17/32 and GIU 17/011 from the University of the Basque Country, UPV/EHU, and Grupo de Investigación IT-928-16 from the Basque Government