Model predictive control techniques for hybrid systems

This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.Ministerio de Eduación y Ciencia DPI2007-66718-C04-01Ministerio de Eduación y Ciencia DPI2008-0581

Improving the efficiency of the cardiac catheterization laboratories through understanding the stochastic behavior of the scheduled procedures

  Background: In this study, we sought to analyze the stochastic behavior of Catherization Labora­tories (Cath Labs) procedures in our institution. Statistical models may help to improve estimated case durations to support management in the cost-effective use of expensive surgical resources. Methods: We retrospectively analyzed all the procedures performed in the Cath Labs in 2012. The duration of procedures is strictly positive (larger than zero) and has mostly a large mini­mum duration. Because of the strictly positive character of the Cath Lab procedures, a fit of a lognormal model may be desirable. Having a minimum duration requires an estimate of the threshold (shift) parameter of the lognormal model. Therefore, the 3-parameter lognormal model is interesting. To avoid heterogeneous groups of observations, we tested every group-car­diologist-procedure combination for the normal, 2- and 3-parameter lognormal distribution. Results: The total number of elective and emergency procedures performed was 6,393 (8,186 h). The final analysis included 6,135 procedures (7,779 h). Electrophysiology (intervention) pro­cedures fit the 3-parameter lognormal model 86.1% (80.1%). Using Friedman test statistics, we conclude that the 3-parameter lognormal model is superior to the 2-parameter lognormal model. Furthermore, the 2-parameter lognormal is superior to the normal model. Conclusions: Cath Lab procedures are well-modelled by lognormal models. This information helps to improve and to refine Cath Lab schedules and hence their efficient use.

Lagrangean decomposition for large-scale two-stage stochastic mixed 0-1 problems

In this paper we study solution methods for solving the dual problem corresponding to the Lagrangean Decomposition of two stage stochastic mixed 0-1 models. We represent the two stage stochastic mixed 0-1 problem by a splitting variable representation of the deterministic equivalent model, where 0-1 and continuous variables appear at any stage. Lagrangean Decomposition is proposed for satisfying both the integrality constraints for the 0-1 variables and the non-anticipativity constraints. We compare the performance of four iterative algorithms based on dual Lagrangean Decomposition schemes, as the Subgradient method, the Volume algorithm, the Progressive Hedging algorithm and the Dynamic Constrained Cutting Plane scheme. We test the conditions and properties of convergence for medium and large-scale dimension stochastic problems. Computational results are reported.Progressive Hedging algorithm, volume algorithm, Lagrangean decomposition, subgradient method

A parallelizable algorithmic framework for solving large scale multi-stage stochastic mixed 0-1 problems under uncertainty

Preprint submitted to Computers & Operations Researchmulti-stage stochastic mixed 0-1 optimization, nonsymmetric scenario trees, implicit and explicit nonanticipativity constraints, splitting variable and compact representations, scenario cluster partitioning

Parametric error bounds for convex approximations of two-stage mixed-integer recourse models with a random second-stage cost vector

We consider two-stage recourse models with integer restrictions in the second stage. These models are typically nonconvex and hence, hard to solve. There exist convex approximations of these models with accompanying error bounds. However, it is unclear how these error bounds depend on the distributions of the second-stage cost vector q.In this paper, we derive parametric error bounds whose dependence on the distribution of q is explicit: they scale linearly in the expected value of the `1-norm of q

Discrepancy distances and scenario reduction in two-stage stochastic integer programming

Polyhedral discrepancies are relevant for the quantitative stability of mixed-integer two-stage and chance constrained stochastic programs. We study the problem of optimal scenario reduction for a discrete probability distribution with respect to certain polyhedral discrepancies and develop algorithms for determining the optimally reduced distribution approximately. Encouraging numerical experience for optimal scenario reduction is provided

Lagrangean decomposition for large-scale two-stage stochastic mixed 0-1 problems

In this paper we study solution methods for solving the dual problem corresponding to the Lagrangean Decomposition of two stage stochastic mixed 0-1 models. We represent the two stage stochastic mixed 0-1 problem by a splitting variable representation of the deterministic equivalent model, where 0-1 and continuous variables appear at any stage. Lagrangean Decomposition is proposed for satisfying both the integrality constraints for the 0-1 variables and the non-anticipativity constraints. We compare the performance of four iterative algorithms based on dual Lagrangean Decomposition schemes, as the Subgradient method, the Volume algorithm, the Progressive Hedging algorithm and the Dynamic Constrained Cutting Plane scheme. We test the conditions and properties of convergence for medium and large-scale dimension stochastic problems. Computational results are reported.This research has been partially supported by the projects ECO2008-00777 ECON from the Ministry of Education and Science, Grupo de Investigación IT-347-10 from the Basque Government, grant FPU ECO-2006 from the Ministry of Education and Science, grants RM URJC-CM-2008-CET-3703 and RIESGOS CM from Comunidad de Madrid, and PLANIN MTM2009-14087-C04-01 from Ministry of Science and Innovation, Spain

A parallelizable algorithmic framework for solving large scale multi-stage stochastic mixed 0-1 problems under uncertainty

Preprint submitted to Computers & Operations ResearchIn this paper we present a parallelizable scheme of the Branch-and-Fix Coordination algorithm for solving medium and large scale multi-stage mixed 0-1 optimization problems under uncertainty. The uncertainty is represented via a nonsymmetric scenario tree. An information structuring for scenario cluster partitioning of nonsymmetric scenario trees is also presented, given the general model formulation of a multi-stage stochastic mixed 0-1 problem. The basic idea consists of explicitly rewriting the nonanticipativity constraints (NAC) of the 0-1 and continuous variables in the stages with common information. As a result an assignment of the constraint matrix blocks into independent scenario cluster submodels is performed by a so-called cluster splitting-compact representation. This partitioning allows to generate a new information structure to express the NAC which link the related clusters, such that the explicit NAC linking the submodels together is performed by a splitting variable representation. The new algorithm has been implemented in a C++ experimental code that uses the open source optimization engine COIN-OR, for solving the auxiliary linear and mixed 0-1 submodels. Some computational experience is reported to validate the new proposed approach. We give computational evidence of the model tightening effect that have preprocessing techniques in stochastic integer optimization as well, by using the probing and Gomory and clique cuts identification and appending schemes of the optimization engine.This research has been partially supported by the projects ECO2008-00777 ECON from the Ministry of Education and Science, Grupo de Investigación IT-347-10 from the Basque Government, URJC-CM-2008-CET-3703 and RIESGOS CM from Comunidad de Madrid, and PLANIN MTM2009-14087-C04-01 from Ministry of Science and Innovation, Spain