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

Time consistent expected mean-variance in multistage stochastic quadratic optimization: a model and a matheuristic

In this paper, we present a multistage time consistent Expected Conditional Risk Measure for minimizing a linear combination of the expected mean and the expected variance, so-called Expected Mean-Variance. The model is formulated as a multistage stochastic mixed-integer quadratic programming problem combining risk-sensitive cost and scenario analysis approaches. The proposed problem is solved by a matheuristic based on the Branch-and-Fix Coordination method. The multistage scenario cluster primal decomposition framework is extended to deal with large-scale quadratic optimization by means of stage-wise reformulation techniques. A specific case study in risk-sensitive production planning is used to illustrate that a remarkable decrease in the expected variance (risk cost) is obtained. A competitive behavior on the part of our methodology in terms of solution quality and computation time is shown when comparing with plain use of CPLEX in 150 benchmark instances, ranging up to 711,845 constraints and 193,000 binary variables.project MTM2015-65317-P (MINECO/FEDER/EU); BERC 2014-2017; IT-928-16; and by the University of the Basque Country UPV/EHU; BCAM Severo Ochoa excellence accreditation Grant SEV-2013-0323; BERC 2014-201

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

On parallel computing for stochastic optimization models and algorithms

167 p.Esta tesis tiene como objetivo principal la resolución de problemas de optimización bajo incertidumbre a gran escala, mediante la interconexión entre las disciplinas de Optimización estocástica y Computación en paralelo. Se describen algoritmos de descomposición desde la perspectivas de programación matemática y del aprovechamiento de recursos computacionales con el fin de resolver problemas de manera más rápida, de mayores dimensiones o/y obtener mejores resultados que sus técnicas homónimas en serie. Se han desarrollado dos estrategias de paralelización, denotadas como inner y outer. La primera de las cuales, realiza tareas en paralelo dentro de un esquema algorítmico en serie, mientras que la segunda ejecuta de manera simultánea y coordinada varios algoritmos secuenciales. La mayor descomposición del problema original, compartiendo el área de factibilidad, creando fases de sincronización y comunicación entre ejecuciones paralelas o definiendo condiciones iniciales divergentes, han sido claves en la eficacia de los diseños de los algoritmos propuestos. Como resultado, se presentan tanto algoritmos exactos como matheurísticos, que combinan metodologías metaheurísticas y técnicas de programación matemática. Se analiza la escalabilidad de cada algoritmo propuesto, y se consideran varios bancos de problemas de diferentes dimensiones, hasta un máximo de 58 millones de restricciones y 54 millones de variables (de las cuales 15 millones son binarias). La experiencia computacional ha sido principalmente realizada en el cluster ARINA de SGI/IZO-SGIker de la UPV/EHU

A parallel Branch-and-Fix Coordination based matheuristic algorithm for solving large sized multistage stochastic mixed 0-1 problems

A parallel matheuristic algorithm is presented as a spin-off from the exact Branch-and-Fix Coordination (BFC) algorithm for solving multistage stochastic mixed 0-1 problems. Some steps to guarantee the solution’s optimality are relaxed in the BFC algorithm, such that an incomplete backward branching scheme is considered for solving large sized problems. Additionally, a new branching criterion is considered, based on dynamically-guided and stage-wise ordering schemes, such that fewer Twin Node Families are expected to be visited during the execution of the so-called H-DBFC algorithm. The inner parallelization IH-DBFC of the new approach, allows to solve in parallel scenario clusters MIP submodels at different steps of the algorithm. The outer parallel version, OH-DBFC, considers independent paths and allows iterative incumbent solution values exchanges to obtain tighter bounds of the solution value of the original problem. A broad computational experience is reported for assessing the quality of the matheuristic solution for large sized instances. The instances dimensions that are considered are up to two orders of magnitude larger than in some other works that we are aware of. The optimality gap of the H-DBFC solution value versus the one obtained by a state-of-the-artMIP solver is very small, if any. The new approach frequently outperforms it in terms of solution’s quality and computing time. A comparison with our Stochastic Dynamic Programming algorithm is also reported. The use of parallel computing provides, on one hand, a perspective for solving very large sized instances and, on the other hand, an expected large reduction in elapsed time.MTM2015-65317-P, MTM2015-63710-P, IT928-16; UFI BETS 2011; IZO-SGI SGIke

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

Solving Electric Market Quadratic Problems by Branch and Fix Coordination Methods

The electric market regulation in Spain (MIBEL) establishes the rules for bilateral and futures contracts in the day-ahead optimal bid problem. Our model allows a price-taker generation company to decide the unit commitment of the thermal units, the economic dispatch of the bilateral and futures contracts between the thermal units and the optimal sale bids for the thermal units observing the MIBEL regulation. The uncertainty of the spot prices is represented through scenario sets. We solve this model on the framework of the Branch and Fix Coordination metodology as a quadratic two-stage stochastic problem. In order to gain computational efficiency, we use scenario clusters and propose to use perspective cuts. Numerical results are reportedPeer Reviewe

Modelling and solution methods for stochastic optimisation

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.In this thesis we consider two research problems, namely, (i) language constructs for modelling stochastic programming (SP) problems and (ii) solution methods for processing instances of different classes of SP problems. We first describe a new design of an SP modelling system which provides greater extensibility and reuse. We implement this enhanced system and develop solver connections. We also investigate in detail the following important classes of SP problems: singlestage SP with risk constraints, two-stage linear and stochastic integer programming problems. We report improvements to solution methods for single-stage problems with second-order stochastic dominance constraints and two-stage SP problems. In both cases we use the level method as a regularisation mechanism. We also develop novel heuristic methods for stochastic integer programming based on variable neighbourhood search. We describe an algorithmic framework for implementing decomposition methods such as the L-shaped method within our SP solver system. Based on this framework we implement a number of established solution algorithms as well as a new regularisation method for stochastic linear programming. We compare the performance of these methods and their scale-up properties on an extensive set of benchmark problems. We also implement several solution methods for stochastic integer programming and report a computational study comparing their performance. The three solution methods, (a) processing of a single-stage problem with second-order stochastic dominance constraints, (b) regularisation by the level method for two-stage SP and (c) method for solving integer SP problems, are novel approaches and each of these makes a contribution to knowledge.Financial support was obtained from OptiRisk Systems

TWO MULTI-OBJECTIVE STOCHASTIC MODELS FOR PROJECT TEAM FORMATION UNDER UNCERTAINTY IN TIME REQUIREMENTS

Team formation is one of the key stages in project management. The cost associated with the individuals who form a team and the quality of the tasks completed by the team are two of the main concerns in team formation problems. In this study, two mathematical models to optimize simultaneously cost and quality in a team formation problem are developed. Because team formation problem arises in uncertain environment, different scenarios are defined for the time requirement of the project. Two-stage stochastic programming and multi-stage stochastic programming are applied to solve the first and the second model respectively. The presented models and their solution methodology can be applied in different types of projects. In this study, a project that involves an overhaul of an aircraft is presented as a case study in which the goals are to minimize staffing costs and maximize the reliability of the aircraft by staffing workforce with high competency

MODELING SUSTAINABILITY IN RENEWABLE ENERGY SUPPLY CHAIN SYSTEMS

This dissertation aims at modeling sustainability of renewable fuel supply chain systems against emerging challenges. In particular, the dissertation focuses on the biofuel supply chain system design, and manages to develop advanced modeling framework and corresponding solution methods in tackling challenges in sustaining biofuel supply chain systems. These challenges include: (1) to integrate \u27environmental thinking\u27 into the long-term biofuel supply chain planning; (2) to adopt multimodal transportation to mitigate seasonality in biofuel supply chain operations; (3) to provide strategies in hedging against uncertainty from conversion technology; and (4) to develop methodologies in long-term sequential planning of the biofuel supply chain under uncertainties. All models are mixed integer programs, which also involves multi-objective programming method and two-stage/multistage stochastic programming methods. In particular for the long-term sequential planning under uncertainties, to reduce the computational challenges due to the exponential expansion of the scenario tree, I also developed efficient ND-Max method which is more efficient than CPLEX and Nested Decomposition method. Through result analysis of four independent studies, it is found that the proposed modeling frameworks can effectively improve the economic performance, enhance environmental benefits and reduce risks due to systems uncertainties for the biofuel supply chain systems