Matheuristics:survey and synthesis

In integer programming and combinatorial optimisation, people use the term matheuristics to refer to methods that are heuristic in nature, but draw on concepts from the literature on exact methods. We survey the literature on this topic, with a particular emphasis on matheuristics that yield both primal and dual bounds (i.e., upper and lower bounds in the case of a minimisation problem). We also make some comments about possible future developments

Network design under uncertainty and demand elasticity

Network design covers a large class of fundamental problems ubiquitous in the fields of transportation and communication. These problems are modelled mathematically using directed graphs and capture the trade-off between initial investment in infrastructure and operational costs. This thesis presents the use of mixed integer programming theory and algorithms to solve network design problems and their extensions. We focus on two types of network design problems, the first is a hub location problem in which the initial investments are in the form of fixed costs for installing infrastructure at nodes for them to be equipped for the transhipment of commodities. The second is a fixed-charge multicommodity network design problem in which investments are in the form of installing infrastructure on arcs so that they may be used to transport commodities. We first present an extension of the hub location problem where both demand and transportation cost uncertainty are considered. We propose mixed integer linear programming formulations and a branch-and-cut algorithm to solve robust counterparts for this problem. Comparing the proposed models' solutions to those obtained from a commensurate stochastic counterpart, we note that their performance is similar in the risk-neutral setting while solutions from the robust counterparts are significantly superior in the risk-averse setting. We next present exact algorithms based on Benders decomposition capable of solving large-scale instances of the classic uncapacitated fixed-charge multicommodity network design problem. The method combines the use of matheuristics, general mixed integer valid inequalities, and a cut-and-solve enumeration scheme. Computational experiments show the proposed approaches to be up to three orders of magnitude faster than the state-of-the-art general purpose mixed integer programming solver. Finally, we extend the classic fixed-charge multicommodity network design problem to a profit-oriented variant that accounts for demand elasticity, commodity selection, and service commitment. An arc-based and a path-based formulation are proposed. The former is a mixed integer non-convex problem solved with a general purpose global optimization solver while the latter is an integer linear formulation with exponentially many variables solved with a hybrid matheuristic. Further analysis shows the impact of considering demand elasticity to be significant in strategic network design

An Algorithmic approach to shift structure optimization

Workforce scheduling in organizations often consists of three major phases: workload prediction, shift generation, and staff rostering. Workload prediction involves using historical behaviour of e.g. customers to predict future demand for work. Shift generation is the process of transforming the determined workload into shifts as accurately as possible. In staff rostering, the generated shifts are assigned to employees. In general the problem and even its subproblems are NP-hard, which makes them highly challenging for organizations to solve. Heuristic optimization methods can be used to solve practical instances within reasonable running times, which in turn can result in e.g. improved revenue, improved service, or more satisfied employees for the organizations. This thesis presents some specific subproblems along with practical solution methods--- Työvoiman aikataulutusprosessi koostuu kolmesta päävaiheesta: työtarpeen ennustaminen, työvuorojen muodostus ja työvuorojen miehitys. Tulevaa työtarvetta ennustetaan pääasiassa menneisyyden asiakaskäytöksen perusteella käyttäen esimerkiksi tilastollisia malleja tai koneoppimiseen perustuvia menetelmiä. Työvuorojen muodostuksessa tehdään työvuororakenne, joka noudattaa ennustettua ja ennalta tiedettyä työtarvetta mahdollisimman tarkasti. Työvuorojen miehityksessä määritetään työvuoroille tekijät. Jokainen vaihe itsessään on haasteellinen ratkaistava. Erityisesti työvuorojen miehitys on yleensä NP-kova ongelma. On kuitenkin mahdollista tuottaa käytännöllisiä ratkaisuja järkevässä ajassa käyttäen heuristisia optimointimenetelmiä. Näin on saavutettavissa mitattavia hyötyjä mm. tuottoon, asiakkaiden palvelutasoon sekä työntekijöiden työtyyväisyyteen. Tässä väitöskirjassa esitellään eräitä työvoiman aikataulutuksen aliongelmia sekä niihin sopivia ratkaisumenetelmiä

Model-Based Heuristics for Combinatorial Optimization

Many problems arising in several and different areas of human knowledge share the characteristic of being intractable in real cases. The relevance of the solution of these problems, linked to their domain of action, has given birth to many frameworks of algorithms for solving them. Traditional solution paradigms are represented by exact and heuristic algorithms. In order to overcome limitations of both approaches and obtain better performances, tailored combinations of exact and heuristic methods have been studied, giving birth to a new paradigm for solving hard combinatorial optimization problems, constituted by model-based metaheuristics. In the present thesis, we deepen the issue of model-based metaheuristics, and present some methods, belonging to this class, applied to the solution of combinatorial optimization problems

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

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes

Operational research:methods and applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order