Short Term Unit Commitment as a Planning Problem

‘Unit Commitment’, setting online schedules for generating units in a power system to ensure supply meets demand, is integral to the secure, efficient, and economic daily operation of a power system. Conflicting desires for security of supply at minimum cost complicate this. Sustained research has produced methodologies within a guaranteed bound of optimality, given sufficient computing time. Regulatory requirements to reduce emissions in modern power systems have necessitated increased renewable generation, whose output cannot be directly controlled, increasing complex uncertainties. Traditional methods are thus less efficient, generating more costly schedules or requiring impractical increases in solution time. Meta-Heuristic approaches are studied to identify why this large body of work has had little industrial impact despite continued academic interest over many years. A discussion of lessons learned is given, and should be of interest to researchers presenting new Unit Commitment approaches, such as a Planning implementation. Automated Planning is a sub-field of Artificial Intelligence, where a timestamped sequence of predefined actions manipulating a system towards a goal configuration is sought. This differs from previous Unit Commitment formulations found in the literature. There are fewer times when a unit’s online status switches, representing a Planning action, than free variables in a traditional formulation. Efficient reasoning about these actions could reduce solution time, enabling Planning to tackle Unit Commitment problems with high levels of renewable generation. Existing Planning formulations for Unit Commitment have not been found. A successful formulation enumerating open challenges would constitute a good benchmark problem for the field. Thus, two models are presented. The first demonstrates the approach’s strength in temporal reasoning over numeric optimisation. The second balances this but current algorithms cannot handle it. Extensions to an existing algorithm are proposed alongside a discussion of immediate challenges and possible solutions. This is intended to form a base from which a successful methodology can be developed

Decomposition, Reformulation, and Diving in University Course Timetabling

In many real-life optimisation problems, there are multiple interacting components in a solution. For example, different components might specify assignments to different kinds of resource. Often, each component is associated with different sets of soft constraints, and so with different measures of soft constraint violation. The goal is then to minimise a linear combination of such measures. This paper studies an approach to such problems, which can be thought of as multiphase exploitation of multiple objective-/value-restricted submodels. In this approach, only one computationally difficult component of a problem and the associated subset of objectives is considered at first. This produces partial solutions, which define interesting neighbourhoods in the search space of the complete problem. Often, it is possible to pick the initial component so that variable aggregation can be performed at the first stage, and the neighbourhoods to be explored next are guaranteed to contain feasible solutions. Using integer programming, it is then easy to implement heuristics producing solutions with bounds on their quality. Our study is performed on a university course timetabling problem used in the 2007 International Timetabling Competition, also known as the Udine Course Timetabling Problem. In the proposed heuristic, an objective-restricted neighbourhood generator produces assignments of periods to events, with decreasing numbers of violations of two period-related soft constraints. Those are relaxed into assignments of events to days, which define neighbourhoods that are easier to search with respect to all four soft constraints. Integer programming formulations for all subproblems are given and evaluated using ILOG CPLEX 11. The wider applicability of this approach is analysed and discussed.Comment: 45 pages, 7 figures. Improved typesetting of figures and table

Survey on Combinatorial Register Allocation and Instruction Scheduling

Register allocation (mapping variables to processor registers or memory) and instruction scheduling (reordering instructions to increase instruction-level parallelism) are essential tasks for generating efficient assembly code in a compiler. In the last three decades, combinatorial optimization has emerged as an alternative to traditional, heuristic algorithms for these two tasks. Combinatorial optimization approaches can deliver optimal solutions according to a model, can precisely capture trade-offs between conflicting decisions, and are more flexible at the expense of increased compilation time. This paper provides an exhaustive literature review and a classification of combinatorial optimization approaches to register allocation and instruction scheduling, with a focus on the techniques that are most applied in this context: integer programming, constraint programming, partitioned Boolean quadratic programming, and enumeration. Researchers in compilers and combinatorial optimization can benefit from identifying developments, trends, and challenges in the area; compiler practitioners may discern opportunities and grasp the potential benefit of applying combinatorial optimization

Models and Algorithms for the Optimisation of Replenishment, Production and Distribution Plans in Industrial Enterprises

Tesis por compendio[ES] La optimización en las empresas manufactureras es especialmente importante, debido a las grandes inversiones que realizan, ya que a veces estas inversiones no obtienen el rendimiento esperado porque los márgenes de beneficio de los productos son muy ajustados. Por ello, las empresas tratan de maximizar el uso de los recursos productivos y financieros minimizando el tiempo perdido y, al mismo tiempo, mejorando los flujos de los procesos y satisfaciendo las necesidades del mercado. El proceso de planificación es una actividad crítica para las empresas. Esta tarea implica grandes retos debido a los cambios del mercado, las alteraciones en los procesos de producción dentro de la empresa y en la cadena de suministro, y los cambios en la legislación, entre otros. La planificación del aprovisionamiento, la producción y la distribución desempeña un papel fundamental en el rendimiento de las empresas manufactureras, ya que una planificación ineficaz de los proveedores, los procesos de producción y los sistemas de distribución contribuye a aumentar los costes de los productos, a alargar los plazos de entrega y a reducir los beneficios. La planificación eficaz es un proceso complejo que abarca una amplia gama de actividades para garantizar que los equipos, los materiales y los recursos humanos estén disponibles en el momento y el lugar adecuados. Motivados por la complejidad de la planificación en las empresas manufactureras, esta tesis estudia y desarrolla herramientas cuantitativas para ayudar a los planificadores en los procesos de la planificación del aprovisionamiento, producción y distribución. Desde esta perspectiva, se proponen modelos realistas y métodos eficientes para apoyar la toma de decisiones en las empresas industriales, principalmente en las pequeñas y medianas empresas (PYMES). Las aportaciones de esta tesis suponen un avance científico basado en una exhaustiva revisión bibliográfica sobre la planificación del aprovisionamiento, la producción y la distribución que ayuda a comprender los principales modelos y algoritmos utilizados para resolver estos planes, y pone en relieve las tendencias y las futuras direcciones de investigación. También proporciona un marco holístico para caracterizar los modelos y algoritmos centrándose en la planificación de la producción, la programación y la secuenciación. Esta tesis también propone una herramienta de apoyo a la decisión para seleccionar un algoritmo o método de solución para resolver problemas concretos de la planificación del aprovisionamiento, producción y distribución en función de su complejidad, lo que permite a los planificadores no duplicar esfuerzos de modelización o programación de técnicas de solución. Por último, se desarrollan nuevos modelos matemáticos y enfoques de solución de última generación, como los algoritmos matheurísticos, que combinan la programación matemática y las técnicas metaheurísticas. Los nuevos modelos y algoritmos comprenden mejoras en términos de rendimiento computacional, e incluyen características realistas de los problemas del mundo real a los que se enfrentan las empresas de fabricación. Los modelos matemáticos han sido validados con un caso de una importante empresa del sector de la automoción en España, lo que ha permitido evaluar la relevancia práctica de estos novedosos modelos utilizando instancias de gran tamaño, similares a las existentes en la empresa objeto de estudio. Además, los algoritmos matheurísticos han sido probados utilizando herramientas libres y de código abierto. Esto también contribuye a la práctica de la investigación operativa, y proporciona una visión de cómo desplegar estos métodos de solución y el tiempo de cálculo y rendimiento de la brecha que se puede obtener mediante el uso de software libre o de código abierto.[CA] L'optimització a les empreses manufactureres és especialment important, a causa de les grans inversions que realitzen, ja que de vegades aquestes inversions no obtenen el rendiment esperat perquè els marges de benefici dels productes són molt ajustats. Per això, les empreses intenten maximitzar l'ús dels recursos productius i financers minimitzant el temps perdut i, alhora, millorant els fluxos dels processos i satisfent les necessitats del mercat. El procés de planificació és una activitat crítica per a les empreses. Aquesta tasca implica grans reptes a causa dels canvis del mercat, les alteracions en els processos de producció dins de l'empresa i la cadena de subministrament, i els canvis en la legislació, entre altres. La planificació de l'aprovisionament, la producció i la distribució té un paper fonamental en el rendiment de les empreses manufactureres, ja que una planificació ineficaç dels proveïdors, els processos de producció i els sistemes de distribució contribueix a augmentar els costos dels productes, allargar els terminis de lliurament i reduir els beneficis. La planificació eficaç és un procés complex que abasta una àmplia gamma d'activitats per garantir que els equips, els materials i els recursos humans estiguen disponibles al moment i al lloc adequats. Motivats per la complexitat de la planificació a les empreses manufactureres, aquesta tesi estudia i desenvolupa eines quantitatives per ajudar als planificadors en els processos de la planificació de l'aprovisionament, producció i distribució. Des d'aquesta perspectiva, es proposen models realistes i mètodes eficients per donar suport a la presa de decisions a les empreses industrials, principalment a les petites i mitjanes empreses (PIMES). Les aportacions d'aquesta tesi suposen un avenç científic basat en una exhaustiva revisió bibliogràfica sobre la planificació de l'aprovisionament, la producció i la distribució que ajuda a comprendre els principals models i algorismes utilitzats per resoldre aquests plans, i posa de relleu les tendències i les futures direccions de recerca. També proporciona un marc holístic per caracteritzar els models i algorismes centrant-se en la planificació de la producció, la programació i la seqüenciació. Aquesta tesi també proposa una eina de suport a la decisió per seleccionar un algorisme o mètode de solució per resoldre problemes concrets de la planificació de l'aprovisionament, producció i distribució en funció de la seua complexitat, cosa que permet als planificadors no duplicar esforços de modelització o programació de tècniques de solució. Finalment, es desenvolupen nous models matemàtics i enfocaments de solució d'última generació, com ara els algoritmes matheurístics, que combinen la programació matemàtica i les tècniques metaheurístiques. Els nous models i algoritmes comprenen millores en termes de rendiment computacional, i inclouen característiques realistes dels problemes del món real a què s'enfronten les empreses de fabricació. Els models matemàtics han estat validats amb un cas d'una important empresa del sector de l'automoció a Espanya, cosa que ha permés avaluar la rellevància pràctica d'aquests nous models utilitzant instàncies grans, similars a les existents a l'empresa objecte d'estudi. A més, els algorismes matheurístics han estat provats utilitzant eines lliures i de codi obert. Això també contribueix a la pràctica de la investigació operativa, i proporciona una visió de com desplegar aquests mètodes de solució i el temps de càlcul i rendiment de la bretxa que es pot obtindre mitjançant l'ús de programari lliure o de codi obert.[EN] Optimisation in manufacturing companies is especially important, due to the large investments they make, as sometimes these investments do not obtain the expected return because the profit margins of products are very tight. Therefore, companies seek to maximise the use of productive and financial resources by minimising lost time and, at the same time, improving process flows while meeting market needs. The planning process is a critical activity for companies. This task involves great challenges due to market changes, alterations in production processes within the company and in the supply chain, and changes in legislation, among others. Planning of replenishment, production and distribution plays a critical role in the performance of manufacturing companies because ineffective planning of suppliers, production processes and distribution systems contributes to higher product costs, longer lead times and less profits. Effective planning is a complex process that encompasses a wide range of activities to ensure that equipment, materials and human resources are available in the right time and the right place. Motivated by the complexity of planning in manufacturing companies, this thesis studies and develops quantitative tools to help planners in the replenishment, production and delivery planning processes. From this perspective, realistic models and efficient methods are proposed to support decision making in industrial companies, mainly in small- and medium-sized enterprises (SMEs). The contributions of this thesis represent a scientific breakthrough based on a comprehensive literature review about replenishment, production and distribution planning that helps to understand the main models and algorithms used to solve these plans, and highlights trends and future research directions. It also provides a holistic framework to characterise models and algorithms by focusing on production planning, scheduling and sequencing. This thesis also proposes a decision support tool for selecting an algorithm or solution method to solve concrete replenishment, production and distribution planning problems according to their complexity, which allows planners to not duplicate efforts modelling or programming solution techniques. Finally, new state-of-the-art mathematical models and solution approaches are developed, such as matheuristic algorithms, which combine mathematical programming and metaheuristic techniques. The new models and algorithms comprise improvements in computational performance terms, and include realistic features of real-world problems faced by manufacturing companies. The mathematical models have been validated with a case of an important company in the automotive sector in Spain, which allowed to evaluate the practical relevance of these novel models using large instances, similarly to those existing in the company under study. In addition, the matheuristic algorithms have been tested using free and open-source tools. This also helps to contribute to the practice of operations research, and provides insight into how to deploy these solution methods and the computational time and gap performance that can be obtained by using free or open-source software.This work would not have been possible without the following funding sources: Conselleria de Educación, Investigación, Cultura y Deporte, Generalitat Valenciana for hiring predoctoral research staff with Grant (ACIF/2018/170) and the European Social Fund with the Grant Operational Programme of FSE 2014-2020. Conselleria de Educación, Investigación, Cultura y Deporte, Generalitat Valenciana for predoctoral contract students to stay in research centers outside the research centers outside the Valencian Community (BEFPI/2021/040) and the European Social Fund.Guzmán Ortiz, BE. (2022). Models and Algorithms for the Optimisation of Replenishment, Production and Distribution Plans in Industrial Enterprises [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/187461Compendi

Global Optimisation for Energy System

The goal of global optimisation is to find globally optimal solutions, avoiding local optima and other stationary points. The aim of this thesis is to provide more efficient global optimisation tools for energy systems planning and operation. Due to the ongoing increasing of complexity and decentralisation of power systems, the use of advanced mathematical techniques that produce reliable solutions becomes necessary. The task of developing such methods is complicated by the fact that most energy-related problems are nonconvex due to the nonlinear Alternating Current Power Flow equations and the existence of discrete elements. In some cases, the computational challenges arising from the presence of non-convexities can be tackled by relaxing the definition of convexity and identifying classes of problems that can be solved to global optimality by polynomial time algorithms. One such property is known as invexity and is defined by every stationary point of a problem being a global optimum. This thesis investigates how the relation between the objective function and the structure of the feasible set is connected to invexity and presents necessary conditions for invexity in the general case and necessary and sufficient conditions for problems with two degrees of freedom. However, nonconvex problems often do not possess any provable convenient properties, and specialised methods are necessary for providing global optimality guarantees. A widely used technique is solving convex relaxations in order to find a bound on the optimal solution. Semidefinite Programming relaxations can provide good quality bounds, but they suffer from a lack of scalability. We tackle this issue by proposing an algorithm that combines decomposition and linearisation approaches. In addition to continuous non-convexities, many problems in Energy Systems model discrete decisions and are expressed as mixed-integer nonlinear programs (MINLPs). The formulation of a MINLP is of significant importance since it affects the quality of dual bounds. In this thesis we investigate algebraic characterisations of on/off constraints and develop a strengthened version of the Quadratic Convex relaxation of the Optimal Transmission Switching problem. All presented methods were implemented in mathematical modelling and optimisation frameworks PowerTools and Gravity

Optimising airline maintenance scheduling decisions

Airline maintenance scheduling (AMS) studies how plans or schedules are constructed to ensure that a fleet is efficiently maintained and that airline operational demands are met. Additionally, such schedules must take into consideration the different regulations airlines are subject to, while minimising maintenance costs. In this thesis, we study different formulations, solution methods, and modelling considerations, for the AMS and related problems to propose two main contributions. First, we present a new type of multi-objective mixed integer linear programming formulation which challenges traditional time discretisation. Employing the concept of time intervals, we efficiently model the airline maintenance scheduling problem with tail assignment considerations. With a focus on workshop resource allocation and individual aircraft flight operations, and the use of a custom iterative algorithm, we solve large and long-term real-world instances (16000 flights, 529 aircraft, 8 maintenance workshops) in reasonable computational time. Moreover, we provide evidence to suggest, that our framework provides near-optimal solutions, and that inter-airline cooperation is beneficial for workshops. Second, we propose a new hybrid solution procedure to solve the aircraft recovery problem. Here, we study how to re-schedule flights and re-assign aircraft to these, to resume airline operations after an unforeseen disruption. We do so while taking operational restrictions into account. Specifically, restrictions on aircraft, maintenance, crew duty, and passenger delay are accounted for. The flexibility of the approach allows for further operational restrictions to be easily introduced. The hybrid solution procedure involves the combination of column generation with learning-based hyperheuristics. The latter, adaptively selects exact or metaheuristic algorithms to generate columns. The five different algorithms implemented, two of which we developed, were collected and released as a Python package (Torres Sanchez, 2020). Findings suggest that the framework produces fast and insightful recovery solutions

An investigation of computer based tools for mathematical programming modelling

This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University.Science and Engineering Research Counci

Routing and scheduling optimisation under uncertainty for engineering applications

The thesis aims to develop a viable computational approach suitable for solving large vehicle routing and scheduling optimisation problems affected by uncertainty. The modelling framework is built upon recent advances in Stochastic Optimisation, Robust Optimisation and Distributionally Robust Optimization. The utility of the methodology is presented on two classes of discrete optimisation problems: scheduling satellite communication, which is a variant of Machine Scheduling, and the Vehicle Routing Problem with Time Windows and Synchronised Visits. For each problem class, a practical engineering application is formulated using data coming from the real world. The significant size of the problem instances reinforced the need to apply a different computational approach for each problem class. Satellite communication is scheduled using a Mixed-Integer Programming solver. In contrast, the vehicle routing problem with synchronised visits is solved using a hybrid method that combines Iterated Local Search, Constraint Programming and the Guided Local Search metaheuristic. The featured application of scheduling satellite communication is the Satellite Quantum Key Distribution for a system that consists of one spacecraft placed in the Lower Earth Orbit and a network of optical ground stations located in the United Kingdom. The satellite generates cryptographic keys and transmits them to individual ground stations. Each ground station should receive the number of keys in proportion to the importance of the ground station in the network. As clouds containing water attenuate the signal, reliable scheduling needs to account for cloud cover predictions, which are naturally affected by uncertainty. A new uncertainty sets tailored for modelling uncertainty in predictions of atmospheric phenomena is the main contribution to the methodology. The uncertainty set models the evolution of uncertain parameters using a Multivariate Vector Auto-Regressive Time Series, which preserves correlations over time and space. The problem formulation employing the new uncertainty set compares favourably to a suite of alternative models adapted from the literature considering both the computational time and the cost-effectiveness of the schedule evaluated in the cloud cover conditions observed in the real world. The other contribution of the thesis in the satellite scheduling domain is the formulation of the Satellite Quantum Key Distribution problem. The proof of computational complexity and thorough performance analysis of an example Satellite Quantum Key Distribution system accompany the formulation. The Home Care Scheduling and Routing Problem, which instances are solved for the largest provider of such services in Scotland, is the application of the Vehicle Routing Problem with Time Windows and Synchronised Visits. The problem instances contain over 500 visits. Around 20% of them require two carers simultaneously. Such problem instances are well beyond the scalability limitations of the exact method and considerably larger than instances of similar problems considered in the literature. The optimisation approach proposed in the thesis found effective solutions in attractive computational time (i.e., less than 30 minutes) and the solutions reduced the total travel time threefold compared to alternative schedules computed by human planners. The Essential Riskiness Index Optimisation was incorporated into the Constraint Programming model to address uncertainty in visits' duration. Besides solving large problem instances from the real world, the solution method reproduced the majority of the best results reported in the literature and strictly improved the solutions for several instances of a well-known benchmark for the Vehicle Routing Problem with Time Windows and Synchronised Visits.The thesis aims to develop a viable computational approach suitable for solving large vehicle routing and scheduling optimisation problems affected by uncertainty. The modelling framework is built upon recent advances in Stochastic Optimisation, Robust Optimisation and Distributionally Robust Optimization. The utility of the methodology is presented on two classes of discrete optimisation problems: scheduling satellite communication, which is a variant of Machine Scheduling, and the Vehicle Routing Problem with Time Windows and Synchronised Visits. For each problem class, a practical engineering application is formulated using data coming from the real world. The significant size of the problem instances reinforced the need to apply a different computational approach for each problem class. Satellite communication is scheduled using a Mixed-Integer Programming solver. In contrast, the vehicle routing problem with synchronised visits is solved using a hybrid method that combines Iterated Local Search, Constraint Programming and the Guided Local Search metaheuristic. The featured application of scheduling satellite communication is the Satellite Quantum Key Distribution for a system that consists of one spacecraft placed in the Lower Earth Orbit and a network of optical ground stations located in the United Kingdom. The satellite generates cryptographic keys and transmits them to individual ground stations. Each ground station should receive the number of keys in proportion to the importance of the ground station in the network. As clouds containing water attenuate the signal, reliable scheduling needs to account for cloud cover predictions, which are naturally affected by uncertainty. A new uncertainty sets tailored for modelling uncertainty in predictions of atmospheric phenomena is the main contribution to the methodology. The uncertainty set models the evolution of uncertain parameters using a Multivariate Vector Auto-Regressive Time Series, which preserves correlations over time and space. The problem formulation employing the new uncertainty set compares favourably to a suite of alternative models adapted from the literature considering both the computational time and the cost-effectiveness of the schedule evaluated in the cloud cover conditions observed in the real world. The other contribution of the thesis in the satellite scheduling domain is the formulation of the Satellite Quantum Key Distribution problem. The proof of computational complexity and thorough performance analysis of an example Satellite Quantum Key Distribution system accompany the formulation. The Home Care Scheduling and Routing Problem, which instances are solved for the largest provider of such services in Scotland, is the application of the Vehicle Routing Problem with Time Windows and Synchronised Visits. The problem instances contain over 500 visits. Around 20% of them require two carers simultaneously. Such problem instances are well beyond the scalability limitations of the exact method and considerably larger than instances of similar problems considered in the literature. The optimisation approach proposed in the thesis found effective solutions in attractive computational time (i.e., less than 30 minutes) and the solutions reduced the total travel time threefold compared to alternative schedules computed by human planners. The Essential Riskiness Index Optimisation was incorporated into the Constraint Programming model to address uncertainty in visits' duration. Besides solving large problem instances from the real world, the solution method reproduced the majority of the best results reported in the literature and strictly improved the solutions for several instances of a well-known benchmark for the Vehicle Routing Problem with Time Windows and Synchronised Visits

New variants of variable neighbourhood search for 0-1 mixed integer programming and clustering

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Many real-world optimisation problems are discrete in nature. Although recent rapid developments in computer technologies are steadily increasing the speed of computations, the size of an instance of a hard discrete optimisation problem solvable in prescribed time does not increase linearly with the computer speed. This calls for the development of new solution methodologies for solving larger instances in shorter time. Furthermore, large instances of discrete optimisation problems are normally impossible to solve to optimality within a reasonable computational time/space and can only be tackled with a heuristic approach. In this thesis the development of so called matheuristics, the heuristics which are based on the mathematical formulation of the problem, is studied and employed within the variable neighbourhood search framework. Some new variants of the variable neighbourhood searchmetaheuristic itself are suggested, which naturally emerge from exploiting the information from the mathematical programming formulation of the problem. However, those variants may also be applied to problems described by the combinatorial formulation. A unifying perspective on modern advances in local search-based metaheuristics, a so called hyper-reactive approach, is also proposed. Two NP-hard discrete optimisation problems are considered: 0-1 mixed integer programming and clustering with application to colour image quantisation. Several new heuristics for 0-1 mixed integer programming problem are developed, based on the principle of variable neighbourhood search. One set of proposed heuristics consists of improvement heuristics, which attempt to find high-quality near-optimal solutions starting from a given feasible solution. Another set consists of constructive heuristics, which attempt to find initial feasible solutions for 0-1 mixed integer programs. Finally, some variable neighbourhood search based clustering techniques are applied for solving the colour image quantisation problem. All new methods presented are compared to other algorithms recommended in literature and a comprehensive performance analysis is provided. Computational results show that the methods proposed either outperform the existing state-of-the-art methods for the problems observed, or provide comparable results. The theory and algorithms presented in this thesis indicate that hybridisation of the CPLEX MIP solver and the VNS metaheuristic can be very effective for solving large instances of the 0-1 mixed integer programming problem. More generally, the results presented in this thesis suggest that hybridisation of exact (commercial) integer programming solvers and some metaheuristic methods is of high interest and such combinations deserve further practical and theoretical investigation. Results also show that VNS can be successfully applied to solving a colour image quantisation problem.Support from the Mathematical Institute, Serbian Academy of Sciences and Arts, are acknowledged for this research