Metaheuristics for the unit commitment problem : The Constraint Oriented Neighbourhoods search strategy

Tese de mestrado. Faculdade de Engenharia. Universidade do Porto. 199

Metaheuristic Optimization of Power and Energy Systems: Underlying Principles and Main Issues of the `Rush to Heuristics'

In the power and energy systems area, a progressive increase of literature contributions that contain applications of metaheuristic algorithms is occurring. In many cases, these applications are merely aimed at proposing the testing of an existing metaheuristic algorithm on a specific problem, claiming that the proposed method is better than other methods that are based on weak comparisons. This ‘rush to heuristics’ does not happen in the evolutionary computation domain, where the rules for setting up rigorous comparisons are stricter but are typical of the domains of application of the metaheuristics. This paper considers the applications to power and energy systems and aims at providing a comprehensive view of the main issues that concern the use of metaheuristics for global optimization problems. A set of underlying principles that characterize the metaheuristic algorithms is presented. The customization of metaheuristic algorithms to fit the constraints of specific problems is discussed. Some weaknesses and pitfalls that are found in literature contributions are identified, and specific guidelines are provided regarding how to prepare sound contributions on the application of metaheuristic algorithms to specific problems

Treasure hunt : a framework for cooperative, distributed parallel optimization

Orientador: Prof. Dr. Daniel WeingaertnerCoorientadora: Profa. Dra. Myriam Regattieri DelgadoTese (doutorado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Informática. Defesa : Curitiba, 27/05/2019Inclui referências: p. 18-20Área de concentração: Ciência da ComputaçãoResumo: Este trabalho propõe um framework multinível chamado Treasure Hunt, que é capaz de distribuir algoritmos de busca independentes para um grande número de nós de processamento. Com o objetivo de obter uma convergência conjunta entre os nós, este framework propõe um mecanismo de direcionamento que controla suavemente a cooperação entre múltiplas instâncias independentes do Treasure Hunt. A topologia em árvore proposta pelo Treasure Hunt garante a rápida propagação da informação pelos nós, ao mesmo tempo em que provê simutaneamente explorações (pelos nós-pai) e intensificações (pelos nós-filho), em vários níveis de granularidade, independentemente do número de nós na árvore. O Treasure Hunt tem boa tolerância à falhas e está parcialmente preparado para uma total tolerância à falhas. Como parte dos métodos desenvolvidos durante este trabalho, um método automatizado de Particionamento Iterativo foi proposto para controlar o balanceamento entre explorações e intensificações ao longo da busca. Uma Modelagem de Estabilização de Convergência para operar em modo Online também foi proposto, com o objetivo de encontrar pontos de parada com bom custo/benefício para os algoritmos de otimização que executam dentro das instâncias do Treasure Hunt. Experimentos em benchmarks clássicos, aleatórios e de competição, de vários tamanhos e complexidades, usando os algoritmos de busca PSO, DE e CCPSO2, mostram que o Treasure Hunt melhora as características inerentes destes algoritmos de busca. O Treasure Hunt faz com que os algoritmos de baixa performance se tornem comparáveis aos de boa performance, e os algoritmos de boa performance possam estender seus limites até problemas maiores. Experimentos distribuindo instâncias do Treasure Hunt, em uma rede cooperativa de até 160 processos, demonstram a escalabilidade robusta do framework, apresentando melhoras nos resultados mesmo quando o tempo de processamento é fixado (wall-clock) para todas as instâncias distribuídas do Treasure Hunt. Resultados demonstram que o mecanismo de amostragem fornecido pelo Treasure Hunt, aliado à maior cooperação entre as múltiplas populações em evolução, reduzem a necessidade de grandes populações e de algoritmos de busca complexos. Isto é especialmente importante em problemas de mundo real que possuem funções de fitness muito custosas. Palavras-chave: Inteligência artificial. Métodos de otimização. Algoritmos distribuídos. Modelagem de convergência. Alta dimensionalidade.Abstract: This work proposes a multilevel framework called Treasure Hunt, which is capable of distributing independent search algorithms to a large number of processing nodes. Aiming to obtain joint convergences between working nodes, Treasure Hunt proposes a driving mechanism that smoothly controls the cooperation between the multiple independent Treasure Hunt instances. The tree topology proposed by Treasure Hunt ensures quick propagation of information, while providing simultaneous explorations (by parents) and exploitations (by children), on several levels of granularity, regardless the number of nodes in the tree. Treasure Hunt has good fault tolerance and is partially prepared to full fault tolerance. As part of the methods developed during this work, an automated Iterative Partitioning method is proposed to control the balance between exploration and exploitation as the search progress. A Convergence Stabilization Modeling to operate in Online mode is also proposed, aiming to find good cost/benefit stopping points for the optimization algorithms running within the Treasure Hunt instances. Experiments on classic, random and competition benchmarks of various sizes and complexities, using the search algorithms PSO, DE and CCPSO2, show that Treasure Hunt boosts the inherent characteristics of these search algorithms. Treasure Hunt makes algorithms with poor performances to become comparable to good ones, and algorithms with good performances to be capable of extending their limits to larger problems. Experiments distributing Treasure Hunt instances in a cooperative network up to 160 processes show the robust scaling of the framework, presenting improved results even when fixing a wall-clock time for the instances. Results show that the sampling mechanism provided by Treasure Hunt, allied to the increased cooperation between multiple evolving populations, reduce the need for large population sizes and complex search algorithms. This is specially important on real-world problems with time-consuming fitness functions. Keywords: Artificial intelligence. Optimization methods. Distributed algorithms. Convergence modeling. High dimensionality

Optimisation de la planification court-terme d’un système de production hydroélectrique de grande taille

RÉSUMÉ: La planification de la production hydroélectrique vise à optimiser l’utilisation future d’un ensemble de centrales, afin de maximiser son efficacité tout en satisfaisant la charge électrique et de très nombreuses contraintes opérationnelles. A court terme, l’horizon étudié est typiquement de 7 à 15 jours au pas de temps horaire. Les décisions concernent l’état de fonctionnement de chaque groupe turbine-alternateur dans les centrales, les débits turbinés par les groupes en fonctionnement et les débits déversés par les ouvrages d’évacuation. Les contraintes opérationnelles se rapportent notamment à la sécurité des équipements et des personnes, à la fiabilité du système de production en énergie, en puissance et en transport, aux maintenances des équipements, aux transactions sur le marché de l’énergie et aux accords touristiques et environnementaux. Ces contraintes proviennent de très nombreux agents avec des objectifs parfois contradictoires. Ce problème est complexe à résoudre, car il est combinatoire et de très grande taille. De plus, les vallées hydrauliques lient les décisions dans le temps et dans l’espace. Il existe de très nombreuses méthodes de résolution pour ce problème, mais aucune ne permet de résoudre des problèmes réels de grande taille dans des temps opérationnels. L’objectif de cette thèse est de développer des méthodes de résolution rapides et précises pour des systèmes de production de grande taille, comme celui d’Hydro-Québec. Afin de répondre à cet objectif, nous proposons trois modèles et méthodes de résolution qui exploitent la structure du problème de planification court-terme dans chacun de ses contextes d’utilisation. La première méthode de résolution est dédiée aux analyses d’impact, qui permettent aux planificateurs d’évaluer le coût d’une décision de gestion. Les décisions évaluées sont par exemple des retraits d’équipement pour maintenance. La méthode de résolution doit fournir des solutions quasi optimales, ainsi qu’une mesure de la distance à la solution optimale. Nous avons donc développé un modèle de programmation linéaire en nombres entiers (PLNE) ainsi qu’une méthode de décomposition qui tire parti du petit nombre de contraintes liantes entre les vallées hydrauliques. Le système de production est partitionné en sous-systèmes géographiques, sans restriction sur la partition. La méthode de résolution est basée sur la relaxation lagrangienne et se déroule en trois phases. Tout d’abord, la relaxation linéaire est résolue, afin d’estimer la valeur duale des contraintes liant les sous-systèmes. Ensuite, les sousproblèmes de planification associés aux sous-systèmes sont résolus en conservant les variables entières. Enfin, le problème global est résolu en fixant les variables entières avec les résultats obtenus dans la résolution des sous-problèmes. De plus, la valeur de la relaxation linéair permet de calculer une borne sur l’écart à la solution optimale. Les résultats numériques montrent que notre méthode fournit des solutions extrêmement proches de l’optimum dans des temps opérationnels. La deuxième méthode vise à ajuster rapidement un plan de production suite à une perturbation dans les intrants. L’objectif est ici de permettre aux planificateurs de valider rapidement la faisabilité du plan de production moyen-terme en considérant toutes les contraintes opérationnelles. Nous proposons un modèle mathématique précis et une méthode de résolution basée sur la recherche tabou. Afin de rendre la recherche efficace, nous avons développé de nouveaux voisinages larges qui exploitent les écarts entre l’offre et la demande, ainsi que la configuration des centrales dans les vallées. De plus, nous avons décomposé l’horizon par journée pour paralléliser la recherche tabou. Ce parallélisme permet de gérer de longs horizons, ce qui est essentiel pour attacher la planification court-terme aux décisions prises à moyen terme. Nous avons comparé notre méthode à un modèle de PLNE résolu avec un solveur générique. Même avec la solution initiale la plus naïve, notre recherche tabou parvient à des solutions proches de l’optimum dans des temps opérationnels, et jusqu’à 235 fois plus vite qu’un solveur générique. La troisième méthode considère le processus opérationnel de planification court-terme à Hydro-Québec, qui a pour but de fournir des consignes de production aux répartiteurs. Afin de gérer l’incertitude sur les intrants, les planificateurs fournissent des règles de gestion plutôt qu’un plan de production. Nous avons donc développé une nouvelle forme de règles de gestion, adaptée aux vallées hydrauliques complexes et aux réservoirs très contraints. Ces règles sont évaluées sur un arbre de scénarios, représentant l’incertitude sur les apports en eau et la charge électrique. Nous avons optimisé l’ordre d’engagement des centrales défini dans ces règles à l’aide d’une recherche tabou. De plus, nous avons étudié la nécessité de prendre en compte cette incertitude dans l’optimisation. Les résultats numériques montrent que l’optimisation stochastique permet de réduire significativement la valeur objectif de la solution. Afin de répondre aux contraintes de temps opérationnelles, nous proposons une optimisation hybride : déterministe durant les premières itérations de la recherche tabou, puis stochastique. Cette méthode hybride permet d’améliorer la valeur objective moyenne de 10% lorsque les apports prévus sont moyens ou élevés.----------ABSTRACT: Hydropower production planning aims at determining the future use of a set of hydro plants to maximize their efficiency, while satisfying the electrical load and a large number of operational constraints. At short-term, the horizon ranges from 7 to 15 days with hourly time steps. Decisions concern the operating status of each generating unit in hydro plants, the turbined flow in the functioning units, and the spilled flow in spillways. Operational constraints involve for instance safety of equipment and people, reliability of the production system, regulations on environment and tourism, equipment maintenance and transactions in the energy market. All these constraints are requests from many stakeholders with sometimes contradictory objectives. The short-term hydropower production planning is hard to solve, because it is of large scale and combinatorial. Moreover, hydro-valleys link decision variables both in time and space. One can find many solution approaches in the literature, but they are not adapted to realworld large-scale production systems. The purpose of this thesis is to develop fast and accurate solution approaches for large-scale hydropower production systems, in particular Hydro-Québec’s. We propose two new models and three new solution methods, which exploit the problem structure in each context of use. The first approach is dedicated to impact analysis. Planners make this type of analysis to evaluate the cost of a given decision, for example the some equipment outage for maintenance. Therefore, the solution approach must provide near-optimal solutions and a measure of the gap to the optimum. We developed a new mixed-integer linear problem (MILP) and a new solution method. Our three-phase method approach exploits the small number of constraints between hydro valleys and is based on lagrangian decomposition. First, we solve the linear relaxation of the problem to estimate the dual value of the linking constraints. Then, the production system is partitioned into subsystems and the associated MILP subproblems are solved. Finally, the initial planning problem is solved with the commitment decisions fixed as in the subproblems solutions. Numerical experiments show that our solution approach leads to near-optimal solutions within operational computation time. The second approach aims at quickly adjusting a given production planning after some perturbation in the data. Short-term planners will then be able to quickly validate the feasibility of the medium-term planning decisions while considering all operational constraints. We developed a new non-restrictive mathematical model and a solution method based on tabu search. To find good solutions quickly, we proposed new neighborhoods which consider the current solution flexibility to satisfy the total load and reservoir volume bounds. Moreover, tabu search is performed in parallel for each day of the horizon. Hence, our approach can handle a long horizon. We compared our method with a classical MILP approach. Even with the most naive initial solution, our tabu search obtain solutions close to the optimum within operational time. The third approach concerns the operational planning process from the short term to real time at Hydro-Québec. Short-term planners must provide daily instructions to real-time operators. To tackle uncertainty, planners provide operating rules instead of production schedules. We developed a new form of operating rules specially designed to handle large hydropower production systems with complex hydro-valleys and tightly bounded reservoirs. These rules are evaluated on a scenario tree, representing uncertain water inflows and electrical load, and optimized in a tabu search framework. We also evaluated the value of stochastic optimization for operating rules. Numerical results show that stochastic optimization has a significant value on scenarios with moderate or high inflows. However, it must be coupled with deterministic optimization to obtain good solutions when computational time is limited

Metaheuristic optimization of power and energy systems: underlying principles and main issues of the 'rush to heuristics'

In the power and energy systems area, a progressive increase of literature contributions containing applications of metaheuristic algorithms is occurring. In many cases, these applications are merely aimed at proposing the testing of an existing metaheuristic algorithm on a specific problem, claiming that the proposed method is better than other methods based on weak comparisons. This 'rush to heuristics' does not happen in the evolutionary computation domain, where the rules for setting up rigorous comparisons are stricter, but are typical of the domains of application of the metaheuristics. This paper considers the applications to power and energy systems, and aims at providing a comprehensive view of the main issues concerning the use of metaheuristics for global optimization problems. A set of underlying principles that characterize the metaheuristic algorithms is presented. The customization of metaheuristic algorithms to fit the constraints of specific problems is discussed. Some weaknesses and pitfalls found in literature contributions are identified, and specific guidelines are provided on how to prepare sound contributions on the application of metaheuristic algorithms to specific problems

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

Efficient methods for solving power system operation scheduling challenges: the thermal unit commitment problem with staircase cost and the very short-term load forecasting problem

This dissertation addresses two crucial power system operational scheduling aspects: the thermal unit commitment problem and real-time load demand forecasting. These two are important challenges that need the development of models and efficient algorithms. To tackle the generator scheduling problem, we propose and develop five matheuristic methods, including four variations of local branching (LB) and one using kernel search (KS). Additionally, we have introduced a novel constructive approach named HARDUC, which effectively generates high-quality initial solutions for the matheuristic methods. To assess the effectiveness of the proposed matheuristic algorithms, tests were con ducted on instances simulating scenarios where an analyst must deliver a generation sched ule within one or two hours. A comparison with CPLEX, an off-the-shelf solver, under two scenarios (i) using the solver from scratch and (ii) using the solver with an initial feasible solution from the heuristic, revealed interesting insights. For small instances, the off-the-shelf solver outperformed the matheuristic methods. However, in medium-sized instances, the solver sometimes struggled to find a feasible solution. When solutions were found, there were no significant differences in performance between the solver and the methods. However, the proposed methods excelled and achieved remarkable results for large instances where the solver left many instances unsolved. Furthermore, we tested the proposed constructive method by comparing it with the best UCP constructive method from the literature. The results, supported by statistical tests, indicate the superiority of our proposed method. Our implementation of the KS algo rithm outperformed both the solver and the LB method in terms of relative optimality gap, especially in challenging instances. This discovery is significant as it reveals tremendous potential in utilizing KS for solving the UCP, paving the way for further research. As expected, as complexity increased, matheuristic methods outperformed the solver, delivering quicker, more e↵ective solutions. Matheuristics have a proven track record and are incorporated into commercial solvers for efficient solutions in mixed-integer linear programming problems. In our research, we customized matheuristics for the termal UCP by identifying dominant variables and addressing implementation challenges of the KS method, improving its efficacy. In addition, we introduced a novel method called the Analogue with Moving Av erage (AnMA) approach in very short-term load demand forecasting. AnMA exploits the seasonal characteristics of load demand time series by selecting the most correlated days. Its adaptability to real-time data positions it as an ideal choice for accommodating new demand patterns, rectifying biases, and enhancing accuracy. AnMA was compared against other methods recognized for their efficency and precision in the literature. The results showcased AnMA’s superiority, outperforming naive algorithms and exponential smoothing methods in accuracy, computational speed, and cost-e↵ectiveness. Addition ally, AnMA achieved comparable accuracy to ARIMA models while requiring significantly fewer computational resources and less time. Our research addresses critical challenges in power system operational scheduling, highlighting the e↵ectiveness of tailored methods that align with problem-specific char acteristics. These findings hold practical significance for the electricity industry, as our approach leverages a profound understanding of problem characteristics to improve opera tional scheduling. The success of our methods could potentially guide the development of future hybrid heuristic approaches combining mixed-integer programming or matheuris tics alongside analogy-based forecasting techniques, o↵ering substantial practical advance ments in the electricity sector

Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject