Methods for integrating machine learning and constrained optimization

In the framework of industrial problems, the application of Constrained Optimization is known to have overall very good modeling capability and performance and stands as one of the most powerful, explored, and exploited tool to address prescriptive tasks. The number of applications is huge, ranging from logistics to transportation, packing, production, telecommunication, scheduling, and much more. The main reason behind this success is to be found in the remarkable effort put in the last decades by the OR community to develop realistic models and devise exact or approximate methods to solve the largest variety of constrained or combinatorial optimization problems, together with the spread of computational power and easily accessible OR software and resources. On the other hand, the technological advancements lead to a data wealth never seen before and increasingly push towards methods able to extract useful knowledge from them; among the data-driven methods, Machine Learning techniques appear to be one of the most promising, thanks to its successes in domains like Image Recognition, Natural Language Processes and playing games, but also the amount of research involved. The purpose of the present research is to study how Machine Learning and Constrained Optimization can be used together to achieve systems able to leverage the strengths of both methods: this would open the way to exploiting decades of research on resolution techniques for COPs and constructing models able to adapt and learn from available data. In the first part of this work, we survey the existing techniques and classify them according to the type, method, or scope of the integration; subsequently, we introduce a novel and general algorithm devised to inject knowledge into learning models through constraints, Moving Target. In the last part of the thesis, two applications stemming from real-world projects and done in collaboration with Optit will be presented

Algoritmos evolutivos para alguns problemas em telecomunicações

Orientadores: Flavio Keidi Miyazawa, Mauricio Guilherme de Carvalho ResendeTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Nos últimos anos, as redes de telecomunicação tem experienciado um grande aumento no fluxo de dados. Desde a utilização massiva de vídeo sob demanda até o incontável número de dispositivos móveis trocando texto e vídeo, o tráfego alcançou uma escala capaz de superar a capacidade das redes atuais. Portanto, as companhias de telecomunicação ao redor do mundo tem sido forçadas a aumentar a capacidade de suas redes para servir esta crescente demanda. Como o custo de instalar uma infraestrutura de rede é geralmente muito grande, o projeto de redes usa fortemente ferramentas de otimização para manter os custos tão baixos quanto possível. Nesta tese, nós analisamos vários aspectos do projeto e implementação de redes de telecomunicação. Primeiramente, nós apresentamos um novo problema de projeto de redes usado para servir demandas sem fio de dispositivos móveis e rotear tal tráfego para a rede principal. Tais redes de acesso são baseadas em tecnologias sem fio modernos como Wi-Fi, LTE e HSPA. Este problema consideramos várias restrições reais e é difícil de ser resolvido. Nós estudamos casos reais nas vizinhanças de uma grande cidade nos Estados Unidos. Em seguida, nós apresentamos uma variação do problema de localização de hubs usado para modelar as redes principais (backbones ou laços centrais). Este problema também pode ser utilizado para modelar redes de transporte de cargas e passageiros. Nós também estudamos o problema de clusterização correlacionada com sobreposições usado para modelar o comportamento dos usuários quando utilizam seus equipamentos móveis. Neste problema, nós podemos rotular um objeto usando múltiplos rótulos e analisar a conexão entre eles. Este problema é adequado para análise de mobilidade de equipamentos que pode ser usada para estimar o tráfego em uma dada região. E finalmente, nós analisamos o licenciamento de espectro sobre uma perspectiva governamental. Nestes casos, uma agência do governo deseja vender licenças para companhias de telecomunicação para que operem em uma dada faixa de espectro. Este processo usualmente é conduzido usando leilões combinatoriais. Para todos problemas, nós propomos algoritmos genéticos de chaves aleatórias viciadas e modelos de programação linear inteira mista para resolvê-los (exceto para o problema de clusterização correlacionada com sobreposição, devido sua natureza não-linear). Os algoritmos que propusemos foram capazes de superar algoritmos do estado da arte para todos problemasAbstract: Cutting and packing problems are common problems that occur in many industry and business process. Their optimized resolution leads to great profits in several sectors. A common problem, that occur in textil and paper industries, is to cut a strip of some material to obtain several small items, using the minimum length of material. This problem, known by Two Dimensional Strip Packing Problem (2SP), is a hard combinatorial optimization problem. In this work, we present an exact algorithm to 2SP, restricted to two staged cuts (known by Two Dimensional Level Strip Packing, 2LSP). The algorithm uses the branch-and-price technique, and heuristics based on approximation algorithms to obtain upper bounds. The algorithm obtained optimal or almost optimal for small and moderate sized instancesAbstract: In last twenty years, telecommunication networks have experienced a huge increase in data utilization. From massive on-demand video to uncountable mobile devices exchanging text and video, traffic reached scales that overcame the network capacities. Therefore, telecommunication companies around the world have been forced to increase their capacity to serve this increasing demand. As the cost to deploy network infrastructure is usually very large, the design of a network heavily uses optimization tools to keep costs as low as possible. In this thesis, we analyze several aspects of the design and deployment of communication networks. First, we present a new network design problem used to serve wireless demands from mobile devices and route the traffic to the core network. Such access networks are based on modern wireless access technologies such as Wi-Fi, LTE, and HSPA. This problem has several real world constraints and it is hard to solve. We study real cases of the vicinity of a large city in the United States. Following, we present a variation of the hub-location problem used to model these core networks. Such problem is also suitable to model transportation networks. We also study the overlapping correlation clustering problem used to model the user's behavior when using their mobile devices. In such problem, one can label an object with multiple labels and analyzes the connections between them. Although this problem is very generic, it is suitable to analyze device mobility which can be used to estimate traffic in geographical regions. Finally, we analyze spectrum licensing from a governmental perspective. In these cases, a governmental agency wants to sell rights for telecommunication companies to operate over a given spectrum range. This process usually is conducted using combinatorial auctions. For all problems we propose biased random-key genetic algorithms and mixed integer linear programming models (except in the case of the overlapping correlation clustering problem due its non-linear nature). Our algorithms were able to overcome the state of the art algorithms for all problemsDoutoradoCiência da ComputaçãoDoutor em Ciência da Computaçã

Xqx Based Modeling For General Integer Programming Problems

We present a new way to model general integer programming (IP) problems with in- equality and equality constraints using XQX. We begin with the definition of IP problems folloby their practical applications, and then present the existing XQX based models to handle such problems. We then present our XQX model for general IP problems (including binary IP) with equality and inequality constraints, and also show how this model can be applied to problems with just inequality constraints. We then present the local optima based solution procedure for our XQX model. We also present new theorems and their proofs for our XQX model. Next, we present a detailed literature survey on the 0-1 multidimensional knapsack problem (MDKP) and apply our XQX model using our simple heuristic procedure to solve benchmark problems. The 0-1 MDKP is a binary IP problem with inequality con- straints and variables with binary values. We apply our XQX model using a heuristics we developed on 0-1 MDKP problems of various sizes and found that our model can handle any problem sizes and can provide reasonable quality results in reasonable time. Finally, we apply our XQX model developed for general integer programming problems on the general multi-dimensional knapsack problems. The general MDKP is a general IP problem with inequality constraints where the variables are positive integers. We apply our XQX model on GMDKP problems of various sizes and find that it can provide reasonable quality results in reasonable time. We also find that it can handle problems of any size and provide fea- sible and good quality solutions irrespective of the starting solutions. We conclude with a discussion of some issues related with our XQX model

Algorithm Engineering für einige komplexe PraxisproblemeExakte Verfahren, Heuristiken und hybride evolutionäre Algorithmen

This work deals with the design of exact algorithms and heuristics for complex optimization problems that origin from three practical applications and one classical combinatorial task. We obtain exact algorithms by modeling our problems in terms of mathematical optimization problems and applying suitable software tools to solve this models. Because of the complexity of our problems, exact algorithms cannot solve large instances within adequate time. Therefore, on the one hand, we derive efficient heuristics by adapting algorithms for similar mathematical problems in a suitable manner. On the other hand, evolutionary algorithms have shown to be successfully applicable to many hard mathematical problems. For that reason, we experimentally determine appropriate EA frameworks, hybridizing the evolutionary operators with our problem specific heuristics.Diese Arbeit befasst sich mit dem Entwurf von exakten und heuristischen Lösungsverfahren für schwere Optimierungsprobleme, die aus drei praktischen Anwendungen und einer klassischen kombinatorischen Fragestellung stammen. Exakte Verfahren bekommen wir durch die Modellierung als mathematische Optimierungsprobleme und die Anwendung geeigneter Software für deren Lösung. Da die Komplexität der behandelten Probleme das exakte Lösen großer Instanzen in adäquater Zeit verbietet, werden zum Einen effiziente Heuristiken durch geeignete Erweiterungen bekannter Verfahren für verwandte mathematische Probleme der vorliegenden Praxisaufgaben gewonnen. Zum Anderen haben sich evolutionäre Algorithmen sehr erfolgreich bei der Bewältigung vieler mathematisch schwerer Optimierungsprobleme gezeigt. Daher werden experimentell geeignete EA-Rahmenwerke für die gegebenen Problemstellungen ermittelt und mit den zuvor gewonnenen Heuristiken hybridisiert

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

Incorporating Memory and Learning Mechanisms Into Meta-RaPS

Due to the rapid increase of dimensions and complexity of real life problems, it has become more difficult to find optimal solutions using only exact mathematical methods. The need to find near-optimal solutions in an acceptable amount of time is a challenge when developing more sophisticated approaches. A proper answer to this challenge can be through the implementation of metaheuristic approaches. However, a more powerful answer might be reached by incorporating intelligence into metaheuristics. Meta-RaPS (Metaheuristic for Randomized Priority Search) is a metaheuristic that creates high quality solutions for discrete optimization problems. It is proposed that incorporating memory and learning mechanisms into Meta-RaPS, which is currently classified as a memoryless metaheuristic, can help the algorithm produce higher quality results. The proposed Meta-RaPS versions were created by taking different perspectives of learning. The first approach taken is Estimation of Distribution Algorithms (EDA), a stochastic learning technique that creates a probability distribution for each decision variable to generate new solutions. The second Meta-RaPS version was developed by utilizing a machine learning algorithm, Q Learning, which has been successfully applied to optimization problems whose output is a sequence of actions. In the third Meta-RaPS version, Path Relinking (PR) was implemented as a post-optimization method in which the new algorithm learns the good attributes by memorizing best solutions, and follows them to reach better solutions. The fourth proposed version of Meta-RaPS presented another form of learning with its ability to adaptively tune parameters. The efficiency of these approaches motivated us to redesign Meta-RaPS by removing the improvement phase and adding a more sophisticated Path Relinking method. The new Meta-RaPS could solve even the largest problems in much less time while keeping up the quality of its solutions. To evaluate their performance, all introduced versions were tested using the 0-1 Multidimensional Knapsack Problem (MKP). After comparing the proposed algorithms, Meta-RaPS PR and Meta-RaPS Q Learning appeared to be the algorithms with the best and worst performance, respectively. On the other hand, they could all show superior performance than other approaches to the 0-1 MKP in the literature

A review on the self and dual interactions between machine learning and optimisation

Machine learning and optimisation are two growing fields of artificial intelligence with an enormous number of computer science applications. The techniques in the former area aim to learn knowledge from data or experience, while the techniques from the latter search for the best option or solution to a given problem. To employ these techniques automatically and effectively aligning with the real aim of artificial intelligence, both sets of techniques are frequently hybridised, interacting with each other and themselves. This study focuses on such interactions aiming at (1) presenting a broad overview of the studies on self and dual interactions between machine learning and optimisation; (2) providing a useful tutorial for researchers and practitioners in both fields in support of collaborative work through investigation of the recent advances and analyses of the advantages and disadvantages of different techniques to tackle the same or similar problems; (3) clarifying the overlapping terminologies having different meanings used in both fields; (4) identifying research gaps and potential research directions

MATHEMATICAL PROGRAMMING ALGORITHMS FOR TRANSPORTATION PROBLEMS

The thesis deals with the study of transportation problems, and in particular focuses on developing new exact and heuristic algorithms for two interesting variants of the well known Vehicle Routing Problem: the multi-depot heterogeneous-fleet vehicle routing problem with time windows and the multi-depot heterogeneous-fleet pickup and delivery problem with soft time windows. The studied problems consider additional real-world requirements, often neglected in the literature. They lead to more involved problems but on the other hand more realistic ones, that call for powerful optimization methods in order to tackle such difficult applications. The proposed algorithms are based on mathematical programming techniques, such as branch-and-price, column generation and dynamic programming. The performance of the algorithms is analyzed with extensive computational experiments and compared with the most effective algorithms from the literature, showing the usefulness of the proposed methods

Multi-stage stochastic optimization and reinforcement learning for forestry epidemic and covid-19 control planning

This dissertation focuses on developing new modeling and solution approaches based on multi-stage stochastic programming and reinforcement learning for tackling biological invasions in forests and human populations. Emerald Ash Borer (EAB) is the nemesis of ash trees. This research introduces a multi-stage stochastic mixed-integer programming model to assist forest agencies in managing emerald ash borer insects throughout the U.S. and maximize the public benets of preserving healthy ash trees. This work is then extended to present the first risk-averse multi-stage stochastic mixed-integer program in the invasive species management literature to account for extreme events. Significant computational achievements are obtained using a scenario dominance decomposition and cutting plane algorithm.The results of this work provide crucial insights and decision strategies for optimal resource allocation among surveillance, treatment, and removal of ash trees, leading to a better and healthier environment for future generations. This dissertation also addresses the computational difficulty of solving one of the most difficult classes of combinatorial optimization problems, the Multi-Dimensional Knapsack Problem (MKP). A novel 2-Dimensional (2D) deep reinforcement learning (DRL) framework is developed to represent and solve combinatorial optimization problems focusing on MKP. The DRL framework trains different agents for making sequential decisions and finding the optimal solution while still satisfying the resource constraints of the problem. To our knowledge, this is the first DRL model of its kind where a 2D environment is formulated, and an element of the DRL solution matrix represents an item of the MKP. Our DRL framework shows that it can solve medium-sized and large-sized instances at least 45 and 10 times faster in CPU solution time, respectively, with a maximum solution gap of 0.28% compared to the solution performance of CPLEX. Applying this methodology, yet another recent epidemic problem is tackled, that of COVID-19. This research investigates a reinforcement learning approach tailored with an agent-based simulation model to simulate the disease growth and optimize decision-making during an epidemic. This framework is validated using the COVID-19 data from the Center for Disease Control and Prevention (CDC). Research results provide important insights into government response to COVID-19 and vaccination strategies

Of keyboards and beyond - optimization in human-computer interaction

In this thesis, we present optimization frameworks in the area of Human-Computer Interaction. At first, we discuss keyboard layout problems with a special focus on a project we participated in, which aimed at designing the new French keyboard standard. The special nature of this national-scale project and its optimization ingredients are discussed in detail; we specifically highlight our algorithmic contribution to this project. Exploiting the special structure of this design problem, we propose an optimization framework that was efficiently computes keyboard layouts and provides very good optimality guarantees in form of tight lower bounds. The optimized layout that we showed to be nearly optimal was the basis of the new French keyboard standard recently published in the National Assembly in Paris. Moreover, we propose a relaxation for the quadratic assignment problem (a generalization of keyboard layouts) that is based on semidefinite programming. In a branch-and-bound framework, this relaxation achieves competitive results compared to commonly used linear programming relaxations for this problem. Finally, we introduce a modeling language for mixed integer programs that especially focuses on the challenges and features that appear in participatory optimization problems similar to the French keyboard design process.Diese Arbeit behandelt Ansätze zu Optimierungsproblemen im Bereich Human-Computer Interaction. Zuerst diskutieren wir Tastaturbelegungsprobleme mit einem besonderen Fokus auf einem Projekt, an dem wir teilgenommen haben: die Erstellung eines neuen Standards für die französische Tastatur. Wir gehen auf die besondere Struktur dieses Problems und unseren algorithmischen Beitrag ein: ein Algorithmus, der mit Optimierungsmethoden die Struktur dieses speziellen Problems ausnutzt. Mithilfe dieses Algorithmus konnten wir effizient Tastaturbelegungen berechnen und die Qualität dieser Belegungen effektiv (in Form von unteren Schranken) nachweisen. Das finale optimierte Layout, welches mit unserer Methode bewiesenermaßen nahezu optimal ist, diente als Grundlage für den kürzlich in der französischen Nationalversammlung veröffentlichten neuen französischen Tastaturstandard. Darüberhinaus beschreiben wir eine Relaxierung für das quadratische Zuweisungsproblem (eine Verallgemeinerung des Tastaturbelegungsproblems), die auf semidefinieter Programmierung basiert. Wir zeigen, dass unser Algorithmus im Vergleich zu üblich genutzten linearen Relaxierung gut abschneidet. Abschließend definieren und diskutieren wir eine Modellierungssprache für gemischt integrale Programme. Diese Sprache ist speziell auf die besonderen Herausforderungen abgestimmt, die bei interaktiven Optimierungsproblemen auftreten, welche einen ähnlichen Charakter haben wie der Prozess des Designs der französischen Tastatur