Distributed Domain Propagation

Portfolio parallelization is an approach that runs several solver instances in parallel and terminates when one of them succeeds in solving the problem. Despite its simplicity, portfolio parallelization has been shown to perform well for modern mixed-integer programming (MIP) and boolean satisfiability problem (SAT) solvers. Domain propagation has also been shown to be a simple technique in modern MIP and SAT solvers that effectively finds additional domain reductions after the domain of a variable has been reduced. In this paper we introduce distributed domain propagation, a technique that shares bound tightenings across solvers to trigger further domain propagations. We investigate its impact in modern MIP solvers that employ portfolio parallelization. Computational experiments were conducted for two implementations of this parallelization approach. While both share global variable bounds and solutions, they communicate differently. In one implementation the communication is performed only at designated points in the solving process and in the other it is performed completely asynchronously. Computational experiments show a positive performance impact of communicating global variable bounds and provide valuable insights in communication strategies for parallel solvers

Large-scale parallelism for constraint-based local search: the costas array case study

International audienceWe present the parallel implementation of a constraint-based Local Search algorithm and investigate its performance on several hardware plat-forms with several hundreds or thousands of cores. We chose as the basis for these experiments the Adaptive Search method, an efficient sequential Local Search method for Constraint Satisfaction Problems (CSP). After preliminary experiments on some CSPLib benchmarks, we detail the modeling and solving of a hard combinatorial problem related to radar and sonar applications: the Costas Array Problem. Performance evaluation on some classical CSP bench-marks shows that speedups are very good for a few tens of cores, and good up to a few hundreds of cores. However for a hard combinatorial search problem such as the Costas Array Problem, performance evaluation of the sequential version shows results outperforming previous Local Search implementations, while the parallel version shows nearly linear speedups up to 8,192 cores. The proposed parallel scheme is simple and based on independent multi-walks with no communication between processes during search. We also investigated a cooperative multi-walk scheme where processes share simple information, but this scheme does not seem to improve performance

On High-Performance Benders-Decomposition-Based Exact Methods with Application to Mixed-Integer and Stochastic Problems

RÉSUMÉ : La programmation stochastique en nombres entiers (SIP) combine la difficulté de l’incertitude et de la non-convexité et constitue une catégorie de problèmes extrêmement difficiles à résoudre. La résolution efficace des problèmes SIP est d’une grande importance en raison de leur vaste applicabilité. Par conséquent, l’intérêt principal de cette dissertation porte sur les méthodes de résolution pour les SIP. Nous considérons les SIP en deux étapes et présentons plusieurs algorithmes de décomposition améliorés pour les résoudre. Notre objectif principal est de développer de nouveaux schémas de décomposition et plusieurs techniques pour améliorer les méthodes de décomposition classiques, pouvant conduire à résoudre optimalement divers problèmes SIP. Dans le premier essai de cette thèse, nous présentons une revue de littérature actualisée sur l’algorithme de décomposition de Benders. Nous fournissons une taxonomie des améliorations algorithmiques et des stratégies d’accélération de cet algorithme pour synthétiser la littérature et pour identifier les lacunes, les tendances et les directions de recherche potentielles. En outre, nous discutons de l’utilisation de la décomposition de Benders pour développer une (méta- )heuristique efficace, décrire les limites de l’algorithme classique et présenter des extensions permettant son application à un plus large éventail de problèmes. Ensuite, nous développons diverses techniques pour surmonter plusieurs des principaux inconvénients de l’algorithme de décomposition de Benders. Nous proposons l’utilisation de plans de coupe, de décomposition partielle, d’heuristiques, de coupes plus fortes, de réductions et de stratégies de démarrage à chaud pour pallier les difficultés numériques dues aux instabilités, aux inefficacités primales, aux faibles coupes d’optimalité ou de réalisabilité, et à la faible relaxation linéaire. Nous testons les stratégies proposées sur des instances de référence de problèmes de conception de réseau stochastique. Des expériences numériques illustrent l’efficacité des techniques proposées. Dans le troisième essai de cette thèse, nous proposons une nouvelle approche de décomposition appelée méthode de décomposition primale-duale. Le développement de cette méthode est fondé sur une reformulation spécifique des sous-problèmes de Benders, où des copies locales des variables maîtresses sont introduites, puis relâchées dans la fonction objective. Nous montrons que la méthode proposée atténue significativement les inefficacités primales et duales de la méthode de décomposition de Benders et qu’elle est étroitement liée à la méthode de décomposition duale lagrangienne. Les résultats de calcul sur divers problèmes SIP montrent la supériorité de cette méthode par rapport aux méthodes classiques de décomposition. Enfin, nous étudions la parallélisation de la méthode de décomposition de Benders pour étendre ses performances numériques à des instances plus larges des problèmes SIP. Les variantes parallèles disponibles de cette méthode appliquent une synchronisation rigide entre les processeurs maître et esclave. De ce fait, elles souffrent d’un important déséquilibre de charge lorsqu’elles sont appliquées aux problèmes SIP. Cela est dû à un problème maître difficile qui provoque un important déséquilibre entre processeur et charge de travail. Nous proposons une méthode Benders parallèle asynchrone dans un cadre de type branche-et-coupe. L’assouplissement des exigences de synchronisation entraine des problèmes de convergence et d’efficacité divers auxquels nous répondons en introduisant plusieurs techniques d’accélération et de recherche. Les résultats indiquent que notre algorithme atteint des taux d’accélération plus élevés que les méthodes synchronisées conventionnelles et qu’il est plus rapide de plusieurs ordres de grandeur que CPLEX 12.7.----------ABSTRACT : Stochastic integer programming (SIP) combines the difficulty of uncertainty and non-convexity, and constitutes a class of extremely challenging problems to solve. Efficiently solving SIP problems is of high importance due to their vast applicability. Therefore, the primary focus of this dissertation is on solution methods for SIPs. We consider two-stage SIPs and present several enhanced decomposition algorithms for solving them. Our main goal is to develop new decomposition schemes and several acceleration techniques to enhance the classical decomposition methods, which can lead to efficiently solving various SIP problems to optimality. In the first essay of this dissertation, we present a state-of-the-art survey of the Benders decomposition algorithm. We provide a taxonomy of the algorithmic enhancements and the acceleration strategies of this algorithm to synthesize the literature, and to identify shortcomings, trends and potential research directions. In addition, we discuss the use of Benders decomposition to develop efficient (meta-)heuristics, describe the limitations of the classical algorithm, and present extensions enabling its application to a broader range of problems. Next, we develop various techniques to overcome some of the main shortfalls of the Benders decomposition algorithm. We propose the use of cutting planes, partial decomposition, heuristics, stronger cuts, and warm-start strategies to alleviate the numerical challenges arising from instabilities, primal inefficiencies, weak optimality/feasibility cuts, and weak linear relaxation. We test the proposed strategies with benchmark instances from stochastic network design problems. Numerical experiments illustrate the computational efficiency of the proposed techniques. In the third essay of this dissertation, we propose a new and high-performance decomposition approach, called Benders dual decomposition method. The development of this method is based on a specific reformulation of the Benders subproblems, where local copies of the master variables are introduced and then priced out into the objective function. We show that the proposed method significantly alleviates the primal and dual shortfalls of the Benders decomposition method and it is closely related to the Lagrangian dual decomposition method. Computational results on various SIP problems show the superiority of this method compared to the classical decomposition methods as well as CPLEX 12.7. Finally, we study parallelization of the Benders decomposition method. The available parallel variants of this method implement a rigid synchronization among the master and slave processors. Thus, it suffers from significant load imbalance when applied to the SIP problems. This is mainly due to having a hard mixed-integer master problem that can take hours to be optimized. We thus propose an asynchronous parallel Benders method in a branchand- cut framework. However, relaxing the synchronization requirements entails convergence and various efficiency problems which we address them by introducing several acceleration techniques and search strategies. In particular, we propose the use of artificial subproblems, cut generation, cut aggregation, cut management, and cut propagation. The results indicate that our algorithm reaches higher speedup rates compared to the conventional synchronized methods and it is several orders of magnitude faster than CPLEX 12.7

Heuristinen yhteistyöhaku ohjelmistoagenttien avulla

Parallel algorithms extend the notion of sequential algorithms by permitting the simultaneous execution of independent computational steps. When the independence constraint is lifted and executions can freely interact and intertwine, parallel algorithms become concurrent and may behave in a nondeterministic way. Parallelism has over the years slowly risen to be a standard feature of high-performance computing, but concurrency, being even harder to reason about, is still considered somewhat notorious and undesirable. As such, the implicit randomness available in concurrency is rarely made use of in algorithms. This thesis explores concurrency as a means to facilitate algorithmic cooperation in a heuristic search setting. We use agents, cooperating software entities, to build a single-source shortest path (SSSP) search algorithm based on parallelized A∗, dubbed A!. We show how asynchronous information sharing gives rise to implicit randomness, which cooperating agents use in A! to maintain a collective secondary ranking heuristic and focus search space exploration. We experimentally show that A! consistently outperforms both vanilla A∗ and a noncooperative, explicitly randomized A∗ variant in the standard n-puzzle sliding tile problem context. The results indicate that A! performance increases with the addition of more agents, but that the returns are diminishing. A! is observed to be sensitive to heuristic improvement, but also constrained by search overhead from limited path diversity. A hybrid approach combining both implicit and explicit randomness is also evaluated and found to not be an improvement over A! alone. The studied A! implementation based on vanilla A∗ is not as such competitive against state-of-the-art parallel A∗ algorithms, but rather a first step in applying concurrency to speed up heuristic SSSP search. The empirical results imply that concurrency and nondeterministic cooperation can successfully be harnessed in algorithm design, inviting further inquiry into algorithms of this kind.Rinnakkaisalgoritmit sallivat useiden riippumattomien ohjelmakäskyjen suorittamisen samanaikaisesti. Kun riippumattomuusrajoite poistetaan ja käskyjen suorittamisen järjestystä ei hallita, rinnakkaisalgoritmit voivat käskysuoritusten samanaikaisuuden vuoksi käyttäytyä epädeterministisellä tavalla. Rinnakkaisuus on vuosien saatossa noussut tärkeään rooliin tietotekniikassa ja samalla hallitsematonta samanaikaisuutta on yleisesti alettu pitää ongelmallisena ja ei-toivottuna. Samanaikaisuudesta kumpuavaa epäsuoraa satunnaisuutta hyödynnetään harvoin algoritmeissa. Tämä työ käsittelee käskysuoritusten samanaikaisuuden hyödyntämistä osana heuristista yhteistyöhakua. Työssä toteutetaan agenttien, yhteistyökykyisten ohjelmistokomponenttien, avulla uudenlainen A!-hakualgoritmi. A! perustuu rinnakkaiseen A∗ -algoritmiin, joka ratkaisee yhden lähteen lyhimmän polun hakuongelman. Työssä näytetään, miten ajastamaton viestintä agenttien välillä johtaa epäsuoraan satunnaisuuteen, jota A!-agentit kollektiivisesti hyödyntävät toissijaisen järjestämisheuristiikan ylläpitämisessä ja edelleen haun kohdentamisessa. Työssä näytetään kokeellisesti, kuinka A! suoriutuu niin tavanomaista kuin satunnaistettuakin A∗ -algoritmia paremmin n-puzzle pulmapelin ratkaisemisessa. Tulokset osoittavat, että A!-algoritmin suorituskyky kasvaa lisäagenttien myötä, mutta myös sen, että hyöty on joka lisäyksen jälkeen suhteellisesti pienempi. A! osoittautuu heuristiikan hyödyntämisen osalta verrokkeja herkemmäksi, mutta myös etsintäpolkujen monimuotoisuuden kannalta vaatimattomaksi. Yksinkertaisen suoraa ja epäsuoraa satunnaisuutta yhdistävän hybridialgoritmin ei todeta tuovan lisäsuorituskykyä A!-algoritmiin verrattuna. Empiiriset kokeet osoittavat, että hallitsematonta samanaikaisuutta ja epädeterminististä yhteistyötä voi onnistuneesti hyödyntää algoritmisuunnittelussa, mikä kannustaa lisätutkimuksiin näitä soveltavan algoritmiikan parissa

Massivel y parallel declarative computational models

Current computer archictectures are parallel, with an increasing number of processors. Parallel programming is an error-prone task and declarative models such as those based on constraints relieve the programmer from some of its difficult aspects, because they abstract control away. In this work we study and develop techniques for declarative computational models based on constraints using GPI, aiming at large scale parallel execution. The main contributions of this work are: A GPI implementation of a scalable dynamic load balancing scheme based on work stealing, suitable for tree shaped computations and effective for systems with thousands of threads. A parallel constraint solver, MaCS, implemented to take advantage of the GPI programming model. Experimental evaluation shows very good scalability results on systems with hundreds of cores. A GPI parallel version of the Adaptive Search algorithm, including different variants. The study on different problems advances the understanding of scalability issues known to exist with large numbers of cores; ### SUMÁRIO: Actualmente as arquitecturas de computadores são paralelas, com um crescente número de processadores. A programação paralela é uma tarefa propensa a erros e modelos declarativos baseados em restrições aliviam o programador de aspectos difíceis dado que abstraem o controlo. Neste trabalho estudamos e desenvolvemos técnicas para modelos de computação declarativos baseados em restrições usando o GPI, uma ferramenta e modelo de programação recente. O Objectivo é a execução paralela em larga escala. As contribuições deste trabalho são as seguintes: a implementação de um esquema dinâmico para balanceamento da computação baseado no GPI. O esquema é adequado para computações em árvores e efectiva em sistemas compostos por milhares de unidades de computação. Uma abordagem à resolução paralela de restrições denominadas de MaCS, que tira partido do modelo de programação do GPI. A Avaliação experimental revelou boa escalabilidade num sistema com centenas de processadores. Uma versão paralela do algoritmo Adaptive Search baseada no GPI, que inclui diferentes variantes. O estudo de diversos problemas aumenta a compreensão de aspectos relacionados com a escalabilidade e presentes na execução deste tipo de algoritmos num grande número de processadores

Optimization of heterogeneous employee scheduling problems

RÉSUMÉ: Le problème de planification d’horaires du personnel consiste à créer les horaires de travail des employés d’une organisation. Le nombre d’employés requis par unité de temps, appelé la demande en employés par période, est donné pour un horizon de planification. Différentes règles et contraintes régissent l’élaboration des horaires des employés. Ces règles dépendent des besoins de l’organisation, des contrats des employés et de la convention collective de travail. Le problème de planification est dit hétérogène quand il concerne des employés ayant des qualifications différentes, habituellement, dans le cadre d’un problème de planification d’employés multi-tâches ou multi-départements. Dans un contexte multi-départements avec transferts entre départements, un quart de travail peut être effectué dans son ensemble dans un département, ou un transfert de département peut avoir lieu au sein du quart de travail lorsque l’employé a les qualifications requises. Lorsque les transferts sont autorisés, le nombre de quarts de travail possibles par employé devient énorme. L’optimisation d’un tel problème est souvent essentielle pour le succès de l’organisation. Par contre, sa résolution directe comme un programme linéaire en nombres entiers s’avère impossible pour les grandes instances. Dans la première partie de cette thèse, nous proposons une heuristique de décomposition en plusieurs phases (MP-DH) pour le problème de planification des employés avec transferts. Dans ce problème, la sous-couverture et la sur-couverture sont acceptées mais pénalisés dans la fonction objectif. Un département d’origine est introduit pour chaque employé où l’employé doit travailler la majorité de son temps. En plus, il/elle peut être qualifié(e) pour travailler dans plusieurs autres départements. La première phase commence par déduire la demande en employés qui ne peut pas être couverte par les employés du département. Ces pièces de demandes extraites sont appelées intervalles critiques, car elles nécessitent des employés transférés d’autres départements pour y travailler. Cela se fait en résolvant un programme en nombres entiers de planification d’horaires de personnel anonyme pour chaque département séparément, puis en extrayant la demande non-couverte qui définit un ensemble d’intervalles critiques. Pour chacun des intervalles critiques, la deuxième phase choisit un département qui lui attribue la responsabilité de transférer un de ses employés pour travailler pendant cet intervalle critique. Ceci est accompli en résolvant un autre programme en nombres entiers de planification d’horaires de personnel anonyme avec transferts, pour un seul jour, pour chacun des jours de l’horizon. La décomposition journalière rend la taille du problème gérable spécialement pour les grandes instances. Cette phase se termine par la migration de toute demande d’un département d1 couverte par un employé d’un département d2, formant la demande de transfert d’employé de d2 vers d1. Finalement, pour chaque département, la troisième phase résout un programme en nombres entiers de planification d’horaires de personnel mono-départemental avec transfert. La demande utilisée est la nouvelle demande résultant de la migration de toutes les demandes de transfert pendant la deuxième phase. L’heuristique MP-DH a réussi à décomposer le problème de planification d’employés multidépartements en plusieurs, plus petits, problèmes de planification d’employés mono départementaux, ce qui a permis de réduire de beaucoup les temps de calcul et de transformer les grandes instances non résolubles en instances résolubles avec une légère baisse dans la qualité des solutions obtenues. Chacune des trois phases de MP-DH utilise le parallélisme. Dans la première phase, les programmes en nombres entiers des départements s’optimisent en parallèle. La deuxième phase exécute chaque problème journalier en parallèle. Enfin, la troisième phase optimise chaque département en parallèle. À la fin de chaque phase, tous les résultats des problèmes parallèles sont fusionnés pour former la solution finale. Dans les tests réalisés pour l’heuristique MP-DH, les deux premières phases sont extrêmement rapides, tandis que la troisième phase peut atteindre deux heures de temps de résolution pour les grandes instances. Pour pallier à cet inconvénient, nous présentons une heuristique hybride dans la deuxième partie de la thèse, visant à réduire fortement le temps d’exécution de la troisième phase tout en conservant la qualité de la solution. L’heuristique hybride utilise deux modèles de manière interchangeable afin de résoudre la troisième phase le plus précisément et rapidement possible. Le premier modèle est celui déjà presenté pour la troisième phase du MP-DH que nous appelons le modèle de base. Le second est un problème de planification d’horaires du personnel mono-département avec transfert semi-anonyme que nous appelons le modèle semi-anonyme. La version semi-anonyme réduit le nombre d’employés pour lesquels les horaires sont optimisés et remplace les quarts des employés restants par un ensemble de quarts anonymes agrégés, puis résout le problème pour les employés restants par la suite. L’heuristique hybride commence par résoudre le modèle de base. Si après un délai donné, l’écart d’optimalité est supérieur à un seuil donné, la résolution de modèle de base est annulé et une version semi-anonyme est résolue. Cette opération est répétée jusqu’à ce que tous les horaires des employés soient optimisés. L’heuristique hybride a réussi à réduire le temps d’exécution de la troisième phase jusqu’à 87% en moyenne, tout en perdant seulement 4 % dans le coût de la solution en moyenne. Dans la troisième partie de la thèse, nous abordons une version différente du problème de planification d’horaires de personnel, soit le problème de planification d’horaires de personnel multi-tâches, où ni les transferts ni la sous-couverture ne sont autorisés. À la place de la sous-couverture, des quarts anonymes appelés open-shifts sont utilisés pour couvrir la demande incouvrable par aucun employé. Nous développons une métaheuristique parallèle de recherche à grands voisinage (LNS) pour ce problème. Le concept de sub-scope est utilisé comme unité de décomposition dans l’algorithme LNS. Un sub-scope est défini comme: un sous-ensemble d’employés, un sous-ensemble de tâches et un sous-ensemble continu de l’horizon du problème. L’heuristique LNS est définie par des procédures de destruction et de réparation. Notre procédure de destruction choisit des sub-scopes, entraînant un coût élevé, à détruire. Lorsqu’un sub-scope d’une solution est détruit, tous les quarts travaillés pendant l’horizon du sub-scope par un employé appartenant au sub-scope, pour l’une des tâches du sub-scope, sont supprimés de la solution. Les coûts principaux affectant la fonction objectif sont les suivants: le coût de la surcouverture, le coût d’utilisation des open-shifts et la pénalité pour la violation des heures de travail minimales des employés. La procédure de destruction se concentre donc sur la destruction des sub-scopes entraînant de tels coûts dans une solution donnée. Après la destruction des sub-scopes d’une solution, la procédure de réparation reconstruit une nouvelle solution améliorée. La procédure de réparation que nous proposons résout un programme en nombres entiers de planification d’horaires de personnel multi-tâches pour les sub-scopes déjà détruits. Les procédures de destruction et de réparation sont répétées séquentiellement jusqu’à ce que la condition d’arrêt soit atteinte. La procédure de destruction parallèle détruit plusieurs sub-scopes disjoints, puis chaque subscope est réparé dans un fil (thread) parallèle différent. Nous comparons l’heuristique présentée avec le modèle exact résolu dans le système commercial WFC par Kronos Inc. Les résultats expérimentaux montrent qu’en moyenne, l’algorithme LNS parallèle peut réduire les temps d’exécution jusqu’à 80% et améliorer les coûts des solutions jusqu’à 1, 8%.----------ABSTRACT: The employee scheduling problem consists of creating working schedules for an organization staff. The number of required employees per time unit, called employee requirement per period, is given for the full problem horizon. Different rules and constraints govern an employee scheduling problem, these rules depends on the organization needs, employees contracts and the collective labor agreement. A heterogeneous employee scheduling problem deals with employees having different working skills, usually within a multi-job or multi-department employee scheduling context, where one employee can be qualified for several of the organization activities, and can work for any activity he/she is qualified for. One working shift can be accomplished in a single department, or a department transfer can take place within a shift when the employee has the required skills. When a department transfer within a shift is allowed, the number of possible working shifts per employee becomes huge. Optimizing such heterogeneous employee scheduling problem is often essential for organizational success. However, solving such problems directly as a mixed integer linear program (MILP) is intractable for large instances. In the first part of this thesis, we propose a multi-phase decomposition heuristic (MP-DH) for the employee scheduling problem with inter-department transfers. In this problem, the concept of department of origin is introduced, where each employee is qualified to work in several departments, but he/she has exactly one department of origin, where the employee should work the majority of his/her time. The first phase starts by extracting from each department employee requirement, the uncoverable requirement parts by internal employees,i.e. if only the department internal employees can work. These extracted requirement parts are called critical intervals, because they need transferred employees from other departments to fulfill them. This is done by solving an anonymous employee scheduling problem modeled as a MILP for each department apart, before extracting the uncovered requirement parts that form the set of critical intervals. For each of the critical intervals, in the second phase, one department is chosen to assign it the responsibility of fulfilling this critical interval requirement, i.e. to transfer one of its employees to work during the critical interval. This is accomplished by solving a one-day anonymous employee scheduling problem with inter-department transfers for the critical intervals modeled as a MILP, for each of the problem horizon days. The day decomposition renders the problem size manageable in computer memory, especially for large instances (up to 25 departments). This phase ends by migrating any department d1 requirement covered by an employee from department d2, building a new employee transfer requirement from d2 to d1. The third phase solves, for each department, a mono-department employee scheduling problem with derived inter-department transfers as a MILP. The input to the third phase is the new final requirement resulting from the requirement migration of phase two. The MP-DH heuristic succeeds to decompose the multi-department employee scheduling problem into several mono-department employee scheduling problems to save substantial computational time. This allows to solve large instances while not deteriorating much the solution quality. Each phase of the MP-DH algorithm uses parallelism. In the first phase, all department MILPs and post-processing are accomplished in parallel. The second phase runs all singleday problems in parallel. Finally the third phase optimizes all department problems in parallel. At the end of each phase, all parallel problem solutions are merged to form the final solution. In the reported computational experiments, we observe that the first two phases are solved extremely fast compared to the third phase. The size of the solved MILPs in the first two phases is not proportional with the size of the optimized instance, while the third phase MILP size is. To overcome the computational issues of the third phase we present the hybrid heuristic in the second part of the thesis. The hybrid heuristic aims at greatly reducing the MP-DH third phase computational time, while maintaining the solution quality. The hybrid heuristic uses two models interchangeably in order to solve the third phase as accurate and as fast as possible. The first is the third phase MILP of the MP-DH algorithm, which we call the basic model. The second is a semi-anonymous employee scheduling problem with derived inter-department transfers modeled as a MILP that we call the semi-anonymous model. The semi-anonymous version reduces the number of employees for whom the schedules are optimized, and replaces the remaining employee shifts by a set of aggregated anonymous shifts. Once such a model is solved, the schedules of the selected employees are fixed and the algorithm moves on to solving another MILP where another set of employees must be scheduled. The hybrid heuristic starts by solving the basic model, then if, after a given time limit, the MILP optimality gap is higher than a given threshold, the resolution of the basic model is stopped and a semi-anonymous version is solved. This is done repeatedly until all employee schedules are optimized. The hybrid heuristic succeeded in reducing on average up to 87% of the third phase computational time while only loosing 4% in the solution quality. In the third part of the thesis, we tackle a different employee scheduling problem variant: the multi-job employee scheduling problem, where neither transfers nor under-coverage is allowed. Instead, anonymous shifts called open-shifts are used to cover any unavoidable under-coverage. The three main costs composing the objective function are: Over-coverage cost, open-shift usage cost, and minimum employees working hours violation penalty. A parallel large neighborhood search (LNS) metaheuristic for the multi-job employee scheduling problem is developed. Where a sub-scope denotes: a subset of the employees, a subset of the jobs and a continuous subset of the problem horizon. The LNS heuristic is defined by destroy and repair procedures. Our destroy procedure chooses sub-scopes coupled with a high cost in the objective function to be destroyed. When a solution sub-scope is destroyed, all shifts, occurring within the sub-scope horizon and worked by an employee belonging to the sub-scope, for one of the sub-scope jobs, are removed from the current solution schedule.Once the solution sub-scopes are destroyed, the repair operator tries to build an enhanced solution. Our proposed repair operator solves a MILP restricted to the destroyed sub-scopes. The parallel LNS destroy operator creates several disjoint sub-scopes, then each sub-scope is repaired in a different parallel thread. We compare the presented heuristic with the formal MILP solved within the commercial system WFC for Kronos Inc. Experimental results show that the parallel LNS algorithm can save up to an average of 80% in the computational time and 1.8% in the solution cost

Energy Awareness and Scheduling in Mobile Devices and High End Computing

In the context of the big picture as energy demands rise due to growing economies and growing populations, there will be greater emphasis on sustainable supply, conservation, and efficient usage of this vital resource. Even at a smaller level, the need for minimizing energy consumption continues to be compelling in embedded, mobile, and server systems such as handheld devices, robots, spaceships, laptops, cluster servers, sensors, etc. This is due to the direct impact of constrained energy sources such as battery size and weight, as well as cooling expenses in cluster-based systems to reduce heat dissipation. Energy management therefore plays a paramount role in not only hardware design but also in user-application, middleware and operating system design. At a higher level Datacenters are sprouting everywhere due to the exponential growth of Big Data in every aspect of human life, the buzz word these days is Cloud computing. This dissertation, focuses on techniques, specifically algorithmic ones to scale down energy needs whenever the system performance can be relaxed. We examine the significance and relevance of this research and develop a methodology to study this phenomenon. Specifically, the research will study energy-aware resource reservations algorithms to satisfy both performance needs and energy constraints. Many energy management schemes focus on a single resource that is dedicated to real-time or nonreal-time processing. Unfortunately, in many practical systems the combination of hard and soft real-time periodic tasks, a-periodic real-time tasks, interactive tasks and batch tasks must be supported. Each task may also require access to multiple resources. Therefore, this research will tackle the NP-hard problem of providing timely and simultaneous access to multiple resources by the use of practical abstractions and near optimal heuristics aided by cooperative scheduling. We provide an elegant EAS model which works across the spectrum which uses a run-profile based approach to scheduling. We apply this model to significant applications such as BLAT and Assembly of gene sequences in the Bioinformatics domain. We also provide a simulation for extending this model to cloud computing to answers “what if” scenario questions for consumers and operators of cloud resources to help answers questions of deadlines, single v/s distributed cluster use and impact analysis of energy-index and availability against revenue and ROI

On the development of a stochastic optimisation algorithm with capabilities for distributed computing

In this thesis, we devise a new stochastic optimisation method (cascade optimisation algorithm) by incorporating the concepts from Markov process whilst eliminating the inherent sequential nature that is the major deficit preventing the exploitation of advances in distributed computing infrastructures. This method introduces partitions and pools to store intermediate solution and corresponding objectives. A Markov process increases the population of partitions and pools. The population is distributed periodically following an external certain. With the use of partitions and pools, multiple Markov processes can be launched simultaneously for different partitions and pools. The cascade optimisation algorithm is suitable for parallel and distributed computing environments. In addition, this method has the potential to integrate knowledge acquisition techniques (e. g. data mining and ontology) to achieve effective knowledge-based decision making. Several features are extracted and studied in this thesis. The application problems involve both the small-scale and the large-scale optimisation problems. Comparisons with the stochastic optimisation methods are made and results show that the cascade optimisation algorithm can converge to the optimal solutions in agreement with other methods more quickly. The cascade optimisation algorithm is also studied on parallel and distributed computing environments in terms of the reduction in computation time.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

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