Augmented neural networks and problem-structure based heuristics for the bin-packing problem

In this paper, we apply the Augmented-neural-networks (AugNN) approach for solving the classical bin-packing problem (BPP). AugNN is a metaheuristic that combines a priority- rule heuristic with the iterative search approach of neural networks to generate good solutions fast. This is the first time this approach has been applied to the BPP. We also propose a decomposition approach for solving harder BPP, in which sub problems are solved using a combination of AugNN approach and heuristics that exploit the problem structure. We discuss the characteristics of problems on which such problem-structure based heuristics could be applied. We empirically show the effectiveness of the AugNN and the decomposition approach on many benchmark problems in the literature. For the 1210 benchmark problems tested, 917 problems were solved to optimality and the average gap between the obtained solution and the upper bound for all the problems was reduced to under 0.66% and computation time averaged below 33 seconds per problem. We also discuss the computational complexity of our approach

Improving the Bin Packing Heuristic through Grammatical Evolution Based on Swarm Intelligence

In recent years Grammatical Evolution (GE) has been used as a representation of Genetic Programming (GP) which has been applied to many optimization problems such as symbolic regression, classification, Boolean functions, constructed problems, and algorithmic problems. GE can use a diversity of searching strategies including Swarm Intelligence (SI). Particle Swarm Optimisation (PSO) is an algorithm of SI that has two main problems: premature convergence and poor diversity. Particle Evolutionary Swarm Optimization (PESO) is a recent and novel algorithm which is also part of SI. PESO uses two perturbations to avoid PSO’s problems. In this paper we propose using PESO and PSO in the frame of GE as strategies to generate heuristics that solve the Bin Packing Problem (BPP); it is possible however to apply this methodology to other kinds of problems using another Grammar designed for that problem. A comparison between PESO, PSO, and BPP’s heuristics is performed through the nonparametric Friedman test. The main contribution of this paper is proposing a Grammar to generate online and offline heuristics depending on the test instance trying to improve the heuristics generated by other grammars and humans; it also proposes a way to implement different algorithms as search strategies in GE like PESO to obtain better results than those obtained by PSO

Applying the big bang-big crunch metaheuristic to large-sized operational problems

In this study, we present an investigation of comparing the capability of a big bang-big crunch metaheuristic (BBBC) for managing operational problems including combinatorial optimization problems. The BBBC is a product of the evolution theory of the universe in physics and astronomy. Two main phases of BBBC are the big bang and the big crunch. The big bang phase involves the creation of a population of random initial solutions, while in the big crunch phase these solutions are shrunk into one elite solution exhibited by a mass center. This study looks into the BBBC’s effectiveness in assignment and scheduling problems. Where it was enhanced by incorporating an elite pool of diverse and high quality solutions; a simple descent heuristic as a local search method; implicit recombination; Euclidean distance; dynamic population size; and elitism strategies. Those strategies provide a balanced search of diverse and good quality population. The investigation is conducted by comparing the proposed BBBC with similar metaheuristics. The BBBC is tested on three different classes of combinatorial optimization problems; namely, quadratic assignment, bin packing, and job shop scheduling problems. Where the incorporated strategies have a greater impact on the BBBC's performance. Experiments showed that the BBBC maintains a good balance between diversity and quality which produces high-quality solutions, and outperforms other identical metaheuristics (e.g. swarm intelligence and evolutionary algorithms) reported in the literature

Solving Bin Packing Problems Using VRPSolver Models

International audienceWe propose branch-cut-and-price algorithms for the classic bin packing problem and also for the following related problems: vector packing, variable sized bin packing and variable sized bin packing with optional items. The algorithms are defined as models for VRPSolver, a generic solver for vehicle routing problems. In that way, a simple parameterization enables the use of several branch-cut-and-price advanced elements: automatic stabilization by smoothing, limited-memory rank-1 cuts, enumeration, hierarchical strong branching and limited discrepancy search diving heuristics. As an original theoretical contribution, we prove that the branching over accumulated resource consumption (Gélinas et al. 1995), that does not increase the difficulty of the pricing subproblem, is sufficient for those bin packing models. Extensive computational results on instances from the literature show that the VRPSolver models have a performance that is very robust over all those problems, being often superior to the existing exact algorithms on the hardest instances. Several instances could be solved to optimality for the first time

Iterative restricted space search : a solving approach based on hybridization

Face à la complexité qui caractérise les problèmes d'optimisation de grande taille l'exploration complète de l'espace des solutions devient rapidement un objectif inaccessible. En effet, à mesure que la taille des problèmes augmente, des méthodes de solution de plus en plus sophistiquées sont exigées afin d'assurer un certain niveau d 'efficacité. Ceci a amené une grande partie de la communauté scientifique vers le développement d'outils spécifiques pour la résolution de problèmes de grande taille tels que les méthodes hybrides. Cependant, malgré les efforts consentis dans le développement d'approches hybrides, la majorité des travaux se sont concentrés sur l'adaptation de deux ou plusieurs méthodes spécifiques, en compensant les points faibles des unes par les points forts des autres ou bien en les adaptant afin de collaborer ensemble. Au meilleur de notre connaissance, aucun travail à date n'à été effectué pour développer un cadre conceptuel pour la résolution efficace de problèmes d'optimisation de grande taille, qui soit à la fois flexible, basé sur l'échange d'information et indépendant des méthodes qui le composent. L'objectif de cette thèse est d'explorer cette avenue de recherche en proposant un cadre conceptuel pour les méthodes hybrides, intitulé la recherche itérative de l'espace restreint, ±Iterative Restricted Space Search (IRSS)>>, dont, la principale idée est la définition et l'exploration successives de régions restreintes de l'espace de solutions. Ces régions, qui contiennent de bonnes solutions et qui sont assez petites pour être complètement explorées, sont appelées espaces restreints "Restricted Spaces (RS)". Ainsi, l'IRSS est une approche de solution générique, basée sur l'interaction de deux phases algorithmiques ayant des objectifs complémentaires. La première phase consiste à identifier une région restreinte intéressante et la deuxième phase consiste à l'explorer. Le schéma hybride de l'approche de solution permet d'alterner entre les deux phases pour un nombre fixe d'itérations ou jusqu'à l'atteinte d'une certaine limite de temps. Les concepts clés associées au développement de ce cadre conceptuel et leur validation seront introduits et validés graduellement dans cette thèse. Ils sont présentés de manière à permettre au lecteur de comprendre les problèmes que nous avons rencontrés en cours de développement et comment les solutions ont été conçues et implémentées. À cette fin, la thèse a été divisée en quatre parties. La première est consacrée à la synthèse de l'état de l'art dans le domaine de recherche sur les méthodes hybrides. Elle présente les principales approches hybrides développées et leurs applications. Une brève description des approches utilisant le concept de restriction d'espace est aussi présentée dans cette partie. La deuxième partie présente les concepts clés de ce cadre conceptuel. Il s'agit du processus d'identification des régions restreintes et des deux phases de recherche. Ces concepts sont mis en oeuvre dans un schéma hybride heuristique et méthode exacte. L'approche a été appliquée à un problème d'ordonnancement avec deux niveaux de décision, relié au contexte des pâtes et papier: "Pulp Production Scheduling Problem". La troisième partie a permit d'approfondir les concepts développés et ajuster les limitations identifiées dans la deuxième partie, en proposant une recherche itérative appliquée pour l'exploration de RS de grande taille et une structure en arbre binaire pour l'exploration de plusieurs RS. Cette structure a l'avantage d'éviter l'exploration d 'un espace déjà exploré précédemment tout en assurant une diversification naturelle à la méthode. Cette extension de la méthode a été testée sur un problème de localisation et d'allocation en utilisant un schéma d'hybridation heuristique-exact de manière itérative. La quatrième partie généralise les concepts préalablement développés et conçoit un cadre général qui est flexible, indépendant des méthodes utilisées et basé sur un échange d'informations entre les phases. Ce cadre a l'avantage d'être général et pourrait être appliqué à une large gamme de problèmes

A Branch-and-Price Algorithm for Bin Packing Problem

Bin Packing Problem examines the minimum number of identical bins needed to pack a set of items of various sizes. Employing branch-and-bound and column generation usually requires designation of the problem-specific branching rules compatible with the nature of the pricing sub-problem of column generation, or alternatively it requires determination of the k-best solutions of knapsack problem at level kth of the tree. Instead, we present a new approach to deal with the pricing sub-problem of column generation which handles two-dimensional knapsack problems. Furthermore, a set of new upper bounds for Bin Packing Problem is introduced in this work which employs solutions of the continuous relaxation of the set-covering formulation of Bin Packing Problem. These high quality upper bounds are computed inexpensively and dominate the ones generated by state-of-the-art methods

Складання розкладу виконання робіт з урахуванням часових вікон

Пояснювальна записка магістерської дисертації складається з чотирьох розділів, містить 19 рисунків, 19 таблиці, 1 додаток та 30 джерел. Об’єкт дослідження: процес складання розкладу з урахуванням часових вікон. Мета магістерської дисертації: розробити ефективного алгоритму розв’язання задачі складання розкладу з урахуванням часових вікон. Наукова новизна одержаних результатів полягає у вдосконаленні метода розв’язання задачі складання розкладу виконання робіт з урахуванням часових вікон.The explanatory note of the master’s thesis consists of four sections, contains 19 figures, 19 tables, 1 appendix, 30 sources. The object of study: the process of scheduling with time windows. The aim of the master’s thesis: to develop the efficient algorithm for solving the scheduling problem with time windows. The scientific novelty of the obtained result lies in the improvement of method of solving the scheduling problem with time windows

Um algoritmo evolutivo baseado em heurísticas construtivas para problemas de agrupamento aplicado à PCR multiplex

Polymerase chain reaction (PCR) is one of the most widely used molecular biology methods in clinical and research laboratories. Through it, it is possible to generate billions of copies of a given DNA fragment in a short period of time. The potential of this reaction and its variants is explored in a wide range of applications in different scientific fields, which motivates research aimed at optimizing PCR assays. Multiplex PCR is a variation of conventional PCR that allows the amplification of multiple specific DNA fragments in the same assay, saving time, costs, and especially samples of genetic material. Designing this reaction is especially challenging because it requires the difficult task of efficiently grouping the amplifications according to the compatibility of their components. This task is usually abstracted to a combinatorial problem about grouping the primer pairs used, which consist of short sequences of DNA synthesized to delimit specifically each target fragment. In this work, a computational model was developed to solve the multiplex PCR grouping problem aiming at an approach capable of dealing with interests frequently approached in isolation by other works. They are: the use of a robust computational strategy as opposed to deterministic algorithms; the applicability of the model in contexts requiring grouping of amplifications in multiple multiplex PCR tubes; minimizing the number of tubes required; the dissociation of the search method from the set of compatibility measures adopted; and the ability to handle the more complex scenario in which two or more options of primer pairs are provided by amplification, expanding the universe of possibilities and potentially the quality of the results. The construction of the model was inspired by methods previously applied to the known bin packing problem. Thus, an evolutionary algorithm is adapted to the search for specific element permutations aiming at the subsequent decoding of the solutions through a building heuristic. Besides, is presented a search space restriction process that allowed to improve the optimization performance. The approach was initially adapted to the bin packing problem, which allowed an evaluation based on benchmarks widely explored in the literature. In this case, the comparative analysis presented points to the competitiveness of the developed model in relation to the referenced algorithms. Subsequently, the proposal was adapted to the multiplex PCR problem. The results of exploratory experiments conducted indicate the scalability of the model and highlight the relevant contribution arising from the breadth of the approach. Finally, it is presented a comparative experimental analysis with the MultiPLX program, which is available for multiplex PCR design and is based on a similar problem formulation. The results obtained by the developed algorithm were superior in the three considered cases, reinforcing the applicability of the proposed model.A reação em cadeia da polimerase (Polymerase Chain Reaction, PCR) é um dos métodos de biologia molecular mais utilizados em laboratórios clínicos e de pesquisa. Com a PCR é possível gerar bilhões de cópias de um determinado fragmento de DNA em um curto período de tempo. O potencial dessa reação e de suas variantes é explorado em um vasto conjunto de aplicações inseridas em diferentes campos científicos, motivando a pesquisa direcionada à otimização dos ensaios de PCR. A PCR multiplex consiste em uma variação da PCR convencional que permite a amplificação de múltiplos fragmentos específicos de DNA em um mesmo tubo, propiciando economia de tempo, custos e principalmente amostras do material genético. O projeto da reação é especialmente desafiador na medida em que exige a difícil tarefa de agrupar as amplificações de acordo com a compatibilidade dos componentes envolvidos. Geralmente, métodos in silico para essa reação são baseados no problema combinatório decorrente do agrupamento dos pares de primers utilizados, que consistem em sequências curtas de DNA sintetizadas para delimitar especificamente cada fragmento alvo. Neste trabalho, foi desenvolvido um modelo computacional para o problema de agrupamento da PCR multiplex, visando uma abordagem que compreenda, simultaneamente, aspectos determinantes para a aplicabilidade do modelo e a otimização eficiente da reação, a saber: o tratamento de problemas que exijam múltiplos tubos de PCR multiplex para a cobertura dos alvos; a minimização do número de tubos necessários; a utilização de uma estratégia de busca estocástica em oposição a algoritmos determinísticos; o desacoplamento do método de busca em relação ao conjunto de medidas de compatibilidade adotadas; e a capacidade de tratar o cenário mais complexo em que duas ou mais opções pares de primers são fornecidas por amplificação. O modelo é composto pela adaptação de um algoritmo evolutivo à busca de permutações dos elementos e uma heurística construtiva responsável pela decodificação das soluções mapeadas. Além disso, um processo de restrição do espaço de busca é implementado visando aprimorar o desempenho da busca. A construção da proposta foi inspirada em métodos desenvolvidos para a solução do conhecido problema do empacotamento, o que permitiu uma avaliação inicial baseada em benchmarks amplamente explorados na literatura. Nesse caso, a análise comparativa apresentada evidencia a competitividade do modelo desenvolvido diante dos algoritmos referenciados. Posteriormente, o modelo foi adaptado para a otimização da PCR multiplex. Os resultados de experimentos exploratórios realizados indicam a escalabilidade do modelo e ressaltam a relevante contribuição decorrente da amplitude da abordagem. Finalmente, é apresentada uma análise experimental comparativa com o programa MultiPLX, que baseia-se em uma formulação semelhante do problema. Os resultados superiores obtidos pelo algoritmo proposto reforçam a aplicabilidade do modelo desenvolvido.CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superio