Algorithms for the Bin Packing Problem with Scenarios

This paper presents theoretical and practical results for the bin packing problem with scenarios, a generalization of the classical bin packing problem which considers the presence of uncertain scenarios, of which only one is realized. For this problem, we propose an absolute approximation algorithm whose ratio is bounded by the square root of the number of scenarios times the approximation ratio for an algorithm for the vector bin packing problem. We also show how an asymptotic polynomial-time approximation scheme is derived when the number of scenarios is constant. As a practical study of the problem, we present a branch-and-price algorithm to solve an exponential model and a variable neighborhood search heuristic. To speed up the convergence of the exact algorithm, we also consider lower bounds based on dual feasible functions. Results of these algorithms show the competence of the branch-and-price in obtaining optimal solutions for about 59% of the instances considered, while the combined heuristic and branch-and-price optimally solved 62% of the instances considered

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

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

A Classification of Hyper-heuristic Approaches

The current state of the art in hyper-heuristic research comprises a set of approaches that share the common goal of automating the design and adaptation of heuristic methods to solve hard computational search problems. The main goal is to produce more generally applicable search methodologies. In this chapter we present and overview of previous categorisations of hyper-heuristics and provide a unified classification and definition which captures the work that is being undertaken in this field. We distinguish between two main hyper-heuristic categories: heuristic selection and heuristic generation. Some representative examples of each category are discussed in detail. Our goal is to both clarify the main features of existing techniques and to suggest new directions for hyper-heuristic research

A genetic algorithm for the one-dimensional cutting stock problem with setups

This paper investigates the one-dimensional cutting stock problem considering two conflicting objective functions: minimization of both the number of objects and the number of different cutting patterns used. A new heuristic method based on the concepts of genetic algorithms is proposed to solve the problem. This heuristic is empirically analyzed by solving randomly generated instances and also practical instances from a chemical-fiber company. The computational results show that the method is efficient and obtains positive results when compared to other methods from the literature. © 2014 Brazilian Operations Research Society

Evolutionary algorithms and hyper-heuristics for orthogonal packing problems

This thesis investigates two major classes of Evolutionary Algorithms, Genetic Algorithms (GAs) and Evolution Strategies (ESs), and their application to the Orthogonal Packing Problems (OPP). OPP are canonical models for NP-hard problems, the class of problems widely conceived to be unsolvable on a polynomial deterministic Turing machine, although they underlie many optimisation problems in the real world. With the increasing power of modern computers, GAs and ESs have been developed in the past decades to provide high quality solutions for a wide range of optimisation and learning problems. These algorithms are inspired by Darwinian nature selection mechanism that iteratively select better solutions in populations derived from recombining and mutating existing solutions. The algorithms have gained huge success in many areas, however, being stochastic processes, the algorithms' behaviour on different problems is still far from being fully understood. The work of this thesis provides insights to better understand both the algorithms and the problems. The thesis begins with an investigation of hyper-heuristics as a more general search paradigm based on standard EAs. Hyper-heuristics are shown to be able to overcome the difficulty of many standard approaches which only search in partial solution space. The thesis also looks into the fundamental theory of GAs, the schemata theorem and the building block hypothesis, by developing the Grouping Genetic Algorithms (GGA) for high dimensional problems and providing supportive yet qualified empirical evidences for the hypothesis. Realising the difficulties of genetic encoding over combinatorial search domains, the thesis proposes a phenotype representation together with Evolution Strategies that operates on such representation. ESs were previously applied mainly to continuous numerical optimisation, therefore being less understood when searching in combinatorial domains. The work in this thesis develops highly competent ES algorithms for OPP and opens the door for future research in this area

Evolutionary algorithms and hyper-heuristics for orthogonal packing problems

This thesis investigates two major classes of Evolutionary Algorithms, Genetic Algorithms (GAs) and Evolution Strategies (ESs), and their application to the Orthogonal Packing Problems (OPP). OPP are canonical models for NP-hard problems, the class of problems widely conceived to be unsolvable on a polynomial deterministic Turing machine, although they underlie many optimisation problems in the real world. With the increasing power of modern computers, GAs and ESs have been developed in the past decades to provide high quality solutions for a wide range of optimisation and learning problems. These algorithms are inspired by Darwinian nature selection mechanism that iteratively select better solutions in populations derived from recombining and mutating existing solutions. The algorithms have gained huge success in many areas, however, being stochastic processes, the algorithms' behaviour on different problems is still far from being fully understood. The work of this thesis provides insights to better understand both the algorithms and the problems. The thesis begins with an investigation of hyper-heuristics as a more general search paradigm based on standard EAs. Hyper-heuristics are shown to be able to overcome the difficulty of many standard approaches which only search in partial solution space. The thesis also looks into the fundamental theory of GAs, the schemata theorem and the building block hypothesis, by developing the Grouping Genetic Algorithms (GGA) for high dimensional problems and providing supportive yet qualified empirical evidences for the hypothesis. Realising the difficulties of genetic encoding over combinatorial search domains, the thesis proposes a phenotype representation together with Evolution Strategies that operates on such representation. ESs were previously applied mainly to continuous numerical optimisation, therefore being less understood when searching in combinatorial domains. The work in this thesis develops highly competent ES algorithms for OPP and opens the door for future research in this area

Models and advanced optimization algorithms for the integrated management of logistics operations

Tese de Doutoramento em Engenharia Industrial e de Sistemas.In this thesis, we propose a set of algorithms regarding real combinatorial optimization problems in the context of transportation of goods. These problems consist in the combination of the vehicle routing problem with the two-dimensional bin-packing problem, which is also known as the vehicle routing problem with two-dimensional loading constraints. We also analyzed two related problems, namely the elementary shortest path and the vehicle routing problem with mixed linehauls and backhauls. In both problems, two-dimensional loading constraints are explicitly considered. Two column generation based approaches are proposed for the vehicle routing problem with two-dimensional constraints. The rst one relies on a branch-and-price algorithm with di erent branching schemes. A family of dual valid inequalities is also de ned, aiming to accelerate the convergence of the algorithm. The second approach is based on a set of di erent heuristics strategies, which are applied to the reformulated model. The elementary shortest path problem with two-dimensional constraints is addressed due to its importance in solving the subproblem of the column generation algorithms. To the best of our knowledge, we contribute with the rst approach for this problem, through di erent constructive strategies to achieve feasible solutions, and a variable neighborhood search algorithm in order to search for improved solutions. In what concerns the vehicle routing problem with mixed linehaul and backhauls and two-dimensional loading constraints, di erent variable neighborhood search algorithms are proposed. These algorithms explored various neighborhood structures, being some of those developed based on the features of the problem. All the proposed methods were implemented and experimentally tested. An exhaustive set of computational tests was conducted, using, for this purpose, a large group of benchmark instances. In some cases, a large set of benchmark instances was adapted in order asses the quality of the proposed models. All the obtained results are presented and discussed.Nesta tese, propomos um conjunto de algoritmos sobre problemas reais de otimiza c~ao combinat oria no contexto do transporte de bens. Estes problemas consistem na combina c~ao do problema de planeamento de rotas de ve culos com o problema de empacotamento bidimensional, que tamb em e conhecido como o problema de planeamento de rotas de ve culos com restri c~oes de carregamento bidimensional. Analisamos tamb em dois problemas relacionados, nomeadamente o problema de caminho mais curto e o problema de planeamento de rotas ve culos com entregas e recolhas indiferenciadas. Em ambos os problemas, s~ao explicitamente consideradas restri c~oes de carregamento bidimensional. Duas abordagens baseadas em gera c~ao de colunas s~ao propostas para o problema de planeamento de rotas de ve culos com restri c~oes de carregamento bidimensional. O primeiro baseia-se num algoritmo de parti c~ao e gera c~ao de colunas com diferentes estrat egias de parti c~ao. Uma fam lia de desigualdades duais v alidas e tamb em apresentada, com o objetivo de acelerar a converg^encia do algoritmo. A segunda abordagem baseia-se num conjunto de diferentes estrat egias heur sticas, que s~ao aplicadas ao modelo reformulado. O problema do caminho mais curto com restri c~oes de carregamento bidimensional e abordado devido a sua import^ancia na resolu c~ao do subproblema dos aos algoritmos de gera c~ao de colunas. De acordo com o nosso conhecimento, contribu mos com a primeira abordagem para este problema, atrav es de diferentes estrat egias construtivas para obter solu c~oes v alidas, e um algoritmo de pesquisa em vizinhan ca vari avel, com o objetivo de encontrar solu c~oes de melhor qualidade. No que concerne ao problema de planeamento de rotas de ve culos com entregas e recolhas indiferenciadas, diferentes algoritmos de pesquisa em vizinhan ca vari avel s~ao propostos. Estes algoritmos exploram v arias estruturas de vizinhan ca, sendo algumas destas desenvolvidas com base nas caracter sticas do problema. Todos os m etodos propostos foram implementados e testados experimentalmente. Um extenso conjunto de testes computacionais foi efetuado, utilizando um grande grupo de inst^ancias descritas na literatura. Em alguns casos, um grande conjunto de inst^ancias descritas na literatura foi adaptado com o objetivo de avaliar a qualidade dos m etodos propostos