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

Variable size vector bin packing heuristics - Application to the machine reassignment problem

In this paper, we introduce a generalization of the vector bin packing problem, where the bins have variable sizes. This generalization can be used to model virtual machine placement problems. In particular, we study the machine reassignment problem. We propose several greedy heuristics for the variable size vector bin packing problem and show that they are flexible and can be adapted to handle additional constraints. We highlight some structural properties of the machine reassignment problem and use them to adapt our heuristics. We present numerical results on both randomly generated instances and Google realistic instances for the machine reassignment problem

Maximizing space utilization in unit-load warehouses.

In a unit-load warehouse, products are stored and retrieved in pallet quantities. Examples include retail distribution centers (DC), third-party DCs, and transshipment hubs in freight transportation. Expenses related to space are a significant component of the operational cost of unit-load warehouses; therefore, maximizing space utilization is important. Moreover, the continuing revolution of retail e-commerce is changing the role and design of modern distribution centers (Boysen et al., 2018). An important trend with serious implications for design is the desire of many distributors to locate DCs in or near metropolitan areas in order to support same-day service or better (Thuermer, 2018). Land in these areas is very expensive, so there is a need to make the best use of existing space. The ability to store more products in the same space increases inventory availability and therefore service, and the ability to store the same inventory in a smaller footprint reduces costs. In this dissertation, we propose two strategies to improve space utilization in unit-load warehouses. We aim to minimize what we called loss of vertical space within slots (LVS)—the mismatch between the height of the pallet and the height of the slot where it is stored. LVS is a significant problem because it is standard practice to design storage racks in unit-load warehouses with all slots of equal height (maximum pallet height) such that every pallet can fit in every slot; however, pallet heights vary greatly. We propose the use of storage racks with multiple slot heights so that slot heights can better match the distribution of pallet heights. We analyzed historic (forecasted) inventory levels and the pallet heights to determine a robust design that guarantees a desired storage service level. Our method addresses the new warehouse design decisions that arise when having multiple slot heights: How to arrange the different slot heights in the rack-bays? How to organize the layout? How to avoid storage shortages? How do different slot heights affect travel times? We found that using multiple slot heights in unit-load warehouses has significant benefits in terms of footprint, expected travel time, and racking cost. For a typical warehouse, we expect space savings of 25–35 percent, depending on the number of slot types, and savings of 15–25 percent in annual operating cost. Although using multiple slot heights significantly decreases the loss of vertical space within slots, it does not completely eliminate it, and in warehouses where inventory levels are highly variable or product mixes change rapidly, this wasted space can still be significant. Examples of this situation in practice include warehouses with correlated order profiles, demands with seasonal peaks, new product launches, and distribution network consolidations. For such business environments, we propose pallet racks with dynamic heights as a way to maximize space utilization. Contrary to traditional pallet racks, the uprights and beams of pallet racks with dynamic heights are equipped with a mechanism to adjust slot heights easily. We found that pallet racks with dynamic heights have expected space savings of 16–30 percent when compared to traditional pallet racks

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

The capacitated minimum spanning tree problem

In this thesis we focus on the Capacitated Minimum Spanning Tree (CMST), an extension of the minimum spanning tree (MST) which considers a central or root vertex which receives and sends commodities (information, goods, etc) to a group of terminals. Such commodities flow through links which have capacities that limit the total flow they can accommodate. These capacity constraints over the links result of interest because in many applications the capacity limits are inherent. We find the applications of the CMST in the same areas as the applications of the MST; telecommunications network design, facility location planning, and vehicle routing. The CMST arises in telecommunications networks design when the presence of a central server is compulsory and the flow of information is limited by the capacity of either the server or the connection lines. Its study also results specially interesting in the context of the vehicle routing problem, due to the utility that spanning trees can have in constructive methods. By the simple fact of adding capacity constraints to the MST problem we move from a polynomially solvable problem to a non-polynomial one. In the first chapter we describe and define the problem, introduce some notation, and present a review of the existing literature. In such review we include formulations and exact methods as well as the most relevant heuristic approaches. In the second chapter two basic formulations and the most used valid inequalities are presented. In the third chapter we present two new formulations for the CMST which are based on the identification of subroots (vertices directly connected to the root). One way of characterizing CMST solutions is by identifying the subroots and the vertices assigned to them. Both formulations use binary decision variables y to identify the subroots. Additional decision variables x are used to represent the elements (arcs) of the tree. In the second formulation the set of x variables is extended to indicate the depth of the arcs in the tree. For each formulation we present families of valid inequalities and address the separation problem in each case. Also a solution algorithm is proposed. In the fourth chapter we present a biased random-key genetic algorithm (BRKGA) for the CMST. BRKGA is a population-based metaheuristic, that has been used for combinatorial optimization. Decoders, solution representation and exploring strategies are presented and discussed. A final algorithm to obtain upper bounds for the CMST is proposed. Numerical results for the BRKGA and two cutting plane algorithms based on the new formulations are presented in the fifth chapter . The above mentioned results are discussed and analyzed in this same chapter. The conclusion of this thesis are presented in the last chapter, in which we include the opportunity areas suitable for future research.En esta tesis nos enfocamos en el problema del Árbol de Expansión Capacitado de Coste Mínimo (CMST, por sus siglas en inglés), que es una extensión del problema del árbol de expansión de coste mínimo (MST, por sus siglas en inglés). El CMST considera un vértice raíz que funciona como servidor central y que envía y recibe bienes (información, objetos, etc) a un conjunto de vértices llamados terminales. Los bienes solo pueden fluir entre el servidor y las terminales a través de enlaces cuya capacidad es limitada. Dichas restricciones sobre los enlaces dan relevancia al problema, ya que existen muchas aplicaciones en que las restricciones de capacidad son de vital importancia. Dentro de las áreas de aplicación del CMST más importantes se encuentran las relacionadas con el diseño de redes de telecomunicación, el diseño de rutas de vehículos y problemas de localización. Dentro del diseño de redes de telecomunicación, el CMST está presente cuando se considera un servidor central, cuya capacidad de transmisión y envío está limitada por las características de los puertos del servidor o de las líneas de transmisión. Dentro del diseño de rutas de vehículos el CMST resulta relevante debido a la influencia que pueden tener los árboles en el proceso de construcción de soluciones. Por el simple de añadir las restricciones de capacidad, el problema pasa de resolverse de manera exacta en tiempo polinomial usando un algoritmo voraz, a un problema que es muy difícil de resolver de manera exacta. En el primer capítulo se describe y define el problema, se introduce notación y se presenta una revisión bibliográfica de la literatura existente. En dicha revisión bibliográfica se incluyen formulaciones, métodos exactos y los métodos heurísticos utilizados más importantes. En el siguiente capítulo se muestran dos formulaciones binarias existentes, así como las desigualdades válidas más usadas para resolver el CMST. Para cada una de las formulaciones propuestas, se describe un algoritmo de planos de corte. Dos nuevas formulaciones para el CMST se presentan en el tercer capítulo. Dichas formulaciones estás basadas en la identificación de un tipo de vértices especiales llamados subraíces. Los subraíces son aquellos vértices que se encuentran directamente conectados al raíz. Un forma de caracterizar las soluciones del CMST es a través de identificar los nodos subraíces y los nodos dependientes a ellos. Ambas formulaciones utilizan variables para identificar los subraices y variables adicionales para identificar los arcos que forman parte del árbol. Adicionalmente, las variables en la segunda formulación ayudan a identificar la profundidad con respecto al raíz a la que se encuentran dichos arcos. Para cada formulación se presentan desigualdades válidas y se plantean procedimientos para resolver el problema de su separación. En el cuarto capítulo se presenta un algoritmo genético llamado BRKGA para resolver el CMST. El BRKGA está basado en el uso de poblaciones generadas por secuencias de números aleatorios, que posteriormente evolucionan. Diferentes decodificadores, un método de búsqueda local, espacios de búsqueda y estrategias de exploración son presentados y analizados. El capítulo termina presentando un algoritmo final que permite la obtención de cotas superiores para el CMST. Los resultados computacionales para el BRKGA y los dos algoritmos de planos de corte basados en las formulaciones propuestas se muestran en el quinto capítulo. Dichos resultados son analizados y discutidos en dicho capítulo. La tesis termina presentando las conclusiones derivadas del desarrollo del trabajo de investigación, así como las áreas de oportunidad sobre las que es posible realizar futuras investigaciones

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 Multi-Start Algorithm for Solving the Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints

N/