A study on exponential-size neighborhoods for the bin packing problem with conflicts

We propose an iterated local search based on several classes of local and large neighborhoods for the bin packing problem with conflicts. This problem, which combines the characteristics of both bin packing and vertex coloring, arises in various application contexts such as logistics and transportation, timetabling, and resource allocation for cloud computing. We introduce $O(1)$ evaluation procedures for classical local-search moves, polynomial variants of ejection chains and assignment neighborhoods, an adaptive set covering-based neighborhood, and finally a controlled use of 0-cost moves to further diversify the search. The overall method produces solutions of good quality on the classical benchmark instances and scales very well with an increase of problem size. Extensive computational experiments are conducted to measure the respective contribution of each proposed neighborhood. In particular, the 0-cost moves and the large neighborhood based on set covering contribute very significantly to the search. Several research perspectives are open in relation to possible hybridizations with other state-of-the-art mathematical programming heuristics for this problem.Comment: 26 pages, 8 figure

On Conflict-Free Cuts: Algorithms and Complexity

One way to define the Matching Cut problem is: Given a graph $G$, is there an edge-cut $M$ of $G$ such that $M$ is an independent set in the line graph of $G$? We propose the more general Conflict-Free Cut problem: Together with the graph $G$, we are given a so-called conflict graph $\hat{G}$ on the edges of $G$, and we ask for an edge-cutset $M$ of $G$ that is independent in $\hat{G}$. Since conflict-free settings are popular generalizations of classical optimization problems and Conflict-Free Cut was not considered in the literature so far, we start the study of the problem. We show that the problem is $\textsf{NP}$-complete even when the maximum degree of $G$ is 5 and $\hat{G}$ is 1-regular. The same reduction implies an exponential lower bound on the solvability based on the Exponential Time Hypothesis. We also give parameterized complexity results: We show that the problem is fixed-parameter tractable with the vertex cover number of $G$ as a parameter, and we show $\textsf{W[1]}$-hardness even when $G$ has a feedback vertex set of size one, and the clique cover number of $\hat{G}$ is the parameter. Since the clique cover number of $\hat{G}$ is an upper bound on the independence number of $\hat{G}$ and thus the solution size, this implies $\textsf{W[1]}$-hardness when parameterized by the cut size. We list polynomial-time solvable cases and interesting open problems. At last, we draw a connection to a symmetric variant of SAT.Comment: 13 pages, 3 figure

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

Grammatical evolution hyper-heuristic for combinatorial optimization problems

Designing generic problem solvers that perform well across a diverse set of problems is a challenging task. In this work, we propose a hyper-heuristic framework to automatically generate an effective and generic solution method by utilizing grammatical evolution. In the proposed framework, grammatical evolution is used as an online solver builder, which takes several heuristic components (e.g., different acceptance criteria and different neighborhood structures) as inputs and evolves templates of perturbation heuristics. The evolved templates are improvement heuristics, which represent a complete search method to solve the problem at hand. To test the generality and the performance of the proposed method, we consider two well-known combinatorial optimization problems: exam timetabling (Carter and ITC 2007 instances) and the capacitated vehicle routing problem (Christofides and Golden instances). We demonstrate that the proposed method is competitive, if not superior, when compared to state-of-the-art hyper-heuristics, as well as bespoke methods for these different problem domains. In order to further improve the performance of the proposed framework we utilize an adaptive memory mechanism, which contains a collection of both high quality and diverse solutions and is updated during the problem solving process. Experimental results show that the grammatical evolution hyper-heuristic, with an adaptive memory, performs better than the grammatical evolution hyper-heuristic without a memory. The improved framework also outperforms some bespoke methodologies, which have reported best known results for some instances in both problem domains

Passenger-Centric Urban Air Mobility: Fairness Trade-Offs and Operational Efficiency

Urban Air Mobility (UAM) has the potential to revolutionize transportation. It will exploit the third dimension to help smooth ground traffic in densely populated areas. To be successful, it will require an integrated approach able to balance efficiency and safety while harnessing common resources and information. In this work we focus on future urban air-taxi services, and present the first methods and algorithms to efficiently operate air-taxi at scale. Our approach is twofold. First, we use a passenger-centric perspective which introduces traveling classes, and information sharing between transport modes to differentiate quality of services. This helps smooth multimodal journeys and increase passenger satisfaction. Second, we provide a flight routing and recharging solution which minimizes direct operational costs while preserving long term battery life through reduced energy-intense recharging. Our methods, which surpass the performance of a general state-of-the-art commercial solver, are also used to gain meaningful insights on the design space of the air-taxi problem, including solutions to hidden fairness issues.Comment: Submitted to Transportation Research Part C: Emerging Technologie

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

Optimization models and methods for transportation services

Managing transportation services efficiently is essential to both public and private sectors. This dissertation addresses three scheduling problems in modern transportation systems: the network design problem, the train dispatching problem, and the service route design problem. The transportation network design problem with service requirements designs arcs on a directed network and route commodities on the designed arcs so that i) commodities satisfy service requirements and ii) the total cost is minimized. We develop three mathematical programming models: a compact but weak arc-flow formulation, a large but strong path-flow formulation, and a hybrid formulation that uses both the arc-flow and the path-flow representations. We show that the hybrid formulation can significantly strengthen the LP formulation without introducing many variables. To find a good hybrid formulation, we develop columnization and decolumnization algorithms that uses the LP relaxation information to identify commodities that should use the path-flow representation. We also develop valid inequalities for commodities using the path-flow representation. The train dispatching problem schedules the movements of trains on scarce railroad tracks so as to improve the average velocity of trains. We develop a mathematical programming model and strengthen the model using valid inequalities. Besides, we present a heuristic to find a feasible solution quickly, which can serve as the warm-start solution to the MIP solver. For the third problem, we seek to design vehicle routes to deliver and pickup orders for a major grocery chain. We design a GRASP that can incorporate various operational requirements, including warehouse loading capacity, loading sequence, time window requirements, truck volume and weight capacities, and driver time limits. Our GRASP procedure consists of two phases: the solution construction (Phase I) and the Tabu search (Phase II). We show that the neighborhood structure of solutions is highly degenerate, which limits the solution space explored by the Tabu search. We apply the Tabu search with random variable neighborhood to increase the solution space explored.Operations Research and Industrial Engineerin

Stochastic programming for City Logistics: new models and methods

The need for mobility that emerged in the last decades led to an impressive increase in the number of vehicles as well as to a saturation of transportation infrastructures. Consequently, traffic congestion, accidents, transportation delays, and polluting emissions are some of the most recurrent concerns transportation and city managers have to deal with. However, just building new infrastructures might be not sustainable because of their cost, the land usage, which usually lacks in metropolitan regions, and their negative impact on the environment. Therefore, a different way of improving the performance of transportation systems while enhancing travel safety has to be found in order to make people and good transportation operations more efficient and support their key role in the economic development of either a city or a whole country. The concept of City Logistics (CL) is being developed to answer to this need. Indeed, CL focus on reducing the number of vehicles operating in the city, controlling their dimension and characteristics. CL solutions do not only improve the transportation system but the whole logistics system within an urban area, trying to integrate interests of the several. This global view challenges researchers to develop planning models, methods and decision support tools for the optimization of the structures and the activities of the transportation system. In particular, this leads researchers to the definition of strategic and tactical problems belonging to well-known problem classes, including network design problem, vehicle routing problem (VRP), traveling salesman problem (TSP), bin packing problem (BPP), which typically act as sub-problems of the overall CL system optimization. When long planning horizons are involved, these problems become stochastic and, thus, must explicitly take into account the different sources of uncertainty that can affect the transportation system. Due to these reasons and the large-scale of CL systems, the optimization problems arising in the urban context are very challenging. Their solution requires investigations in mathematical and combinatorial optimization methods as well as the implementation of efficient exact and heuristic algorithms. However, contributions answering these challenges are still limited number. This work contributes in filling this gap in the literature in terms of both modeling framework for new planning problems in CL context and developing new and effective heuristic solving methods for the two-stage formulation of these problems. Three stochastic problems are proposed in the context of CL: the stochastic variable cost and size bin packing problem (SVCSBPP), the multi-handler knapsack problem under uncertainty (MHKPu) and the multi-path traveling salesman problem with stochastic travel times (mpTSPs). The SVCSBPP arises in supply-chain management, in which companies outsource the logistics activities to a third-party logistic firm (3PL). The procurement of sufficient capacity, expressed in terms of vehicles, containers or space in a warehouse for varying periods of time to satisfy the demand plays a crucial role. The SVCSBPP focuses on the relation between a company and its logistics capacity provider and the tactical-planning problem of determining the quantity of capacity units to secure for the next period of activity. The SVCSBPP is the first attempt to introduce a stochastic variant of the variable cost and size bin packing problem (VCSBPP) considering not only the uncertainty on the demand to deliver, but also on the renting cost of the different bins and their availability. A large number of real-life situations can be satisfactorily modeled as a MHKPu, in particular in the last mile delivery. Last mile delivery may involve different sequences of consolidation operations, each handled by different workers with different skill levels and reliability. The improper management of consolidation operations can cause delay in the operations reducing the overall profit of the deliveries. Thus, given a set of potential logistics handlers and a set of items to deliver, characterized by volume and random profit, the MHKPu consists in finding a subset of items which maximizes the expected total profit. The profit is given by the sum of a deterministic profit and a stochastic profit oscillation, with unknown probability distribution, due to the random handling costs of the handlers.The mpTSPs arises mainly in City Logistics applications. Cities offer several services, such as garbage collection, periodic delivery of goods in urban grocery distribution and bike sharing services. These services require the planning of fixed and periodic tours that will be used from one to several weeks. However, the enlarged time horizon as well as strong dynamic changes in travel times due to traffic congestion and other nuisances typical of the urban transportation induce the presence of multiple paths with stochastic travel times. Given a graph characterized by a set of nodes connected by arcs, mpTSPs considers that, for every pair of nodes, multiple paths between the two nodes are present. Each path is characterized by a random travel time. Similarly to the standard TSP, the aim of the problem is to define the Hamiltonian cycle minimizing the expected total cost. These planning problems have been formulated as two-stage integer stochastic programs with recourse. Discretization methods are usually applied to approximate the probability distribution of the random parameters. The resulting approximated program becomes a deterministic linear program with integer decision variables of generally very large dimensions, beyond the reach of exact methods. Therefore, heuristics are required. For the MHKPu, we apply the extreme value theory and derive a deterministic approximation, while for the SVCSBPP and the mpTSPs we introduce effective and accurate heuristics based on the progressive hedging (PH) ideas. The PH mitigates the computational difficulty associated with large problem instances by decomposing the stochastic program by scenario. When effective heuristic techniques exist for solving individual scenario, that is the case of the SVCSBPP and the mpTSPs, the PH further reduces the computational effort of solving scenario subproblems by means of a commercial solver. In particular, we propose a series of specific strategies to accelerate the search and efficiently address the symmetry of solutions, including an aggregated consensual solution, heuristic penalty adjustments, and a bundle fixing technique. Yet, although solution methods become more powerful, combinatorial problems in the CL context are very large and difficult to solve. Thus, in order to significantly enhance the computational efficiency, these heuristics implement parallel schemes. With the aim to make a complete analysis of the problems proposed, we perform extensive numerical experiments on a large set of instances of various dimensions, including realistic setting derived by real applications in the urban area, and combinations of different levels of variability and correlations in the stochastic parameters. The campaign includes the assessment of the efficiency of the meta-heuristic, the evaluation of the interest to explicitly consider uncertainty, an analysis of the impact of problem characteristics, the structure of solutions, as well as an evaluation of the robustness of the solutions when used as decision tool. The numerical analysis indicates that the stochastic programs have significant effects in terms of both the economic impact (e.g. cost reduction) and the operations management (e.g. prediction of the capacity needed by the firm). The proposed methodologies outperform the use of commercial solvers, also when small-size instances are considered. In fact, they find good solutions in manageable computing time. This makes these heuristics a strategic tool that can be incorporated in larger decision support systems for CL

Problèmes de Tournées de Véhicules avec Synchronisation de Ressources

This dissertation focuses on vehicle routing problems, one of the major academic problems in logistics. We address NP-Hard problems that model some real world situations particularly those with different temporal constraints including time windows, visit synchronization and service balance.The aim of this research is to develop new algorithms for the considered problems, investigate their performance and compare them with the literature approaches. Two cases are carried out. The first case studies the Vehicle Routing Problem with Time Windows (VRPTW). We propose new lower bound methods for the number of vehicles. Then we present a Particle Swarm Optimization algorithm dealing with the Solomon objective. The second case studies the Vehicle Routing Problem with Time Windows and Synchronized Visits (VRPTWsyn). Both exact methods and heuristics are proposed and compared to the literature approaches.Cette thèse porte sur la résolution de problèmes de transport qui intègrent des contraintes temporelles considérant les fenêtres de temps, la synchronisation des visites et l’équilibrage des services. Ces problèmes trouvent plusieurs applications dans le monde réel.L’objectif de nos recherches est l’élaboration de nouvelles méthodes de résolution pour les problèmes considérés en examinant leur performance avec une étude comparative par rapport aux différentes approches de la littérature. Deux variantes sont traitées. Le premier cas étudie le Problème de Tournées de Véhicules avec Fenêtres de Temps (VRPTW). Nous proposons de nouveaux prétraitements et bornes inférieures pour déterminer le nombre de véhicules nécessaires en s’inspirant de travaux menés en ordonnancement (raisonnement énergétique) et d’autres problèmes combinatoires comme la clique maximum et les problèmes de bin-packing. Nous présentons également un algorithme d’optimisation par essaim particulaire qui traite de la minimisation du nombre de véhicules puis de celle du temps de trajet total. Le deuxième cas étudie le Problème de Tournées de Véhicules avec des Fenêtres de Temps et des Visites Synchronisées (VRPTWSyn). Nous proposons plusieurs méthodes basées sur des approches heuristiques et des formulations linéaires avec l’incorporation d’inégalités valides pour tenir compte de la contrainte de synchronisation