A Literature Review On Combining Heuristics and Exact Algorithms in Combinatorial Optimization

There are several approaches for solving hard optimization problems. Mathematical programming techniques such as (integer) linear programming-based methods and metaheuristic approaches are two extremely effective streams for combinatorial problems. Different research streams, more or less in isolation from one another, created these two. Only several years ago, many scholars noticed the advantages and enormous potential of building hybrids of combining mathematical programming methodologies and metaheuristics. In reality, many problems can be solved much better by exploiting synergies between these approaches than by “pure” classical algorithms. The key question is how to integrate mathematical programming methods and metaheuristics to achieve such benefits. This paper reviews existing techniques for such combinations and provides examples of using them for vehicle routing problems

The Tractor and Semitrailer Routing Considering Carbon Dioxide Emissions

The incorporation of the minimization of carbon dioxide (CO2) emissions in the VRP is important to logistics companies. The paper deals with the tractor and semitrailer routing problem with full truckload between any two depots of the network; an integer programming model with the objective of minimizing CO2 emissions per ton-kilometer is proposed. A two-stage approach with the same core steps of the simulated annealing (SA) in both stages is designed. The number of tractors is provided in the first stage and the CO2 emissions per ton-kilometer are then optimized in the second stage. Computational experiments on small-scale randomly generated instances supported the feasibility and validity of the heuristic algorithm. To a practical-scale problem, the SA algorithm can provide advice on the number of tractors, the routes, and the location of the central depot to realize CO2 emissions decrease

The Effects of the Tractor and Semitrailer Routing Problem on Mitigation of Carbon Dioxide Emissions

The incorporation of CO2 emissions minimization in the vehicle routing problem (VRP) is of critical importance to enterprise practice. Focusing on the tractor and semitrailer routing problem with full truckloads between any two terminals of the network, this paper proposes a mathematical programming model with the objective of minimizing CO2 emissions per ton-kilometer. A simulated annealing (SA) algorithm is given to solve practical-scale problems. To evaluate the performance of the proposed algorithm, a lower bound is developed. Computational experiments on various problems generated randomly and a realistic instance are conducted. The results show that the proposed methods are effective and the algorithm can provide reasonable solutions within an acceptable computational time

Integrated production-distribution systems : Trends and perspectives

During the last two decades, integrated production-distribution problems have attracted a great deal of attention in the operations research literature. Within a short period, a large number of papers have been published and the field has expanded dramatically. The purpose of this paper is to provide a comprehensive review of the existing literature by classifying the existing models into several different categories based on multiple characteristics. The paper also discusses some trends and list promising avenues for future research

Cross-Docking: A Proven LTL Technique to Help Suppliers Minimize Products\u27 Unit Costs Delivered to the Final Customers

This study aims at proposing a decision-support tool to reduce the total supply chain costs (TSCC) consisting of two separate and independent objective functions including total transportation costs (TTC) and total cross-docking operating cost (TCDC). The full-truckload (FT) transportation mode is assumed to handle supplier→customer product transportation; otherwise, a cross-docking terminal as an intermediate transshipment node is hired to handle the less-than-truckload (LTL) product transportation between the suppliers and customers. TTC model helps minimize the total transportation costs by maximization of the number of FT transportation and reduction of the total number of LTL. TCDC model tries to minimize total operating costs within a cross-docking terminal. Both sub-objective functions are formulated as binary mathematical programming models. The first objective function is a binary-linear programming model, and the second one is a binary-quadratic assignment problem (QAP) model. QAP is an NP-hard problem, and therefore, besides a complement enumeration method using ILOG CPLEX software, the Tabu search (TS) algorithm with four diversification methods is employed to solve larger size problems. The efficiency of the model is examined from two perspectives by comparing the output of two scenarios including; i.e., 1) when cross-docking is included in the supply chain and 2) when it is excluded. The first perspective is to compare the two scenarios’ outcomes from the total supply chain costs standpoint, and the second perspective is the comparison of the scenarios’ outcomes from the total supply chain costs standpoint. By addressing a numerical example, the results confirm that the present of cross-docking within a supply chain can significantly reduce total supply chain costs and total transportation costs

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

Méthodes hybrides basées sur la génération de colonnes pour des problèmes de tournées de véhicules avec fenêtres de temps

RÉSUMÉ Un problème de tournées de véhicules avec fenêtres de temps consiste à faire la livraison de marchandise à un ensemble de clients avec une flotte de véhicules ayant un ou plusieurs points de départ appelés dépôts. Chaque client doit être desservi à l'intérieur d'une période prédéfinie, appelée fenêtre de temps. En pratique, on doit pouvoir respecter un grand nombre de contraintes et de caractéristiques complexes telles que des flottes hétérogènes de véhicules, des restrictions sur les routes, etc., en plus de devoir prendre en compte un grand nombre de clients. Il est donc primordial pour les distributeurs d'avoir accès à des outils performants d'optimisation capables de gérer un grand ensemble de contraintes de façon efficace. Dans cette thèse, nous présentons une méthode heuristique pour résoudre un ensemble de problèmes de tournées de véhicules de grande taille avec fenêtres de temps de façon efficace. Les problèmes abordés sont riches dans le sens où ils contiennent des caractéristiques non conventionnelles complexes s'apparentant à des problématiques réelles. La méthode proposée est un hybride entre une méthode métaheuristique de recherche à grands voisinages et une méthode exacte de génération de colonnes, la plus performante à ce jour pour résoudre de façon exacte des problèmes de tournées de véhicules assez contraints. La recherche à grands voisinages est une méthode où l'on vient itérativement détruire (phase de destruction) et reconstruire (reconstruction) des parties d'une solution courante afin d'obtenir de meilleures solutions. Les voisinages, définis dans la phase de destruction, sont explorés dans la phase de reconstruction. Dans notre méthode, les voisinages sont explorés par génération de colonnes gérée de façon heuristique. Une méthode de génération de colonnes sert à résoudre la relaxation linéaire d'un programme linéaire. Elle résout itérativement un problème maître, qui est le programme linéaire restreint à un sous-ensemble de variables, et un ou plusieurs sous-problèmes qui servent à rajouter des variables de coût réduit négatif au problème maître. La résolution se termine lorsque les sous-problèmes ne trouvent plus de variables de coût réduit négatif. Cette méthode est imbriquée dans un algorithme de séparation et évaluation pour obtenir des solutions entières. Plusieurs opérateurs sont définis pour sélectionner des éléments qui seront retirés de la solution courante dans la phase de destruction. À chaque itération, un opérateur est choisi aléatoirement en favorisant ceux qui ont permis d'améliorer la solution courante dans les itérations précédentes. La génération de colonnes sert ensuite à explorer le voisinage ainsi défini (reconstruction). Plusieurs aspects de la génération de colonnes sont gérés de façon heuristique afin d'obtenir de bonnes solutions en des temps raisonnables aux dépens de la certitude de trouver une solution optimale. Les sous-problèmes sont résolus par une méthode de recherche tabou et la génération de colonnes est stoppée après une trop faible amélioration de la valeur de la solution courante de la relaxation linéaire au cours des dernières itérations. Afin d'obtenir des solutions entières, un branchement agressif sur la variable ayant la valeur fractionnaire la plus grande est effectué. Sa valeur est fixée à 1 sans possibilité de retour en arrière.----------ABSTRACT Given a fleet of vehicles assigned to one or more depots, a vehicle routing problem with time windows consists of determining a set of feasible vehicle routes to deliver goods to a set of scattered customers. Every customer must be visited within a prescribed time interval, called a time window. In practice, vehicle routing problems can have many different types of constraints and complex characteristics such as a heterogeneous fleet, restrictions on the routes, etc., while having to serve a large number of customers. Therefore, it is essential for distributors to rely on competitive optimizing tools able to tackle a large number of constraints efficiently. In this thesis, we present an efficient heuristic method for solving a number of large-scale vehicle routing problems with time windows. The problems tackled are rich in the sense that they contain many non-conventional complex characteristics arising in real applications. We propose a hybrid between a large neighborhood search metaheuristic and a column generation exact method, hitherto the most efficient to solve constrained vehicle routing problems exactly. Large neighborhood search is an iterative method where we sequentially remove (destruction phase) and reinsert (reconstruction phase) parts of an incumbent solution in the hope of improving it. Neighborhoods defined in the destruction phase are explored in the reconstruction phase. We propose to explore the neighborhoods by column generation managed heuristically. A column generation method is used to solve the linear relaxation of a linear program. It solves iteratively a master problem, that is the linear program restricted to a subset of variables, and one or many subproblems that attempt to find new negative reduced cost variables to add to the master problem. The process ends when the subproblems cannot find any negative reduced cost variables. This method is embedded within a brand-and-bound algorithm to derive integer solutions. Several operators are defined to select elements that will be removed from the incumbent solution in the destruction phase. At every iteration, an operator is randomly selected favouring those who managed to improve the incumbent solution in the past iterations. Afterwards, column generation is used to explore the neighborhood defined by the operator (reconstruction phase). Many aspects of the column generation approach are managed heuristically in order to obtain good solutions in reasonable time at the expense of ensuring optimality. The subproblems are solved by means of a tabu search algorithm and the column generation is stopped if the value of the solution of the linear relaxation does not improve enough over the last iterations. An aggressive ranching scheme is used to derive integer solutions. Branching is done on the variable with the highest fractional value, which is fixed at 1 without the possibility to backtrack

A flexible metaheuristic framework for solving rich vehicle routing problems

Route planning is one of the most studied research topics in the operations research area. While the standard vehicle routing problem (VRP) is the classical problem formulation, additional requirements arising from practical scenarios such as time windows or vehicle compartments are covered in a wide range of so-called rich VRPs. Many solution algorithms for various VRP variants have been developed over time as well, especially within the class of so-called metaheuristics. In practice, routing software must be tailored to the business rules and planning problems of a specific company to provide valuable decision support. This also concerns the embedded solution methods of such decision support systems. Yet, publications dealing with flexibility and customization of VRP heuristics are rare. To fill this gap this thesis describes the design of a flexible framework to facilitate and accelerate the development of custom metaheuristics for the solution of a broad range of rich VRPs. The first part of the thesis provides background information to the reader on the field of vehicle routing problems and on metaheuristic solution methods - the most common and widely-used solution methods to solve VRPs. Specifically, emphasis is put on methods based on local search (for intensification of the search) and large neighborhood search (for diversification of the search), which are combined to hybrid methods and which are the foundation of the proposed framework. Then, the main part elaborates on the concepts and the design of the metaheuristic VRP framework. The framework fulfills requirements of flexibility, simplicity, accuracy, and speed, enforcing the structuring and standardization of the development process and enabling the reuse of code. Essentially, it provides a library of well-known and accepted heuristics for the standard VRP together with a set of mechanisms to adapt these heuristics to specific VRPs. Heuristics and adaptation mechanisms such as templates for user-definable checking functions are explained on a pseudocode level first, and the most relevant classes of a reference implementation using the Microsoft .NET framework are presented afterwards. Finally, the third part of the thesis demonstrates the use of the framework for developing problem-specific solution methods by exemplifying specific customizations for five rich VRPs with diverse characteristics, namely the VRP with time windows, the VRP with compartments, the split delivery VRP, the periodic VRP, and the truck and trailer routing problem. These adaptations refer to data structures and neighborhood search methods and can serve as a source of inspiration to the reader when designing algorithms for new, so far unstudied VRPs. Computational results are presented to show the effectiveness and efficiency of the proposed framework and methods, which are competitive with current state-of-the-art solvers of the literature. Special attention is given to the overall robustness of heuristics, which is an important aspect for practical application