Matheuristics: using mathematics for heuristic design

Matheuristics are heuristic algorithms based on mathematical tools such as the ones provided by mathematical programming, that are structurally general enough to be applied to different problems with little adaptations to their abstract structure. The result can be metaheuristic hybrids having components derived from the mathematical model of the problems of interest, but the mathematical techniques themselves can define general heuristic solution frameworks. In this paper, we focus our attention on mathematical programming and its contributions to developing effective heuristics. We briefly describe the mathematical tools available and then some matheuristic approaches, reporting some representative examples from the literature. We also take the opportunity to provide some ideas for possible future development

Inbound and outbound flow integration for cross-docking operations

We consider the optimization of the cross-docking operations at three INtermodal LOgistics Platforms (INLOPs) of a large European car manufacturer (ECM). The planning horizon is a week and the time bucket is a day. An inbound flow of products is gradually received over the week by truck from inland suppliers, and has to be loaded into containers which are then shipped to offshore production plants. The full content of a container must be available at the INLOP to enable its loading operations to start, hence temporary storage is needed. The objective is to minimize an inventory penalty, computed as the largest daily volume of temporary product storage observed over the planning horizon. The current practice at ECM is to first optimize the content of the inbound trucks and of the outbound containers independently, and then determine the loading day of each container to be shipped based on these fixed contents. We propose to integrate, within the same optimization framework, the decisions on both truck and container contents, which involve complex loading constraints related to the dimensions and weights of the products, with those on the scheduling of container loading. We model the resulting problem as a mixed integer linear program, and we develop a decomposition scheme for it, as well as a fix-and-optimize matheuristic. We perform extensive computational experiments on real instances provided by ECM. Results show that a combination of these two matheuristics is able to generate solutions that reduce the average inventory penalty by 40%.</p

A matheuristic for customized multi-level multi-criteria university timetabling

Course timetables are the organizational foundation of a university’s educational program. While students and lecturers perceive timetable quality individually according to their preferences, there are also collective criteria derived normatively such as balanced workloads or idle time avoidance. A recent challenge and opportunity in curriculum-based timetabling consists of customizing timetables with respect to individual student preferences and with respect to integrating online courses as part of modern course programs or in reaction to flexibility requirements as posed in pandemic situations. Curricula consisting of (large) lectures and (small) tutorials further open the possibility for optimizing not only the lecture and tutorial plan for all students but also the assignments of individual students to tutorial slots. In this paper, we develop a multi-level planning process for university timetabling: On the tactical level, a lecture and tutorial plan is determined for a set of study programs; on the operational level, individual timetables are generated for each student interlacing the lecture plan through a selection of tutorials from the tutorial plan favoring individual preferences. We utilize this mathematical-programming-based planning process as part of a matheuristic which implements a genetic algorithm in order to improve lecture plans, tutorial plans, and individual timetables so as to find an overall university program with well-balanced timetable performance criteria. Since the evaluation of the fitness function amounts to invoking the entire planning process, we additionally provide a proxy in the form of an artificial neural network metamodel. Computational results exhibit the procedure’s capability of generating high quality schedules

Integer programming techniques for educational timetabling

Educational timetabling problems require the assignment of times and resources to events, while sets of required and desirable constraints must be considered. The XHSTT format was adopted in this work because it models the main features of educational timetabling and it is the most used format in recent studies in the field. This work presents new cuts and reformulations for the existing integer programming model for XHSTT. The proposed cuts improved hugely the linear relaxation of the formulation, leading to an average gap reduction of 32%. Applied to XHSTT-2014 instance set, the alternative formulation pro- vided four new best known lower bounds and, used in a matheuristic framework, improved eleven best known solutions. The computational experiments also show that the resulting integer programming mod- els from the proposed formulation are more effectively solved for most of the instances

Enhancing the Sorting Layers in the Initial Stage of High School Timetabling

The high school timetabling problem (HSTP) is considered as an NP-Complete problem as the optimal solution for it, is still not discovered by any algorithm. Generally, NP-Complete problem was solved firstly by constructing the initial solution, in the construction phase. The initial solution will be improvised in the improvisation phase. KHE is an algorithm that generates initial solution of HSTP. The layer sorting procedure in KHE is based on a certain priority. For every two layers, the layers will be ranked based on the highest value of duration. If both layers have equal value of duration, the layer with the highest value of demand will be at a higher rank. If both layers have equal value of demand. The layer will be arranged according to the index value of the layer. These sorting criteria use the layer properties independently which causes non-good results after the time-assignment phase. Therefore, this study proposed a mathematical model based on the Markov Chain Model for the sorting procedure that combines the layer properties in a formula. The proposed model was executed with 40 datasets of XHSTT2014, and it shows better results on 25 datasets of XHSTT2014 compared to the KHE algorithm. The mathematical model based on Markov Chain proposed in this study is able to improvise the original sorting of KHE

Managing Advanced Synchronization Aspects in Logistics Systems

In this thesis, we model various complex logistics problems and develop appropriate techniques to solve them. We improve industrial practices by introducing synchronized solutions to problems that were previously solved independently. The first part of this thesis focuses on cross-docks. We simultaneously optimize supplier orders and cross-docking operations to either reduce the storage space required or evenly distribute workload over the week. The second part of this thesis is devoted to transport problems in which two types of vehicles are synchronized, one of which can be transported by the other. The areas of application range from home services to parcel delivery to customers. After analyzing the complexity associated with these synchronized solutions (i.e., largescale problems for which the decisions depend on each other), we design algorithms based on the "destroy-and-repair" principle to find efficient solutions. We also introduce mathematical programs for all the considered problems. The problems under study arose directly from collaborations with various industrial partners. In this respect, our achieved solutions have been benchmarked with current industrial practice. Depending on the problem, we have been able to reduce the environmental impact generated by the industrial activities, the overall cost, or the social impact. The achieved gains compared to current industrial practice range from 10 to 70%, depending on the application. -- Dans cette thèse, nous modélisons divers problèmes logistiques complexes et développons des techniques appropriées pour les résoudre. Nous cherchons à améliorer certaines pratiques industrielles en introduisant des solutions synchronisées à des problèmes qui étaient auparavant résolus indépendamment. La première partie de cette thèse porte sur les cross-docks. Nous optimisons simultanément les commandes fournisseurs et les opérations au sein de la plateforme de logistique pour réduire l’espace de stockage requis ou répartir uniformément la charge de travail sur la semaine. La deuxième partie de cette thèse est consacrée aux problèmes de transport dans lesquels deux types de véhicules sont synchronisés, l’un pouvant être transporté par l’autre. Les domaines d’application vont du service à domicile à la livraison de colis chez des clients. Après avoir analysé la complexité des solutions synchronisées (c’est-à-dire des problèmes de grandes dimensions pour lesquels les décisions dépendent les unes des autres), nous concevons des algorithmes basés sur le principe de "destruction / reconstruction" pour trouver des solutions efficaces. Nous modélisons également les problèmes considérés avec la programmation mathématique. Les problèmes à l’étude viennent de collaborations avec divers partenaires industriels. A cet égard, les solutions que nous présentons sont comparées aux pratiques industrielles actuelles. En fonction du problème, nous avons pu réduire l’impact environnemental généré par les activités industrielles, le coût global, ou l’impact social des solutions. Les gains obtenus par rapport aux pratiques industrielles actuelles varient de 10 à 70%, selon l’application. Mot-clefs: Logistique, Synchronisation, Problème de transport, Tournée de véhicules, Plateforme de Cross-dock (transbordement), Programmation Mathématiques, Métaheuristiques, Matheuristiques, Instances Réelle

Solving Practical Railway Crew Scheduling Problems with Attendance Rates

Arising from a practical problem in German rail passenger transport, a prototype for a multi-period railway crew scheduling problem with attendance rates for conductors is developed and evaluated in this paper. The consideration of attendance rates is of increasing importance in regional transport networks and requires decision support. For this purpose business analytics is applied in order to offer an approach to transform real-world data to concrete operational decision support (action). The focus here is on the analysis step using a new set covering model with several essential restrictions integrated for the first time. A hybrid column generation approach is applied, which solves the pricing problem by means of a genetic algorithm. The artifact is evaluated with the help of a case study of three real-world transport networks. It is shown that the hybrid solution approach is able to solve the problem more effectively and efficiently compared to conventional approaches used in practice