The traveling repairman problem

Diese Magisterarbeit gibt einen Überblick über das Traveling Repairman Problem (TRP), das eine Spezialform des Problems des Handlungsreisenden (Traveling Salesman Problem – TSP) darstellt. Beide Modelle werden benutzt, um die Tour eines Handlungsreisenden zu planen, der in einer vorgegebenen Zeitspanne eine bestimmte Anzahl von Kunden besuchen soll. Während das TSP sich darauf konzentriert, die Länge der Tour zu minimieren, versucht das TRP, die Summe der Wartezeiten der Kunden so gering wie möglich zu halten. Der Hauptteil der Arbeit beschäftigt sich mit der Definition und den Varianten des TRP und beschreibt mögliche Modelle und Verfahren, mit deren Hilfe diese zu lösen sind. Dabei werden zuerst die Problemstellungen definiert und dann die mathematischen Formulierungen bzw. die Algorithmen dargestellt. Zu Beginn der Arbeit werden das TSP und das TRP näher definiert und kurz anhand eines Beispiels illustriert (in Kapitel 2). Danach werden das allgemeine TRP und einige Lösungsverfahren dazu näher erläutert (in Kapitel 3). Im Hauptteil werden zuerst einige Variationen des TRP mit einem einzelnen Repairman und Algorithmen zur Lösung dieser Modelle beschrieben (in Kapitel 4). Dann werden das TRP mit mehreren Repairmen sowie einige Spezialformen hierzu erläutert (in Kapitel 5). Zusätzlich werden in dieser Arbeit Anwendungsmöglichkeiten beschrieben, von denen zwei genauer untersucht werden (in Kapitel 6). Schließlich werden noch einige Basisbegriffe und Lösungsmethoden erläutert (in Kapitel 7)

The multi-depot k-traveling repairman problem

In this paper, we study the multi-depot k-traveling repairman problem. This problem extends the traditional traveling repairman problem to the multi-depot case. Its objective, similar to the single depot variant, is the minimization of the sum of the arrival times to customers. We propose two distinct formulations to model the problem, obtained on layered graphs. In order to find feasible solutions for the largest instances, we propose a hybrid genetic algorithm where initial solutions are built using a splitting heuristic and a local search is embedded into the genetic algorithm. The efficiency of the mathematical formulations and of the solution approach are investigated through computational experiments. The proposed models are scalable enough to solve instances up to 240 customers

A hybrid evolutionary algorithm for vehicle routing problem with stochastic demands

In this work we propose a hybrid dynamic programming evolutionary algorithm to solve the vehicle routing problem with stochastic demands, it is a well known NP-hard problem where uncertainty enhances the computational efforts required to obtain a feasible and near-optimal solution. We develop an evolutionary technique where a rollout dynamic programming algorithm is applied as local search method to improve the quality of solutions. Motivated by computational considerations, the rollout algorithm can be applied partially, so, this finds competitive solutions in large instances for which the global rollout dynamic programming strategy is time unfeasible.Resumen. En este trabajo se propone un algoritmo evolutivo hibrido que combina un m ́etodo de programación dinámica estocástica para resolver el problema de enrutamiento de vehículos con demandas estocásticas, este es un problema demostrado como NP-difícil donde la presencia de incertidumbre incrementa los requerimientos computacionales necesarios para obtener soluciones factibles y cercanas a la óptima. Así, para el algoritmo evolutivo desarrollado se aplico un algoritmo rollout de programación dinámica estocástica como operador de búsqueda local para mejorar la calidad de las soluciones. Motivado por requerimientos computacionales, el algoritmo de rollout puede ser aplicado parcialmente, con el objetivo de encontrar soluciones competitivas en instancias lo suficientemente grandes para las cuales la estrategía global no es aplicable por consumir una cantidad de tiempo no tolerable.Maestrí

Multi-Robot Coordination : Applications in Orchard Bin Management and Informative Path Planning

Efficient coordination is desired for multi-robot systems in many scenarios. In this research, we first provide a multi-robot system to help human workers during tree fruit harvest. We present an auction-based method to coordinate a team of self-propelled bin carriers to retrieve fruit bins. Second, we propose a more general information gathering problem in a dynamic environment. In this problem, locations of points of interest change over time. Further, the amount of meaningful information or reward that can be obtained from each point is limited. We propose to use a distributed sampling algorithm for task allocation, and a receding horizon strategy for path planning in this problem. To evaluate its performance, the proposed algorithm is compared to a baseline algorithm that implements sequential auction for task allocation with greedy path planning. Experimental results suggest that the proposed algorithm is more suitable for solving the aforementioned information gathering problem. Finally we present an effective approach to coordinating a team of UAVs (unmanned aerial vehicles) to simultaneous explore, map, and search in unknown environments. The UAVs can perform a weighted trade off between the three sub-tasks. Moreover, human operators can limit the time allowed for each UAV to remain without a valid communication link to the control base station. We compare results to a market-based baseline algorithm. Results suggest that our relay system improves the efficiency of exploring, mapping, and searching tasks

Solving a Location, Allocation, and Capacity Planning Problem with Dynamic Demand and Response Time Service Level

Logistic systems with uncertain demand, travel time, and on-site processing time are studied here where sequential trip travel is allowed. The relationship between three levels of decisions: facility location, demand allocation, and resource capacity (number of service units), satisfying the response time requirement, is analysed. The problem is formulated as a stochastic mixed integer program. A simulation-based hybrid heuristic is developed to solve the dynamic problem under different response time service level. An initial solution is obtained from solving static location-allocation models, followed by iterative improvement of the three levels of decisions by ejection, reinsertion procedure with memory of feasible and infeasible service regions. Results indicate that a higher response time service level could be achieved by allocating a given resource under an appropriate decentralized policy. Given a response time requirement, the general trend is that the minimum total capacity initially decreases with more facilities. During this stage, variability in travel time has more impact on capacity than variability in demand arrivals. Thereafter, the total capacity remains stable and then gradually increases. When service level requirement is high, the dynamic dispatch based on first-come-first-serve rule requires smaller capacity than the one by nearest-neighbour rule

Le problème du postier chinois cumulatif

Résumé Le sujet de cette thèse est le problème du postier chinois cumulatif (PPCC). Dans ce problème, nous considérons l'importance du moment où une arête est traitée complètement. Cette façon de procéder introduit un caractère cumulatif et dynamique dans le coût réel des arêtes, ce qui a pour effet de changer la structure du problème du postier chinois. Nous démontrons que ce problème est fortement NP-difficile et réductible à une version du problème de voyageur de commerce cumulatif. Ce problème est, à notre connaissance, nouveau. Nous continuons ici l'étude entreprise dans notre mémoire de maîtrise. Notre but dans cette thèse est de résoudre exactement ce problème à l'aide des outils de la programmation linéaire en nombres entiers. Notre contribution est de plusieurs ordres. Premièrement, nous développons une vingtaine de modèles différents. Dans cette thèse, nous étudions les huit meilleurs et les comparons aussi bien empiriquement que théoriquement entre eux et démontrons toutes les relations de dominance entre eux. L'aboutissement de nos recherches est le modèle L8. Deuxièmement, nous résolvons ce modèle L8 à l'aide d'un algorithme de séparation et évaluation progressive (Branch and Cut - algorithme BC1). Nous développons plusieurs outils dont nous présentons ici trois branchements, sept pré-traitements, six familles de coupes dont trois que nous généralisons. Ces outils nous permettent déjà de battre le solveur CPLEX par un facteur de 3 à 58 sur nos graphes de référence. Troisièmement, nous développons une meilleure variante du modèle L8 : le modèle L8+ et utilisons une approche avec génération de colonnes (Branch, Price and Cut – algorithme BPC1). Dans la foulée, nous développons cinq familles de coupes et nous généralisons quatre d'entre-elles. Cette nouvelle approche, plus rapide que la première d'un facteur de 2 à 4, nous permet d'être de 2 à 133 fois plus rapide que le solveur CPLEX en utilisant le modèle L8+ sur nos graphes de référence. Quatrièmement, nous améliorons notre approche de génération de colonnes (Branch, Price and Cut – algorithme BPC2) avec une évaluation implicite du dual. Les plus grandes instances du PPCC que nous arrivons à résoudre dans un délai maximal d'une heure comprennent des graphes de 11 sommets et/ou de 55 arêtes, ce qui correspond approximativement à des instances du problème du voyageur de commerce cumulatif à 110 sommets. Mots clefs Tournées sur les arcs, fonction cumulative, problème du postier chinois cumulatif.----------Abstract The subject of this Ph.D. thesis is the Cumulative Chinese Postman Problem (CCPP). We focus on the delay of the service of each arc. This introduces a cumulative and dynamic aspect in the objective function therefore changing the structure of the Chinese Postman Problem. We prove that this problem is strongly NP-hard and reducible to a version of the Cumulative Travelling Salesman Problem. This problem is, to our knowledge, entirely new. The study of this problem was initiated in our master thesis. Our main goal in this thesis is to solve this problem exactly with the help of the tools of linear integer programming. Our contribution is manifold. First, we develop twenty different models. However, in this thesis, we only discuss and compare theoretically and experimentally the best eight models. We prove all dominance relations among them. Model L8 stands out as the best model. Secondly, we solve this model L8 with a Branch and Cut (algorithm BC1). Throughout our study, we develop several tools among which three branching rules, seven presolving algorithms, six families of cuts (three of them generalized). These tools alone allow us to solve the problem faster than CPLEX by a factor of 3 to 58 on our test graphs. Thirdly, we develop an improved model L8+ and use a column generation approach - a Branch, Price and Cut (algorithm BPC1). We also develop five new families of cuts (four of them generalized). This new approach is faster than the previous one by a factor of 2 to 4 and is faster than CPLEX with the new model L8+ by a factor of 2 to 133 on our test graphs. Fourthly, we improve our Branch, Price and Cut algorithm (algorithm BPC2) by using an implicit evaluation of the dual. The largest instances for which we are able to solve the CCPP in less than one hour include graphs with 11 nodes and/or 55 edges which correspond approximately to instances of the Cumulative Travelling Salesman Problem with 110 nodes

Preventing premature convergence and proving the optimality in evolutionary algorithms

http://ea2013.inria.fr//proceedings.pdfInternational audienceEvolutionary Algorithms (EA) usually carry out an efficient exploration of the search-space, but get often trapped in local minima and do not prove the optimality of the solution. Interval-based techniques, on the other hand, yield a numerical proof of optimality of the solution. However, they may fail to converge within a reasonable time due to their inability to quickly compute a good approximation of the global minimum and their exponential complexity. The contribution of this paper is a hybrid algorithm called Charibde in which a particular EA, Differential Evolution, cooperates with a Branch and Bound algorithm endowed with interval propagation techniques. It prevents premature convergence toward local optima and outperforms both deterministic and stochastic existing approaches. We demonstrate its efficiency on a benchmark of highly multimodal problems, for which we provide previously unknown global minima and certification of optimality