DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization

Ant Colony Optimization (ACO) is a meta-heuristic algorithm that has been successfully applied to various Combinatorial Optimization Problems (COPs). Traditionally, customizing ACO for a specific problem requires the expert design of knowledge-driven heuristics. In this paper, we propose DeepACO, a generic framework that leverages deep reinforcement learning to automate heuristic designs. DeepACO serves to strengthen the heuristic measures of existing ACO algorithms and dispense with laborious manual design in future ACO applications. As a neural-enhanced meta-heuristic, DeepACO consistently outperforms its ACO counterparts on eight COPs using a single neural model and a single set of hyperparameters. As a Neural Combinatorial Optimization method, DeepACO performs better than or on par with problem-specific methods on canonical routing problems. Our code is publicly available at https://github.com/henry-yeh/DeepACO.Comment: Accepted at NeurIPS 202

Combining statistical learning with metaheuristics for the multi-depot vehicle routing problem with market segmentation

In real-life logistics and distribution activities it is usual to face situations in which the distribution of goods has to be made from multiple warehouses or depots to the nal customers. This problem is known as the Multi-Depot Vehicle Routing Problem (MDVRP), and it typically includes two sequential and correlated stages: (a) the assignment map of customers to depots, and (b) the corresponding design of the distribution routes. Most of the existing work in the literature has focused on minimizing distance-based distribution costs while satisfying a number of capacity constraints. However, no attention has been given so far to potential variations in demands due to the tness of the customerdepot mapping in the case of heterogeneous depots. In this paper, we consider this realistic version of the problem in which the depots are heterogeneous in terms of their commercial o er and customers show di erent willingness to consume depending on how well the assigned depot ts their preferences. Thus, we assume that di erent customer-depot assignment maps will lead to di erent customer-expenditure levels. As a consequence, market-segmentation strategies need to be considered in order to increase sales and total income while accounting for the distribution costs. To solve this extension of the MDVRP, we propose a hybrid approach that combines statistical learning techniques with a metaheuristic framework. First, a set of predictive models is generated from historical data. These statistical models allow estimating the demand of any customer depending on the assigned depot. Then, the estimated expenditure of each customer is included as part of an enriched objective function as a way to better guide the stochastic local search inside the metaheuristic framework. A set of computational experiments contribute to illustrate our approach and how the extended MDVRP considered here diré in terms of the proposed solutions from the traditional one.Peer ReviewedPreprin

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

A dynamic multiarmed bandit-gene expression programming hyper-heuristic for combinatorial optimization problems

Hyper-heuristics are search methodologies that aim to provide high-quality solutions across a wide variety of problem domains, rather than developing tailor-made methodologies for each problem instance/domain. A traditional hyper-heuristic framework has two levels, namely, the high level strategy (heuristic selection mechanism and the acceptance criterion) and low level heuristics (a set of problem specific heuristics). Due to the different landscape structures of different problem instances, the high level strategy plays an important role in the design of a hyper-heuristic framework. In this paper, we propose a new high level strategy for a hyper-heuristic framework. The proposed high-level strategy utilizes a dynamic multiarmed bandit-extreme value-based reward as an online heuristic selection mechanism to select the appropriate heuristic to be applied at each iteration. In addition, we propose a gene expression programming framework to automatically generate the acceptance criterion for each problem instance, instead of using human-designed criteria. Two well-known, and very different, combinatorial optimization problems, one static (exam timetabling) and one dynamic (dynamic vehicle routing) are used to demonstrate the generality of the proposed framework. Compared with state-of-the-art hyper-heuristics and other bespoke methods, empirical results demonstrate that the proposed framework is able to generalize well across both domains. We obtain competitive, if not better results, when compared to the best known results obtained from other methods that have been presented in the scientific literature. We also compare our approach against the recently released hyper-heuristic competition test suite. We again demonstrate the generality of our approach when we compare against other methods that have utilized the same six benchmark datasets from this test suite

Decomposition strategies for large scale multi depot vehicle routing problems

Das Umfeld in der heutigen Wirtschaft verlangt nach immer bessern Ansätzen, um Transportprobleme möglichst effizient zu lösen. Die Klasse der ”Vehicle Routing Problems” (VRP) beschäftigt sich speziell mit der Optimierung von Tourenplanungsproblemen in dem ein Service-Leister seine Kunden möglichst effizient beliefern muss. Eine der VRP-Varianten ist das ”Multi Depot Vehicle Routing Problem with Time Windows” (MDVRPTW), in dem Kunden von verschiedenen Depots in einem fix vorgegebenen Zeitintervall beliefert beliefert werden müssen. Das MDVRPTW ist im realen Leben dank seiner realitätsnahen Restriktionen sehr oft vertreten. Typische Transportprobleme, wie sie in der Wirklichkeit auftreten, sind jedoch oftmals so groß, dass sie von optimalen Lösungsansätzen nicht zufriedenstellend gelöst werden können. In der vorliegenden Dissertation werden zwei Lösungsansätze präsentiert, wie diese riesigen, realitätsnahen Probleme zufriedenstellend bewältigt werden können. Beide Ansätze benutzen die POPMUSIC Grundstruktur, um das Problem möglichst intelligent zu dekomponieren. Die Dekomponierten und damit kleineren Subprobleme können dann von speziell entwickelten Algorithmen effizienter bearbeitet und letztendlich gelöst werden. Mit dem ersten Ansatz präsentieren wir eine Möglichkeit Transportprobleme zu dekomponieren, wenn populationsbasierte Algorithmen als Problemlöser eingesetzt werden. Dazu wurde ein maßgeschneiderter Memetischer Algorithmus (MA) entwickelt und in das Dekompositionsgerüst eingebaut um ein reales Problem eines österreichischen Transportunternehmens zu lösen. Wir zeigen, dass die Dekomponierung und Optimierung der resultierenden Subprobleme, im Vergleich zu den Ergebnissen des MA ohne Dekomposition, eine Verbesserung der Zielfunktion von rund 20% ermöglicht. Der zweite Ansatz beschäftigt sich mit der Entwicklung einer Dekomponierungsmethode für Lösungsalgorithmen, die nur an einer einzigen Lösung arbeiten. Es wurde ein ”Variable Neigborhood Search” (VNS) als Optimierer in das POPMUSIC Grundgerüst implementiert, um an das vorhandene Echtwelt-Problem heranzugehen. Wir zeigen, dass dieser Ansatz rund 7% bessere Ergebnisse liefert als der pure VNS Lösungsansatz. Außerdem präsentieren wir Ergebnisse des VNS Dekompositionsansatzes die um rund 6% besser sind als die des MA Dekompositionsansatzes. Ein weiterer Beitrag dieser Arbeit ist das Vorstellen von zwei komplett verschiedenen Ansätzen um das Problem in kleinere Sub-Probleme zu zerteilen. Dazu wurden acht verschiedene Nähe-Maße definiert und betrachtet. Es wurde der 2,3 und 4 Depot Fall getestet und im Detail analysiert. Die Ergebnisse werden präsentiert und wir stellen einen eindeutigen Gewinner vor, der alle Testinstanzen am Besten lösen konnte. Wir weisen auch darauf hin, wie einfach die POPMUSIC Dekomponierung an reale Bedürfnisse, wie zum Beispiel eine möglichst schnelle Ergebnisgenerierung, angepasst werden kann. Wir zeigen damit, dass die vorgestellten Dekomponierungsstrategien sehr effizient und flexibel sind, wenn Transportprobleme, wie sie in der realen Welt vorkommen gelöst werden müssen.The optimization of transportation activities is of high importance for companies in today’s economy. The Vehicle Routing Problem (VRP) class is dealing with the routing of vehicles so that the customer base of a company can be served in the most efficient way. One of the many variants in the VRP class is the Multi Depot Vehicle Routing Problem with Time Windows (MDVRPTW) which extends the VRP by additional depots from which customers can be served, as well as an individual time window for each customer in which he is allowed to be served. Modern carrier fleet operators often encounter these MDVRPTW in the real world, and usually they are of very large size so that exact approaches cannot solve them efficiently. This thesis presents two different approaches how this real world large scale MDVRPTWs can be solved. Both approaches are based on the POPMUSIC framework, which intelligently tries to decompose the large scale problem into much smaller sub-problems. The resulting sub-problems can then be solved more efficiently by specialized optimizers. The first approach in this thesis was developed for population based optimizers. A Memetic Algorithm (MA) was developed and used as an optimizer in the framework to solve a real world MDVPRTW from an Austrian carrier fleet operator. We show that decomposing the complete problem and solving the resulting sub-problems improves the solution quality by around 20% compared to using the MA without any decomposition. The second approach specially focuses on decomposition strategies for single solution methods. More precisely, a Variable Neighborhood Search (VNS) was implemented in the POPMUSIC framework to solve the real world instances. We show that decomposing the problem can yield improvements of around 7% compared to using the pure VNS method. Compared to the POPMUSIC MA approach the second approach can further improve the solution quality by around 6%. Another contribution in this thesis is the development of two generally different ways to measure proximity when creating sub-problems. In detail we tested eight different proximity measures and analyzed how good they decompose the problem in different environments. We tested the two, three and four depot case and present a clear winner that can outperform all other measures. Further we demonstrate that the POPMUSIC approach can flexibly be adjusted to real world demands, like a faster solution finding process, while at the same time maintaining high quality solutions. We show that a decomposition strategies combined with state of the art metaheuristic solvers are a very efficient and flexible tool to tackle real world problems with regards to solution quality as well as runtime

A unified matheuristic for solving multi-constrained traveling salesman problems with profits

International audienceIn this paper, we address a rich Traveling Salesman Problem with Profits encountered in several real-life cases. We propose a unified solution approach based on variable neighborhood search. Our approach combines several removal and insertion routing neighborhoods and efficient constraint checking procedures. The loading problem related to the use of a multi-compartment vehicle is addressed carefully. Two loading neighborhoods based on the solution of mathematical programs are proposed to intensify the search. They interact with the routing neighborhoods as it is commonly done in matheuristics. The performance of the proposed matheuristic is assessed on various instances proposed for the Orienteer-ing Problem and the Orienteering Problem with Time Window including up to 288 customers. The computational results show that the proposed matheuristic is very competitive compared with the state-of-the-art methods. To better evaluate its performance, we generate a new testbed including instances with various attributes. Extensive computational experiments on the new testbed confirm the efficiency of the matheuristic. A sensitivity analysis highlights which components of the matheuristic contribute most to the solution quality

Service scheduling and vehicle routing problem to minimise the risk of missing appointments

This research studies a workforce scheduling and vehicle routing problem where technicians drive a vehicle to customer locations to perform service tasks. The service times and travel times are subject to stochastic events. There is an agreed time window for starting each service task. The risk of missing the time window for a task is defined as the probability that the technician assigned to the task arrives at the customer site later than the time window. The problem is to generate a schedule that minimises the maximum of risks and the sum of risks of all the tasks considering the effect of skill levels and task priorities. A new approach is taken to build schedules that minimise the risks of missing appointments as well as the risks of technicians not being able to complete their daily tours on time.We first analyse the probability distribution of the arrival time to any customer location considering the distributions of activities prior to this arrival. Based on the analysis, an efficient estimation method for calculating the risks is proposed, which is highly accurate and this is verified by comparing the results of the estimation method with a numerical integral method.We then develop three new workforce scheduling and vehicle routing models that minimise the risks with different considerations such as an identical standard deviation of the duration for all uncertain tasks in the linear risk minimisation model, and task priorities in the priority task risk minimisation model. A simulated annealing algorithm is implemented for solving the models at the start of the day and for re-optimisation during the day. Computational experiments are carried out to compare the results of the risk minimisation models with those of the traditional travel cost model. The performance is measured using risks and robustness. Simulation is used to compare the numbers of missed appointments and test the effect of re-optimisation.The results of the experiments demonstrate that the new models significantly reduce the risks and generate schedules with more contingency time allowances. Simulation results also show that re-optimisation reduces the number of missed appointments significantly. The risk calculation methods and risk minimisation algorithm are applied to a real-world problem in the telecommunication sector.</div

Applications of biased-randomized algorithms and simheuristics in integrated logistics

Transportation and logistics (T&L) activities play a vital role in the development of many businesses from different industries. With the increasing number of people living in urban areas, the expansion of on-demand economy and e-commerce activities, the number of services from transportation and delivery has considerably increased. Consequently, several urban problems have been potentialized, such as traffic congestion and pollution. Several related problems can be formulated as a combinatorial optimization problem (COP). Since most of them are NP-Hard, the finding of optimal solutions through exact solution methods is often impractical in a reasonable amount of time. In realistic settings, the increasing need for 'instant' decision-making further refutes their use in real life. Under these circumstances, this thesis aims at: (i) identifying realistic COPs from different industries; (ii) developing different classes of approximate solution approaches to solve the identified T&L problems; (iii) conducting a series of computational experiments to validate and measure the performance of the developed approaches. The novel concept of 'agile optimization' is introduced, which refers to the combination of biased-randomized heuristics with parallel computing to deal with real-time decision-making.Las actividades de transporte y logística (T&L) juegan un papel vital en el desarrollo de muchas empresas de diferentes industrias. Con el creciente número de personas que viven en áreas urbanas, la expansión de la economía a lacarta y las actividades de comercio electrónico, el número de servicios de transporte y entrega ha aumentado considerablemente. En consecuencia, se han potencializado varios problemas urbanos, como la congestión del tráfico y la contaminación. Varios problemas relacionados pueden formularse como un problema de optimización combinatoria (COP). Dado que la mayoría de ellos son NP-Hard, la búsqueda de soluciones óptimas a través de métodos de solución exactos a menudo no es práctico en un período de tiempo razonable. En entornos realistas, la creciente necesidad de una toma de decisiones "instantánea" refuta aún más su uso en la vida real. En estas circunstancias, esta tesis tiene como objetivo: (i) identificar COP realistas de diferentes industrias; (ii) desarrollar diferentes clases de enfoques de solución aproximada para resolver los problemas de T&L identificados; (iii) realizar una serie de experimentos computacionales para validar y medir el desempeño de los enfoques desarrollados. Se introduce el nuevo concepto de optimización ágil, que se refiere a la combinación de heurísticas aleatorias sesgadas con computación paralela para hacer frente a la toma de decisiones en tiempo real.Les activitats de transport i logística (T&L) tenen un paper vital en el desenvolupament de moltes empreses de diferents indústries. Amb l'augment del nombre de persones que viuen a les zones urbanes, l'expansió de l'economia a la carta i les activitats de comerç electrònic, el nombre de serveis del transport i el lliurament ha augmentat considerablement. En conseqüència, s'han potencialitzat diversos problemes urbans, com ara la congestió del trànsit i la contaminació. Es poden formular diversos problemes relacionats com a problema d'optimització combinatòria (COP). Com que la majoria són NP-Hard, la recerca de solucions òptimes mitjançant mètodes de solució exactes sovint no és pràctica en un temps raonable. En entorns realistes, la creixent necessitat de prendre decisions "instantànies" refuta encara més el seu ús a la vida real. En aquestes circumstàncies, aquesta tesi té com a objectiu: (i) identificar COP realistes de diferents indústries; (ii) desenvolupar diferents classes d'aproximacions aproximades a la solució per resoldre els problemes identificats de T&L; (iii) la realització d'una sèrie d'experiments computacionals per validar i mesurar el rendiment dels enfocaments desenvolupats. S'introdueix el nou concepte d'optimització àgil, que fa referència a la combinació d'heurístiques esbiaixades i aleatòries amb informàtica paral·lela per fer front a la presa de decisions en temps real.Tecnologies de la informació i de xarxe