A bi-objective stochastic approach for stochastic CARP

The Capacitated Arc Routing Problem (CARP) occurs in applications like urban waste collection or winter gritting. It is usually defined in literature on an undirected graph G = (V, E) , with a set V of n nodes and a set E of m edges. A fleet of identical vehicles of capacity Q is based at a depot node. Each edge i has a cost (length) ci and a demand qi (e.g. an amount of waste), and it may be traversed any number of times. The edges with non-zero demands or tasks require service by a vehicle. The goal is to determine a set of vehicle trips (routes) of minimum total cost, such that each trip starts and ends at the depot, each task is serviced by one single trip, and the total demand handled by any vehicle does not exceed Q . To the best of our knowledge the best published method is a memetic algorithm first introduced in 2001. This article provides a new extension of the NSGA II (Non-dominated Sorting Genetic Algorithm) template to comply with the stochastic sight of the CARP. The main contribution is: - to introduce mathematical expression to evaluate both cost and duration of the longest trip and also standard deviation of these two criteria. - to use a NGA-II template to optimize simultaneously the cost and the duration of the longest trip including standard deviation. The numerical experiments managed on the thee well-known benchmark sets of DeArmon, Belenguer and Benavent and Eglese, prove it is possible to obtain robust solutions in four simultaneous criteria in rather short computation times

Applied (Meta)-Heuristic in Intelligent Systems

Engineering and business problems are becoming increasingly difficult to solve due to the new economics triggered by big data, artificial intelligence, and the internet of things. Exact algorithms and heuristics are insufficient for solving such large and unstructured problems; instead, metaheuristic algorithms have emerged as the prevailing methods. A generic metaheuristic framework guides the course of search trajectories beyond local optimality, thus overcoming the limitations of traditional computation methods. The application of modern metaheuristics ranges from unmanned aerial and ground surface vehicles, unmanned factories, resource-constrained production, and humanoids to green logistics, renewable energy, circular economy, agricultural technology, environmental protection, finance technology, and the entertainment industry. This Special Issue presents high-quality papers proposing modern metaheuristics in intelligent systems

A survey of swarm intelligence for dynamic optimization: algorithms and applications

Swarm intelligence (SI) algorithms, including ant colony optimization, particle swarm optimization, bee-inspired algorithms, bacterial foraging optimization, firefly algorithms, fish swarm optimization and many more, have been proven to be good methods to address difficult optimization problems under stationary environments. Most SI algorithms have been developed to address stationary optimization problems and hence, they can converge on the (near-) optimum solution efficiently. However, many real-world problems have a dynamic environment that changes over time. For such dynamic optimization problems (DOPs), it is difficult for a conventional SI algorithm to track the changing optimum once the algorithm has converged on a solution. In the last two decades, there has been a growing interest of addressing DOPs using SI algorithms due to their adaptation capabilities. This paper presents a broad review on SI dynamic optimization (SIDO) focused on several classes of problems, such as discrete, continuous, constrained, multi-objective and classification problems, and real-world applications. In addition, this paper focuses on the enhancement strategies integrated in SI algorithms to address dynamic changes, the performance measurements and benchmark generators used in SIDO. Finally, some considerations about future directions in the subject are given

Enhancement on the modified artificial bee colony algorithm to optimize the vehicle routing problem with time windows

The vehicle routing problem with time windows (VRPTW) is a non-deterministictime hard (NP-hard) with combinatorial optimization problem (COP). The Artificial Bee Colony (ABC) is a popular swarm intelligence algorithm for COP. In this study, existing Modified ABC (MABC) algorithm is revised to solve the VRPTW. While MABC has been reported to be successful, it does have some drawbacks, including a lack of neighbourhood structure selection during the intensification process, a lack of knowledge in population initialization, and occasional stops proceeding the global optimum. This study proposes an enhanced Modified ABC (E-MABC) algorithm which includes (i) N-MABC that overcomes the shortage of neighborhood selection by exchanging the neighborhood structure between two different routes in the solution; (ii) MABC-ACS that solves the issues of knowledge absence in MABC population initialization by incorporating ant colony system heuristics, and (iii) PMABC which addresses the occasional stops proceeding to the global optimum by introducing perturbation that accepts an abandoned solution and jumps out of a local optimum. The proposed algorithm was evaluated using benchmark datasets comprising 56 VRPTW instances and 56 Pickup and Delivery Problems with Time Windows (PDPTW). The performance has been measured using the travelled distance (TD) and the number of deployed vehicles (NV). The results showed that the proposed E-MABC has lower TD and NV than the benchmarked MABC and other algorithms. The E-MABC algorithm is better than the MABC by 96.62%, MOLNS by 87.5%, GAPSO by 53.57%, MODLEM by 76.78%, and RRGA by 42.85% in terms of TD. Additionally, the E-MABC algorithm is better than the MABC by 42.85%, MOLNS by 17.85%, GA-PSO and RRGA by 28.57%, and MODLEN by 46.42% in terms of NV. This indicates that the proposed E-MABC algorithm is promising and effective for the VRPTW and PDPTW, and thus can compete in other routing problems and COPs

A Metaheuristic Genetic Algorithm for Routing Bridge Inspection Robots

The safety and integrity of transportation infrastructure relies heavily on bridge inspections which can be expensive and hazardous for inspectors. Recent advancements in robotics and autonomy has resulted in steel truss climbing robots for bridge inspection that can reduce these costs and improve safety. However, optimally routing multiple robots to traverse and inspect each member of a truss bridge remains a challenging NP-hard problem which we represent by the Min-Max k-Chinese Postman Problem. In this thesis we attack this problem by constructing routes with a Metaheuristic Genetic Algorithm. The results demonstrate that this approach provides high quality solutions in reasonable time. Specifically, on standard benchmarks from literature we reveal that the quality of solutions are statistically indistinguishable compared to a prior state-of-the-art Tabu Search method. Furthermore, our Metaheuristic Genetic Algorithm surpasses the prior best Direct Encoded Genetic Algorithm by producing routes that are on average 15.24% better quality in a fraction (0.05) of the time on 20 new benchmark problems representing four well-known bridge truss structures. We also investigate the impact of multiple robot starting points on the total inspection time in the multi-depot variant of the Min-Max k-Chinese Postman Problem. The Metaheuristic Genetic Algorithm multi-depot solutions outperforms the previous best Genetic Algorithm multi-depot solutions that are on average 41.72% better quality and 22 times faster with three different postman configurations on the 20 new benchmark problems. This thesis therefore indicates that Metaheuristic Genetic Algorithms are a viable approach to the Min-Max k-Chinese Postman Problem and thus for routing autonomous inspection robots for safer, most cost effective bridge inspection. More generally, Metaheuristic Genetic Algorithms may show promise for attacking other similar Arc Routing Problems

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

Iterative restricted space search : a solving approach based on hybridization

Face à la complexité qui caractérise les problèmes d'optimisation de grande taille l'exploration complète de l'espace des solutions devient rapidement un objectif inaccessible. En effet, à mesure que la taille des problèmes augmente, des méthodes de solution de plus en plus sophistiquées sont exigées afin d'assurer un certain niveau d 'efficacité. Ceci a amené une grande partie de la communauté scientifique vers le développement d'outils spécifiques pour la résolution de problèmes de grande taille tels que les méthodes hybrides. Cependant, malgré les efforts consentis dans le développement d'approches hybrides, la majorité des travaux se sont concentrés sur l'adaptation de deux ou plusieurs méthodes spécifiques, en compensant les points faibles des unes par les points forts des autres ou bien en les adaptant afin de collaborer ensemble. Au meilleur de notre connaissance, aucun travail à date n'à été effectué pour développer un cadre conceptuel pour la résolution efficace de problèmes d'optimisation de grande taille, qui soit à la fois flexible, basé sur l'échange d'information et indépendant des méthodes qui le composent. L'objectif de cette thèse est d'explorer cette avenue de recherche en proposant un cadre conceptuel pour les méthodes hybrides, intitulé la recherche itérative de l'espace restreint, ±Iterative Restricted Space Search (IRSS)>>, dont, la principale idée est la définition et l'exploration successives de régions restreintes de l'espace de solutions. Ces régions, qui contiennent de bonnes solutions et qui sont assez petites pour être complètement explorées, sont appelées espaces restreints "Restricted Spaces (RS)". Ainsi, l'IRSS est une approche de solution générique, basée sur l'interaction de deux phases algorithmiques ayant des objectifs complémentaires. La première phase consiste à identifier une région restreinte intéressante et la deuxième phase consiste à l'explorer. Le schéma hybride de l'approche de solution permet d'alterner entre les deux phases pour un nombre fixe d'itérations ou jusqu'à l'atteinte d'une certaine limite de temps. Les concepts clés associées au développement de ce cadre conceptuel et leur validation seront introduits et validés graduellement dans cette thèse. Ils sont présentés de manière à permettre au lecteur de comprendre les problèmes que nous avons rencontrés en cours de développement et comment les solutions ont été conçues et implémentées. À cette fin, la thèse a été divisée en quatre parties. La première est consacrée à la synthèse de l'état de l'art dans le domaine de recherche sur les méthodes hybrides. Elle présente les principales approches hybrides développées et leurs applications. Une brève description des approches utilisant le concept de restriction d'espace est aussi présentée dans cette partie. La deuxième partie présente les concepts clés de ce cadre conceptuel. Il s'agit du processus d'identification des régions restreintes et des deux phases de recherche. Ces concepts sont mis en oeuvre dans un schéma hybride heuristique et méthode exacte. L'approche a été appliquée à un problème d'ordonnancement avec deux niveaux de décision, relié au contexte des pâtes et papier: "Pulp Production Scheduling Problem". La troisième partie a permit d'approfondir les concepts développés et ajuster les limitations identifiées dans la deuxième partie, en proposant une recherche itérative appliquée pour l'exploration de RS de grande taille et une structure en arbre binaire pour l'exploration de plusieurs RS. Cette structure a l'avantage d'éviter l'exploration d 'un espace déjà exploré précédemment tout en assurant une diversification naturelle à la méthode. Cette extension de la méthode a été testée sur un problème de localisation et d'allocation en utilisant un schéma d'hybridation heuristique-exact de manière itérative. La quatrième partie généralise les concepts préalablement développés et conçoit un cadre général qui est flexible, indépendant des méthodes utilisées et basé sur un échange d'informations entre les phases. Ce cadre a l'avantage d'être général et pourrait être appliqué à une large gamme de problèmes

Models and advanced optimization algorithms for the integrated management of logistics operations

Tese de Doutoramento em Engenharia Industrial e de Sistemas.In this thesis, we propose a set of algorithms regarding real combinatorial optimization problems in the context of transportation of goods. These problems consist in the combination of the vehicle routing problem with the two-dimensional bin-packing problem, which is also known as the vehicle routing problem with two-dimensional loading constraints. We also analyzed two related problems, namely the elementary shortest path and the vehicle routing problem with mixed linehauls and backhauls. In both problems, two-dimensional loading constraints are explicitly considered. Two column generation based approaches are proposed for the vehicle routing problem with two-dimensional constraints. The rst one relies on a branch-and-price algorithm with di erent branching schemes. A family of dual valid inequalities is also de ned, aiming to accelerate the convergence of the algorithm. The second approach is based on a set of di erent heuristics strategies, which are applied to the reformulated model. The elementary shortest path problem with two-dimensional constraints is addressed due to its importance in solving the subproblem of the column generation algorithms. To the best of our knowledge, we contribute with the rst approach for this problem, through di erent constructive strategies to achieve feasible solutions, and a variable neighborhood search algorithm in order to search for improved solutions. In what concerns the vehicle routing problem with mixed linehaul and backhauls and two-dimensional loading constraints, di erent variable neighborhood search algorithms are proposed. These algorithms explored various neighborhood structures, being some of those developed based on the features of the problem. All the proposed methods were implemented and experimentally tested. An exhaustive set of computational tests was conducted, using, for this purpose, a large group of benchmark instances. In some cases, a large set of benchmark instances was adapted in order asses the quality of the proposed models. All the obtained results are presented and discussed.Nesta tese, propomos um conjunto de algoritmos sobre problemas reais de otimiza c~ao combinat oria no contexto do transporte de bens. Estes problemas consistem na combina c~ao do problema de planeamento de rotas de ve culos com o problema de empacotamento bidimensional, que tamb em e conhecido como o problema de planeamento de rotas de ve culos com restri c~oes de carregamento bidimensional. Analisamos tamb em dois problemas relacionados, nomeadamente o problema de caminho mais curto e o problema de planeamento de rotas ve culos com entregas e recolhas indiferenciadas. Em ambos os problemas, s~ao explicitamente consideradas restri c~oes de carregamento bidimensional. Duas abordagens baseadas em gera c~ao de colunas s~ao propostas para o problema de planeamento de rotas de ve culos com restri c~oes de carregamento bidimensional. O primeiro baseia-se num algoritmo de parti c~ao e gera c~ao de colunas com diferentes estrat egias de parti c~ao. Uma fam lia de desigualdades duais v alidas e tamb em apresentada, com o objetivo de acelerar a converg^encia do algoritmo. A segunda abordagem baseia-se num conjunto de diferentes estrat egias heur sticas, que s~ao aplicadas ao modelo reformulado. O problema do caminho mais curto com restri c~oes de carregamento bidimensional e abordado devido a sua import^ancia na resolu c~ao do subproblema dos aos algoritmos de gera c~ao de colunas. De acordo com o nosso conhecimento, contribu mos com a primeira abordagem para este problema, atrav es de diferentes estrat egias construtivas para obter solu c~oes v alidas, e um algoritmo de pesquisa em vizinhan ca vari avel, com o objetivo de encontrar solu c~oes de melhor qualidade. No que concerne ao problema de planeamento de rotas de ve culos com entregas e recolhas indiferenciadas, diferentes algoritmos de pesquisa em vizinhan ca vari avel s~ao propostos. Estes algoritmos exploram v arias estruturas de vizinhan ca, sendo algumas destas desenvolvidas com base nas caracter sticas do problema. Todos os m etodos propostos foram implementados e testados experimentalmente. Um extenso conjunto de testes computacionais foi efetuado, utilizando um grande grupo de inst^ancias descritas na literatura. Em alguns casos, um grande conjunto de inst^ancias descritas na literatura foi adaptado com o objetivo de avaliar a qualidade dos m etodos propostos

A Branch-and-Cut based Pricer for the Capacitated Vehicle Routing Problem

openIl Capacitated Vehicle Routing Problem, abbreviato come CVRP, è un problema di ottimizzazione combinatoria d'instradamento nel quale, un insieme geograficamente sparso di clienti con richieste note deve essere servito da una flotta di veicoli stazionati in una struttura centrale. Negli ultimi due decenni, tecniche di Column generation incorporate all'interno di frameworks branch-price-and-cut sono state infatti l'approccio stato dell'arte dominante per la costruzione di algoritmi esatti per il CVRP. Il pricer, un componente critico nella column generation, deve risolvere il Pricing Problem (PP) che richiede la risoluzione di un Elementary Shortest Path Problem with Resource Constraints (ESPPRC) in una rete di costo ridotto. Pochi sforzi scientifici sono stati dedicati allo studio di approcci branch-and-cut per affrontare il PP. L'ESPPRC è stato tradizionalmente rilassato e risolto attraverso algoritmi di programmazione dinamica. Questo approccio, tuttavia, ha due principali svantaggi. Per cominciare, peggiora i dual bounds ottenuti. Inoltre, il tempo di esecuzione diminuisce all'aumentare della lunghezza dei percorsi generati. Per valutare la performance dei loro contributi, la comunità di ricerca operativa ha tradizionalmente utilizzato una serie d'istanze di test storiche e artificiali. Tuttavia, queste istanze di benchmark non catturano le caratteristiche chiave dei moderni problemi di distribuzione del mondo reale, che sono tipicamente caratterizzati da lunghi percorsi. In questa tesi sviluppiamo uno schema basato su un approccio branch-and-cut per risolvere il pricing problem. Studiamo il comportamento e l'efficacia della nostra implementazione nel produrre percorsi più lunghi comparandola con soluzioni all'avanguardia basate su programmazione dinamica. I nostri risultati suggeriscono che gli approcci branch-and-cut possono supplementare il tradizionale algoritmo di etichettatura, indicando che ulteriore ricerca in quest'area possa portare benefici ai risolutori CVRP.The Capacitated Vehicle Routing Problem, CVRP for short, is a combinatorial optimization routing problem in which, a geographically dispersed set of customers with known demands must be served by a fleet of vehicles stationed at a central facility. Column generation techniques embedded within branch-price-and-cut frameworks have been the de facto state-of-the-art dominant approach for building exact algorithms for the CVRP over the last two decades. The pricer, a critical component in column generation, must solve the Pricing Problem (PP), which asks for an Elementary Shortest Path Problem with Resource Constraints (ESPPRC) in a reduced-cost network. Little scientific efforts have been dedicated to studying branch-and-cut based approaches for tackling the PP. The ESPPRC has been traditionally relaxed and solved through dynamic programming algorithms. This approach, however, has two major drawbacks. For starters, it worsens the obtained dual bounds. Furthermore, the running time degrades as the length of the generated routes increases. To evaluate the performance of their contributions, the operations research community has traditionally used a set of historical and artificial test instances. However, these benchmark instances do not capture the key characteristics of modern real-world distribution problems, which are usually characterized by longer routes. In this thesis, we develop a scheme based on a branch-and-cut approach for solving the pricing problem. We study the behavior and effectiveness of our implementation in producing longer routes by comparing it with state-of-the-art solutions based on dynamic programming. Our results suggest that branch-and-cut approaches may supplement the traditional labeling algorithm, indicating that further research in this area may bring benefits to CVRP solvers