Constraint Programming Algorithms for Route Planning Exploiting Geometrical Information

Problems affecting the transport of people or goods are plentiful in industry and commerce and they also appear to be at the origin of much more complex problems. In recent years, the logistics and transport sector keeps growing supported by technological progress, i.e. companies to be competitive are resorting to innovative technologies aimed at efficiency and effectiveness. This is why companies are increasingly using technologies such as Artificial Intelligence (AI), Blockchain and Internet of Things (IoT). Artificial intelligence, in particular, is often used to solve optimization problems in order to provide users with the most efficient ways to exploit available resources. In this work we present an overview of our current research activities concerning the development of new algorithms, based on CLP techniques, for route planning problems exploiting the geometric information intrinsically present in many of them or in some of their variants. The research so far has focused in particular on the Euclidean Traveling Salesperson Problem (Euclidean TSP) with the aim to exploit the results obtained also to other problems of the same category, such as the Euclidean Vehicle Routing Problem (Euclidean VRP), in the future.Comment: In Proceedings ICLP 2020, arXiv:2009.0915

Constraint programming based column generation heuristics for a ship routing and berthing time assignment problem

Author name used in this publication: King-Wah PangRefereed conference paper2010-2011 > Academic research: refereed > Refereed conference paperOther VersionPublishe

An Exact Constraint Logic Programming Algorithm for the Traveling Salesman Problem with Time Windows

This paper presents a constraint logic programming model for the traveling salesman problem with time windows which yields an exact branchand -bound optimization algorithm without any restrictive assumption on the time windows. Unlike dynamic programming approaches whose performance relies heavily on the degree of discretization applied to the data, our algorithm does not suffer from such space-complexity issues. The data-driven mechanism at its core more fully exploits pruning rules developed in operations research by using them not only a priori but also dynamically during the search. Computational results are reported and comparisons are made with both exact and heuristic algorithms. On Solomon's well-known test bed, our algorithm is instrumental in achieving new best solutions for some of the problems in set RC2 and strengthens the presumption of optimality for the best known solutions to the problems in set C2. Introduction In the last few years, constraint programming (cp) has b..

Constraint Programming based Local Search for the Vehicle Routing Problem with Time Windows

El projecte es centra en el "Vehicle Routing Problem with Time Windows". Explora i testeja un mètode basat en una formulació del problema en termes de programació de restriccions. Implementa un mètode de cerca local amb la capacitat de fer grans moviments anomenat "Large Neighbourhood Search"

Caixeiro viajante com janelas temporais: aplicação ao caso da re-food

Trabalho de projecto de mestrado, Matemática Aplicada à Economia e Gestão, Universidade de Lisboa, Faculdade de Ciências, 2015Este trabalho de projeto apresenta um modelo matemático e uma heurística para a determinação das rotas feitas pela equipa de voluntários de Re-Food de Telheiras, uma organização portuguesa sem fins lucrativos constituída como IPSS (Instituição Particular de Solidariedade Social). Nesta organização uma equipa de voluntários tem que percorrer um circuito, iniciando e terminando no centro de operações passando por todos os parceiros alimentares apenas uma vez, respeitando as janelas temporais por eles estabelecidas. Após a recolha de informação junto dos responsáveis da Re-Food e o acompanhamento das equipas de voluntários, verificou-se que estávamos perante um problema de determinação de rotas para um veículo com restrições adicionais de janelas temporais. Assim, este problema pode ser modelado como um problema do caixeiro viajante com restrições temporais. O veículo é a equipa de voluntários que terá que passar uma única vez por todos os parceiros alimentares com localizações geográficas diferentes, recolhendo os seus excedentes alimentares, iniciando e terminando no centro de operações. Tendo como restrições as janelas temporais imposta pelos parceiros alimentares. Neste trabalho é apresentado o modelo matemático correspondente ao problema em estudo e apresenta-se uma heurística composta por duas fases: uma fase construtiva em que se obtém uma solução admissível e uma fase de melhoramento com uma etapa de destruição e de reconstrução da solução. Os dados reais disponibilizados pela Re-Food foram usados considerando o modelo. Geraram-se aleatoriamente dados simulando a realidade da Re-Food. Para estes dados obtiveram-se resultados quer considerando o modelo quer considerando a heurística.This dissertation presents a mathematical model and a heuristic for determining the routes made by the team of volunteers of Re-Food Telheiras, a Portuguese non-profit organization incorporated as IPSS (Private Institution of Social Solidarity). In this organization a team of volunteers go through a circuit, starting and ending at the center of operations through all food partners only once, respecting the time frames established by them. After collecting information from those in charge of Re-Food and monitoring the volunteer teams, it was considered that we were facing the problem of determining routes for a vehicle with time constraints. Therefore, this problem can be modeled as a traveling salesman problem with time window constraints. The vehicle is the team of volunteers who will have to go through all food partners with different geographical locations, collecting their food surpluses, starting and ending at the center of operations. There are temporal windows restrictions imposed by food partners. In this thesis a mathematical model corresponding to the problem in study is presented and also a two-phase heuristic: in the first phase a feasible solution is obtained and in the improvement phase there is a destruction of the current solution followed by a reconstruction phase. The real data provided by Re- Food were used for the model. Random data was generated trying to simulate the Re-Food reality. For this data computational results were obtained both considering the model and the heuristic

Heuristiques de branchement basées sur le dénombrement pour la résolution de problèmes d'arbres de recouvrement contraints

Résumé Ce mémoire se concentre sur la programmation par contraintes (CP), une approche puissante pour résoudre des problèmes combinatoires. Notre travail tourne autour de l'un des concepts clés de la CP : les heuristiques de branchement. Cette composante définit comment l'espace de recherche doit être exploré, quelles régions devraient être visitées en premier pour trouver une solution rapidement. Le progrès sur ce sujet est important, étant donné que la CP n'admet toujours pas d'approche générique efficace pour la recherche. Les heuristiques de branchement basées sur le dénombrement comme maxSD se sont montrées efficaces pour une variété de problèmes de satisfaction de contraintes. Ces heuristiques ont besoin d'un algorithme dédié qui calcule la densité de solution locale pour chaque paire de variable-valeur, pour chaque contrainte, de façon semblable à ce qui a été fait pour les algorithmes de filtrage, pour appliquer l'inférence locale. Cependant, plusieurs contraintes n'ont toujours pas de tel algorithme. Dans notre travail, nous dérivons un algorithme exact qui, en temps polynomial, calcule la densité de solution pour la contrainte d'arbre de recouvrement, à partir d'un résultat connu sur le nombre d'arbres de recouvrement dans un graphe non orienté. Nous étendons ensuite cet algorithme pour les graphes orientés, ce qui nous permet de calculer la densité de solution pour une contrainte d'anti-arborescence, également en temps polynomial. Ensuite, nous comparons empiriquement les heuristiques de branchement basées sur ces résultats avec d'autres approches génériques. Tout d'abord, nous utilisons le problème d'arbres de recouvrement de degré contraint, sur des graphes non orientés pour démontrer l'efficacité de notre approche. Ensuite, pour les graphes orientés, nous utilisons le problème de la k-arborescence.Les heuristiques de branchement basées sur le dénombrement se montrent comme des approches très efficaces, autant pour le cas non orienté que pour le cas orienté, trouvant rapidement des solutions avec un minimum de retours en arrière.----------Abstract This Master's thesis focuses on Constraint Programming (CP), a powerful approach to solve combinational problems. Our work revolves around one of the main components of CP : branching heuristics. This component defines how the search space must be explored, which areas should be visited first in order to quickly find a solution to the problem. Advances on this topic are critical, since CP lacks a generic effective search approach. Counting-based branching heuristics such as maxSD were shown to be effective on a variety of constraint satisfaction problems. These heuristics require that we equip each family of constraints with a dedicated algorithm to compute the local solution density of variable assignments, much as what has been done with filtering algorithms to apply local inference. However, many constraints still lack such an algorithm. In our work, we derive an exact polytime algorithm to compute solution densities for a spanning tree constraint, starting from a known result about the number of spanning trees in an undirected graph. We then extend the algorithm for directed graphs, which allows us to compute solution densities for a reverse arborescence constraint, also in polytime. We then empirically compare branching heuristics based on those results with other generic heuristics. First, we use the degree contrained spanning tree, on undirected graphs, to demonstrate the effectiveness of our approach. Then, for the directed graphs, we use the k-arborescence problem. Counting-based branching heuristics prove to be very effective for both the undirected and directed case, finding solutions quickly and without many backtracks

Une heuristique de recherche à voisinage variable pour le problème du voyageur de commerce avec fenêtres de temps

Nous adaptons une heuristique de recherche à voisinage variable pour traiter le problème du voyageur de commerce avec fenêtres de temps (TSPTW) lorsque l'objectif est la minimisation du temps d'arrivée au dépôt de destination. Nous utilisons des méthodes efficientes pour la vérification de la réalisabilité et de la rentabilité d'un mouvement. Nous explorons les voisinages dans des ordres permettant de réduire l'espace de recherche. La méthode résultante est compétitive avec l'état de l'art. Nous améliorons les meilleures solutions connues pour deux classes d'instances et nous fournissons les résultats de plusieurs instances du TSPTW pour la première fois.We adapt a general variable neighborhood search heuristic to solve the traveling salesman problem with time windows (TSPTW) where the objective is to minimize the completion time. We use efficient methods to check the feasibility and the profitability of a movement. We use a specific order to reduce the search space while exploring the neighborhoods. The resulting method is competitive with the state-of-the-art. We improve the best known solutions for two classes of instances and provide the results of multiple instances of TSPTW for the first time

A Study in Three Practical Management Science Problems

This study of practical problems in Management Science (MS) describes novel mathematical models for three different decision settings. It addresses questions of: (a) what optimal route should be taken through a time-windows and topographically complex network; (b) what optimal sequencing of scheduled surgeries best coordinates flow of patients through central recovery; and (c) what prices should be charged and what stock amounts should be produced for two markets or channels to maximize profit explicitly, given various capacity and uncertainty conditions. The first problem is in a sport analytics context, using a novel Integer Programming and big data from Whistler-Blackcomb ski resort. The second is to coordinate dozens of surgeries at London Health Sciences Centre, using a novel Constraint Programming model mapped to and parameterized with hospital data, including a tool for visualizing process and patient flow. The third problem is relevant to almost any business with a secondary market or sales channel, as it helps them identify profit optimal prices based on simple demand estimates and cost information they can easily provide for their own setting. The studies use fundamentally different operational research techniques, in each case uniquely extended to the problem setting. The first two are combinatorial problems, neither one extremely beyond human cognitive ability, and both involving lots of uncertainty, and thus the sort of problem managers tend to dismiss as not efficient or practical to solve analytically. We show in the first study that vastly more skiers could achieve the challenge by following our route recommendation, unintuitive as are some of its elements, initially. In the second study, our scheduling model consistently outperforms currently unstructured-independent approach at the hospital. The final study is mathematical but demonstrates that by considering distinct market costs in pricing a firm can invariably earn more profit