Accelerating TSP Solving by Using Cost-Based Solution Densities of Relaxations

RÉSUMÉ : Le problème du voyageur de commerce, ou problème du commis voyageur, est l’un des problèmes les plus importants dans le domaine de l’optimisation combinatoire. Il a fait l’objet d’innombrables travaux de recherche, à la fois théoriques et pratiques. Parmi les aspects de ce problème, nous nous intéressons particulièrement, dans le cadre de notre sujet, à certaines de ses relaxations, qui ont aussi été étudiées pour apporter de nouvelles approches à la résolution du problème. Les structures combinatoires de ces relaxations peuvent être encapsulées dans des contraintes globales existantes en programmation par contraintes (PPC), ce qui nous motive à tester une approche basée sur des travaux récents sur les heuristiques de dénombrement en PPC. L’objectif de ce projet est d’améliorer la résolution du problème du voyageur de commerce en appliquant les densités de solution aux relaxations du problème. On pose l’hypothèse qu’une arête a très peu de chance d’appartenir à la solution optimale du problème si plusieurs relaxations retournent de faibles densités de solution pour cette arête et qu’on peut donc l’éliminer pour nettoyer le graphe d’entrée du problème. On évalue donc chaque arête en fonction de leur densité de solution pour chaque relaxation et on élimine les arêtes évaluées comme "mauvaises" par toutes les relaxations. Pour l’expérimentation, cet algorithme de pré-traitement sera appliqué à plusieurs exemplaires de TSPLIB, une bibliothèque d’exemplaires du problème de voyageur de commerce. On évaluera d’abord le temps de calcul de notre méthode. Enfin, on résoudra nos exemplaires élagués avec différents solveurs (concorde, Gurobi et IBM CP Optimizer) et on comparera les résultats obtenus à la résolution des exemplaires originels. L’élagage est efficace si le temps de résolution gagné en pré-traitant les exemplaires compense le temps de pré-traitement.----------ABRACTS : The Traveling Salesman Problem is a combinatorial optimization problem, which, broadly speaking, consists of visiting a certain number n of cities, by passing through each city exactly once and by traveling the shortest possible distance. This problem is very prominent in research, as a representative of the NP-hard class of problems and as a problem with applications in various areas, including routing, networking and scheduling. Nowadays, integer programming methods dominate the landscape of TSP solvers, with the state-of-art solver concorde. As part of the efforts to solve the TSP, several of its relaxations have been studied, for computing lower bounds or domain filtering. Since these relaxations can provide insight on the combinatorial structure of the problem, we believe recent work in Constraint Programming concerning counting-based branching heuristics can bring new effective methods of using these relaxations. In this Master’s thesis, we present an approach to the traveling salesman problem which exploits cost-based solution densities from counting-based search. we propose a method for eliminating edges from the input graph of TSP instances in pre-processing, by using the solution densities from relaxations of the TSP to determine promising edges. Solution densities from different relaxations can also be combined for branching in a constraint programming solver. The efficiency and robustness of our pre-processing algorithm is evaluated by applying it to instances from TSPLIB and comparing the time to solve them with that of the original complete instances. We consider various solvers in our experimentation, namely the IBM CP Optimizer, concorde and Gurobi

The bi-objective travelling salesman problem with profits and its connection to computer networks.

This is an interdisciplinary work in Computer Science and Operational Research. As it is well known, these two very important research fields are strictly connected. Among other aspects, one of the main areas where this interplay is strongly evident is Networking. As far as most recent decades have seen a constant growing of every kind of network computer connections, the need for advanced algorithms that help in optimizing the network performances became extremely relevant. Classical Optimization-based approaches have been deeply studied and applied since long time. However, the technology evolution asks for more flexible and advanced algorithmic approaches to model increasingly complex network configurations. In this thesis we study an extension of the well known Traveling Salesman Problem (TSP): the Traveling Salesman Problem with Profits (TSPP). In this generalization, a profit is associated with each vertex and it is not necessary to visit all vertices. The goal is to determine a route through a subset of nodes that simultaneously minimizes the travel cost and maximizes the collected profit. The TSPP models the problem of sending a piece of information through a network where, in addition to the sending costs, it is also important to consider what “profit” this information can get during its routing. Because of its formulation, the right way to tackled the TSPP is by Multiobjective Optimization algorithms. Within this context, the aim of this work is to study new ways to solve the problem in both the exact and the approximated settings, giving all feasible instruments that can help to solve it, and to provide experimental insights into feasible networking instances

An Integer Programming approach to Bayesian Network Structure Learning

We study the problem of learning a Bayesian Network structure from data using an Integer Programming approach. We study the existing approaches, an in particular some recent works that formulate the problem as an Integer Programming model. By discussing some weaknesses of the existing approaches, we propose an alternative solution, based on a statistical sparsification of the search space. Results show how our approach can lead to promising results, especially for large network

Continuous observation planning for autonomous exploration

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (p. 233-239).Many applications of autonomous robots depend on the robot being able to navigate in real world environments. In order to navigate or path plan, the robot often needs to consult a map of its surroundings. A truly autonomous robot must, therefore, be able to drive about its environment and use its sensors to build a map before performing any tasks that require this map. Algorithms that control a robot's motion for the purpose of building a map of an environment are called autonomous exploration algorithms. Because resources such as time and energy are highly constrained in many mobile robot missions, a key requirement of autonomous exploration algorithms is that they cause the robot to explore efficiently. Planning paths to candidate observation points that will lead to efficient exploration is challenging, however, because the set of candidates, and, therefore, the robot's plan, change frequently as the robot adds information to the map. The main claim of this thesis is that, in situations in which the robot discerns the large scale structure of the environment early on during its exploration, the robot can produce paths that cause it to explore efficiently by planning observations to make over a finite horizon. Planning over a finite horizon entails finding a path that visits candidates with the maximum possible total utility, subject to the constraint that the path cost is less than a given threshold value. Finding such a path corresponds to solving the Selective Traveling Salesman Problem (S-TSP) over the set of candidates.(cont.) In this thesis, we evaluate our claim by implementing full horizon, finite horizon, and greedy approaches to planning observations, and comparing the efficiency of these approaches in both real and simulated environments. In addition, we develop a new approach for solving the S-TSP by framing it as an Optimal Constraint Satisfaction Problem (OCSP).by Bradley R. Hasegawa.M.Eng

Dynamics of Macrosystems; Proceedings of a Workshop, September 3-7, 1984

There is an increasing awareness of the important and persuasive role that instability and random, chaotic motion play in the dynamics of macrosystems. Further research in the field should aim at providing useful tools, and therefore the motivation should come from important questions arising in specific macrosystems. Such systems include biochemical networks, genetic mechanisms, biological communities, neutral networks, cognitive processes and economic structures. This list may seem heterogeneous, but there are similarities between evolution in the different fields. It is not surprising that mathematical methods devised in one field can also be used to describe the dynamics of another. IIASA is attempting to make progress in this direction. With this aim in view this workshop was held at Laxenburg over the period 3-7 September 1984. These Proceedings cover a broad canvas, ranging from specific biological and economic problems to general aspects of dynamical systems and evolutionary theory

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum