1,670 research outputs found

    A Memetic Algorithm for the Generalized Traveling Salesman Problem

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    The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly one city from each group. The recent studies on this subject consider different variations of a memetic algorithm approach to the GTSP. The aim of this paper is to present a new memetic algorithm for GTSP with a powerful local search procedure. The experiments show that the proposed algorithm clearly outperforms all of the known heuristics with respect to both solution quality and running time. While the other memetic algorithms were designed only for the symmetric GTSP, our algorithm can solve both symmetric and asymmetric instances.Comment: 15 pages, to appear in Natural Computing, Springer, available online: http://www.springerlink.com/content/5v4568l492272865/?p=e1779dd02e4d4cbfa49d0d27b19b929f&pi=1

    Edge Elimination in TSP Instances

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    The Traveling Salesman Problem is one of the best studied NP-hard problems in combinatorial optimization. Powerful methods have been developed over the last 60 years to find optimum solutions to large TSP instances. The largest TSP instance so far that has been solved optimally has 85,900 vertices. Its solution required more than 136 years of total CPU time using the branch-and-cut based Concorde TSP code [1]. In this paper we present graph theoretic results that allow to prove that some edges of a TSP instance cannot occur in any optimum TSP tour. Based on these results we propose a combinatorial algorithm to identify such edges. The runtime of the main part of our algorithm is O(n2logn)O(n^2 \log n) for an n-vertex TSP instance. By combining our approach with the Concorde TSP solver we are able to solve a large TSPLIB instance more than 11 times faster than Concorde alone

    A new algorithm for the 2-period Balanced Traveling Salesman Problem in Euclidean graphs

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    In a previous paper, we proposed two heuristic algorithms for the euclidean 2-period Balanced Travelling Salesman Problem (2B-TSP). In this problem, which arises from a similar one introduced by Butler et al., a certain number of customers must be visited at minimum total cost over a period of two days: some customers must be visited daily, and the others on alternate days (even or odd days). Moreover, the number of customers visited in every tour must be ‘balanced’, i.e. it must be the same or, alternatively, the difference between the maximum and the minimum number of visited customers must be less than a given threshold: this kind of constraint does not appear explicitly in the paper by Butler. In this paper a third algorithm is presented which overcomes some inadequacy of the algorithm A2 we proposed in the previous paper. The new algorithm’s performance is then analyzed, with respect particularly with the first proposed algorithm.period routing problem, period travelling salesman problem, logistic, heuristic algorithms

    Network correlated data gathering with explicit communication: NP-completeness and algorithms

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    We consider the problem of correlated data gathering by a network with a sink node and a tree-based communication structure, where the goal is to minimize the total transmission cost of transporting the information collected by the nodes, to the sink node. For source coding of correlated data, we consider a joint entropy-based coding model with explicit communication where coding is simple and the transmission structure optimization is difficult. We first formulate the optimization problem definition in the general case and then we study further a network setting where the entropy conditioning at nodes does not depend on the amount of side information, but only on its availability. We prove that even in this simple case, the optimization problem is NP-hard. We propose some efficient, scalable, and distributed heuristic approximation algorithms for solving this problem and show by numerical simulations that the total transmission cost can be significantly improved over direct transmission or the shortest path tree. We also present an approximation algorithm that provides a tree transmission structure with total cost within a constant factor from the optimal
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