Many problems, and in particular routing problems, require to find one or many circuits in a weighted graph. The weights often express the distance or the travel time between vertices. We propose in this paper various filtering algorithms for the weighted circuit constraint which maintain a circuit in a weighted graph. The filtering algorithms are typical cost based filtering algorithms relying...

The traveling salesman problem (TSP) is one of the most widely studied NP-hard combinatorial optimization problems and traditional genetic algorithm trapped into the local minimum easily for solving this problem. Particle Swarm Optimization (PSO) algorithm was developed under the inspiration of behavior laws of bird flocks, fish schools and human communities. Compared with the genetic algorithm...

This work focuses on improving the Hop eld network for solv ing optimization problems Although much work has been done in this area the performance of the Hop eld network is still not satisfactory in terms of valid convergence and quality of solutions We address this issue in this work by combing a new activation function EBA and a new relax ation procedure CR in order to improve the performanc...

Biogeography-based optimization algorithm(BBO) is a new kind of optimization algorithm based on Biogeography. It is designed based on the migration strategy of animals to solve the problem of optimization. In this paper, a new algorithm-Biogeography Migration Algorithm for Traveling Salesman Problem(TSPBMA) is presented. Migration operator is designed. It is tested on four classical TSP problem...

This paper is concerned with polynomial time approximations schemes for the generalized geometric problems with geographic clustering. We illustrate the approach on the generalized traveling salesman problem which is also known as Group-TSP or TSP with neighborhoods. We prove that under the condition that all regions are non-intersecting and have comparable sizes and shapes, the problem admits ...

Abstract. In this paper, the experiments with local search heuristic algorithms for the traveling salesman problem (TSP) are described. Since the ordinary local search heuristics very seldom yield solutions of high quality, we investigate the enhanced local search algorithms using the extended neighbourhood structures. We also examine the performance of the local search heuristics in an iterate...

We present deterministic approximation algorithms for the multi-criteria maximum traveling salesman problem (Max-TSP). Our algorithms are faster and simpler than the existing randomized algorithms. We devise algorithms for the symmetric and asymmetric multi-criteria Max-TSP that achieve ratios of 1/2k−ε and 1/(4k−2)−ε, respectively, where k is the number of objective functions. For two objectiv...

We improve and derandomize the best known approximation algorithm for the twocriteria metric traveling salesman problem (2-TSP). More precisely, we construct a deterministic 2-approximation which answers an open question by Manthey. Moreover, we show that 2-TSP is randomized (3/2 + ε, 2)-approximable, and we give the first randomized approximations for the two-criteria traveling salesman path p...

Generalized traveling salesman problem (GTSP) is an extension of classical traveling salesman problem (TSP), which is a combinatorial optimization problem and an NP-hard problem. In this paper, an efficient discrete state transition algorithm (DSTA) for GTSP is proposed, where a new local search operator named K-circle, directed by neighborhood information in space, has been introduced to DSTA ...

We describe an artificial ant colony capable of solving the traveling salesman problem (TSP). Ants of the artificial colony are able to generate successively shorter feasible tours by using information accumulated in the form of a pheromone trail deposited on the edges of the TSP graph. Computer simulations demonstrate that the artificial ant colony is capable of generating good solutions to bo...