We introduce a new combinatorial optimization problem, which is a generalization of the Traveling Salesman Problem (TSP) and which we call Traveling Salesman Problem of Second Order (2-TSP). It is motivated by an application in bioinformatics, especially the Permuted Variable Length Markov model. We propose seven elementary heuristics and two exact algorithms for the 2-TSP, some of which are ge...

The Quota Traveling Salesman Problem is a generalization of the well known Traveling Salesman Problem. The goal of the traveling salesman is, in this case, to reach a given quota of the sales, minimizing the amount of time. In this paper we address the on-line version of the problem, where requests are given over time. We present algorithms for various metric spaces, and analyze their performan...

We consider cooperative traveling salesman games with non-negative asymmetric costs satisfying the triangle inequality. We construct a stable cost allocation with budget balance guarantee equal to the Held-Karp integrality gap for the asymmetric traveling salesman problem, using the parsimonious property and a previously unknown connection to linear production games. We also show that our techn...

The Quota Traveling Salesman Problem is a generalization of the well known Traveling Salesman Problem. The goal of the traveling salesman is, in this case, to reach a given quota of the sales, minimizing the amount of time. In this paper we address the on-line version of the problem, where requests are given over time. We present algorithms for various metric spaces, and analyze their performan...

This paper deals with the pickup and delivery traveling salesman problem. First we show how to adapt some classical traveling salesman heuristics to solve this problem, then we propose a new and e$cient composite heuristic. The proposed heuristic is composed of two phases: a solution construction phase including a local optimization component and a deletion and re-insertion improvement phase. T...

This paper presents a heuristic technique that uses the Wang Recurrent Neural Network with the "Winner Takes All" principle to solve the Traveling Salesman Problem. When the Wang Neural Network presents solutions for the Assignment Problem with all constraints satisfied, the "Winner Takes All" principle is applied to the values in the Neural Network’s decision variables, with the additional con...

By introducing the concept of Oracle we propose an approach for improving the performance of genetic algorithms for large-scale asymmetric Traveling Salesman Problems. The results have shown that the proposed approach allows overcoming some traditional problems for creating efficient genetic algorithms. Keywords—Genetic algorithms, Traveling Salesman Problem, optimal decision distribution, Oracle.

The double traveling salesman problem with multiple stacks is a variant of the pickup and delivery traveling salesman problem in which all pickups must be completed before any of the deliveries. In addition, items can be loaded on multiple stacks in the vehicle and each stack must obey the last-in-first-out policy. The problem consists in finding the shortest Hamiltonian cycles covering all pic...