This paper solves the dynamic traveling salesman problem (DTSP) using dynamic Gaussian Process Regression (DGPR) method. The problem of varying correlation tour is alleviated by the nonstationary covariance function interleaved with DGPR to generate a predictive distribution for DTSP tour. This approach is conjoined with Nearest Neighbor (NN) method and the iterated local search to track dynami...

A highly efficient algorithm (HK) devised by Held and Karp for solving the symmetric traveling-salesman problem was presented at the 7th Mathematical Programming Symposium in 1970 and published in Mathematical Programming in 1971. Its outstanding performance is due to a clever exploitation of the relationship between the traveling-salesman problem and minimum spanning trees. However, various im...

The traveling salesman problem (TSP) belongs to the most basic, most important, and most investigated problems in combinatorial optimization. Although it is an NP-hard problem, many of its special cases can be solved efficiently in polynomial time. We survey these special cases with emphasis on the results that have been obtained during the decade 1985–1995. This survey complements an earlier s...

Self-organizing neural networks have topological characteristics that can be effectively used in solving the traveling salesman problem. In this paper we propose a novel problem of maximizing the length of a non-intersecting closed route in which each node, except for the starting point, is only visited once. The self-organizing network algorithm of the traveling salesman problem is modified to...

The Probabilistic Traveling Salesman Problem is in general NP-Hard, the objective of this paper is to look for particular cases which can be solved in an easy way. First we give the relation between the two problems deterministic and probabilistic. Second, we study the stability of the deterministic problem. We prove that in the small traveling salesman problem, several tours were optimal, but ...

Abstract: Multiple traveling salesman problems (MTSP) are a typical computationally complex combinatorial optimization problem, which is an extension of the famous traveling salesman problem (TSP). The MTSP can be generalized to a wide variety of routing and scheduling problems. The paper makes the attempt to show how Genetic Algorithm (GA) can be applied to the MTSP with ability constraint. In...

We analyze relationships among local minima for the traveling salesman and graph bisection problems under standard neighborhood structures. Our work reveals surprising correlations that suggest a globally convex, or \big valley" structure in these optimization cost surfaces. In conjunction with combinatorial results that sharpen previous analyses, our analysis directly motivates a new adaptive ...

In this paper an ant colony system (ACS) with communication strategies is developed. The artificial ants are partitioned into several groups. Seven communication methods for updating the pheromone level between groups in ACS are proposed and work on the traveling salesman problem using our system is presented. Experimental results based on three well-known traveling salesman data sets demonstra...

Almost all real-world problems are dynamic and as such not all problem instances are known a priori. Many strategies to deal with dynamic problems exist in the literature, however they are not fully tested on combinatorial problems due to the deficiency of benchmarks. This paper presents a benchmark generator that uses Genetic Algorithms to produce benchmark problems for the dynamic traveling s...

We empirically study phase transitions of the asymmetric Traveling Salesman. Using random instances of up to 1,500 cities, we show that many properties of the problem, including the backbone and optimal tour cost, experience sharp transitions as the precision of intercity distances increases across a critical value. We also show that the average computational cost of the well-known branch-and-b...