Evolutionary Multi-Objective Optimization is becoming a hot research area and quite a few papers regarding these algorithms have been published. However the role of local search techniques has not been expanded adequately. This paper studies the role of a local search technique called 2opt for the Multi-Objective Travelling Salesman Problem (MOTSP). A new mutation operator called Jumping Gene (...

Graphs (1-skeletons) of Traveling-Salesman-related polytopes have attracted a lot of attention. Pedigree polytopes are extensions of the classical Symmetric Traveling Salesman Problem polytopes (Arthanari 2000) whose graphs contain the TSP polytope graphs as spanning subgraphs (Arthanari 2013). Unlike TSP polytopes, Pedigree polytopes are not “symmetric”, e.g., their graphs are not vertex trans...

We show that the random insertion method for the traveling salesman problem (TSP) may produce a tour (log log n= log log log n) times longer than the optimal tour. The lower bound holds even in the Euclidean Plane. This is in contrast to the fact that the random insertion method performs extremely well in practice. In passing we show that other insertion methods may produce tours (log n= log lo...

This paper presents a new search procedure to tackle multi-objective traveling salesman problem (TSP). This procedure constructs the solution attractor for each of the objectives respectively. Each attractor contains the best solutions found for the corresponding objective. Then, these attractors are merged to find the Pareto-optimal solutions. The goal of this procedure is not only to generate...

The Traveling Salesman Problem (TSP) is a classical problem in discrete optimization. Its paradigmatic character makes it one of the most studied in computer science and operations research and one for which an impressive amount of algorithms (in particular heuristics and approximation algorithms) have been proposed. While in the general case the problem is known not to allow any constant ratio...

In practice, due to the lack of information, imprecise variables which come from experts’ empirical data usually appear. In order to deal with these imprecise variables, uncertainty theory is proposed and has been proved to be an efficient method. This paper introduces uncertainty theory into travelling salesman problem (TSP), in which the link travel times are assumed to be uncertain variables...

The multivariate one-sample location problem is well studied in the literature, and several tests are available for it. But most of the existing tests perform poorly for high dimensional data, and many of them are not applicable when the dimension exceeds the sample size. In this article, we develop and investigate some nonparametric one-sample tests based on functions of interpoint distances. ...

A heuristic is good on a search space to the extent that it allows the prediction of which states are near to the goal. In this paper heuristics are investigated on several different search spaces. A measure is proposed for assessing the predictive accuracy of a given heuristic on a given search space. The measure sheds light on characteristics of the Traveling Salesman Problem that make it com...

Consider a file that resides in a linear storage device with one read head. Suppose that several queries on the file must be answered simultaneously with no prespecified order. To satisfy the ith query the head must be located at point I., of the file and traverse the file up to point R, without interruptions, where 1~ L, < R, 4 N denote positions in the file. We wish to find the execution orde...