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...

A learning problem might have several measures of complexity (e.g., norm and dimensionality) that affect the generalization error. What is the interaction between these complexities? Dimension-free learning theory bounds and parametric asymptotic analyses each provide a partial picture of the full learning curve. In this paper, we use high-dimensional asymptotics on two classical problems—mean ...

> Context • Strict finitism is usually not taken seriously as a possible view on what mathematics is and how it functions. This is due mainly to unfamiliarity with the topic. > Problem • First, it is necessary to present a “decent” history of strict finitism (which is now lacking) and, secondly, to show that common counterarguments against strict finitism can be properly addressed and refuted. ...