A long standing conjecture says that the integrality ratio of the subtour LP for metric TSP is 4/3. A well known family of graphic TSP instances achieves this lower bound asymptotically. For Euclidean TSP the best known lower bound on the integrality ratio was 8/7. We improve this value by presenting a family of Euclidean TSP instances for which the integrality ratio of the subtour LP converges...

This paper presents a powerful genetic algorithm (GA) to solve the traveling salesman problem (TSP). To construct a powerful GA, I use edge swapping(ES) with a local search procedure to determine good combinations of building blocks of parent solutions for generating even better offspring solutions. Experimental results on well studied TSP benchmarks demonstrate that the proposed GA is competit...

We elucidate the relationship between space-llling curves and the Euclidean Traveling 2 Salesman Problem (TSP) by reference to a particular space-lling curve whose scaling behaviour is strongly related to the conjectured scaling behaviour of the optimal TSP tour. We suggest that space-lling curves can be used to generate testbed TSPs: sets of points which in the limit cover a planar surface and...

The Traveling Salesman Problem (TSP) is one of the extensively studied combinatorial optimization problems. Various exact or approximation algorithms are devised for solving Euclidean TSP that determine the shortest route through a given set of points in 3-dimensional Euclidean space. In this paper, we proposed a genetic algorithm-based solution for TSP where all points are on the surface of a ...

We present a new optical method for solving bounded (input-length-restricted) NP-complete combinatorial problems. We have chosen to demonstrate the method with an NP-complete problem called the traveling salesman problem (TSP). The power of optics in this method is realized by using a fast matrix-vector multiplication between a binary matrix, representing all feasible TSP tours, and a gray-scal...

The traveling salesman problem (TSP) consists of finding the length of the shortest closed tour visiting N "cities". We consider the Euclidean TSP where the cities are distributed randomly and independently in a d-dimensional unit hypercube. Working with periodic boundary conditions and inspired by a remarkable universality in the kth nearest neighbor distribution, we find for the average optim...

The traveling salesman problem is a well known optimization problem. Optimal solutions to small instances can be found in reasonable time by linear programming. However, since the TSP is NP-hard, it will be very time consuming to solve larger instances with guaranteed optimality. Setting optimality aside, there’s a bunch of algorithms offering comparably fast running time and still yielding nea...

Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based on general graph properties. We experimentally show that such implied propagators bring robustness to pathological instances and highlight the fact that grap...

We propose a new approach to solving optimization problems based on an adaptive critic design called Action-Dependent Heuristic Dynamic Programming (ADHDP) [1]. We consider the well-known Traveling Salesman Problem (TSP) as a helpful benchmark to highlight main principles of our approach. TSP formulation and many methods to solve it including the classical sequential nearest city algorithm and ...

Traveling Salesman Problem (TSP) is focused to construct the path with the lowest distance between different places (nodes), visiting every one once. This paper proposed an algorithm to solve TSP adding three aspects: time, cost and effort, where the effort is calculated multiplying time, distance and cost factors and dividing by the sum of them; the aim of this estimation is optimizing the bes...