EVERY LONGEST HAMILTONIAN PATH IN EVEN n-GONS

2012 ◽  
Vol 04 (04) ◽  
pp. 1250057 ◽  
Author(s):  
BLANCA I. NIEL
Keyword(s):  
Traveling Salesman Problem ◽  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Traveling Salesman ◽  
Maximum Traveling Salesman Problem ◽  
Longest Path ◽  
Hamiltonian Path Problems ◽  
Planar Rotations

We single out every longest path of n-1 order that solves each of the [Formula: see text] Longest Euclidean Hamiltonian Path Problems on the even nth root of the unity, by means of a geometric and arithmetic procedure. This identification is done regardless of planar rotations and orientation. In addition, the uniqueness of the Euclidean Hamiltonian cycle that resolves the Maximum Traveling Salesman Problem is shown.

scholarly journals Solution of Cluster Traveling Salesman Problem using Heuristic Based Genetic Algorithm with Risk Constraint

2019 ◽  
Vol 9 (2) ◽  
pp. 2523-2526
Keyword(s):  
Genetic Algorithm ◽  
Traveling Salesman Problem ◽  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Traveling Salesman ◽  
Computational Results ◽  
Number Of Clusters ◽  
Risk Constraint ◽  
The Traveling Salesman Problem

This is a heuristic investigation with risk constraint for solving the traveling salesman problem (TSP) dividing given vertices (nodes) between a prespecified number of clusters. A Heuristic based Genetic Algorithm (HbGA) is applied on each cluster to produce a Hamiltonian path based on prespecified nodes of a cluster. Each cluster must have a unique set of nodes. Finally, all Hamiltonian path of each cluster together prepare a possible Hamiltonian cycle. The efficiency of our proposed algorithm has been tested for a number of symmetric TSPLIB instances of various sizes. The computational results show the proposed algorithm works well in realistic manner.

BEE COLONY OPTIMIZATION WITH LOCAL SEARCH FOR TRAVELING SALESMAN PROBLEM

2010 ◽  
Vol 19 (03) ◽  
pp. 305-334 ◽  
Author(s):  
LI-PEI WONG ◽  
MALCOLM YOKE HEAN LOW ◽  
CHIN SOON CHONG
Keyword(s):  
Traveling Salesman Problem ◽  
Hamiltonian Path ◽  
Industrial Applications ◽  
Traveling Salesman ◽  
Benchmark Problems ◽  
Solution Quality ◽  
Routing Problem ◽  
Bee Colony ◽  
Pruning Strategy ◽  
Bee Colony Optimization

Many real world industrial applications involve the Traveling Salesman Problem (TSP), which is a problem that finds a Hamiltonian path with minimum cost. Examples of problems that belong to this category are transportation routing problem, scan chain optimization and drilling problem in integrated circuit testing and production. This paper presents a Bee Colony Optimization (BCO) algorithm for symmetrical TSP. The BCO model is constructed algorithmically based on the collective intelligence shown in bee foraging behaviour. The algorithm is integrated with a fixed-radius near neighbour 2-opt (FRNN 2-opt) heuristic to further improve prior solutions generated by the BCO model. To limit the overhead incurred by the FRNN 2-opt, a frequency-based pruning strategy is proposed. The pruning strategy allows only a subset of the promising solutions to undergo local optimization. Experimental results comparing the proposed BCO algorithm with existing approaches on a set of benchmark problems are presented. For 84 benchmark problems, the BCO algorithm is able to obtain an overall average solution quality of 0.31% from known optimum. The results also show that it is comparable to other algorithms such as Ant Colony Optimization and Particle Swarm Optimization.

Parallel algorithms for the hamiltonian cycle and hamiltonian path problems in semicomplete bipartite digraphs

Algorithmica ◽  
1997 ◽  
Vol 17 (1) ◽  
pp. 67-87 ◽  
Author(s):  
J. Bang-Jensen ◽  
M. El Haddad ◽  
Y. Manoussakis ◽  
T. M. Przytycka
Keyword(s):  
Parallel Algorithms ◽  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Hamiltonian Path Problems

THE MAXIMUM TRAVELING SALESMAN PROBLEM ON BANDED MATRICES

2001 ◽  
Vol 12 (06) ◽  
pp. 809-819 ◽  
Author(s):  
DAVID BLOKH ◽  
EUGENE LEVNER
Keyword(s):  
Traveling Salesman Problem ◽  
Linear Time ◽  
Time Algorithm ◽  
Traveling Salesman ◽  
Problem Size ◽  
Principal Diagonal ◽  
Banded Matrix ◽  
Banded Matrices ◽  
Maximum Traveling Salesman Problem ◽  
Distance Matrices

We investigate the Maximum Traveling Salesman Problem on banded distance matrices. A (p, q)-banded matrix has all its non-zero elements contained within a band consisting of p diagonals above the principal diagonal and q diagonals below it. We investigate the properties of the problem and prove that the number K of different permutations which can be optimal solutions for different instances of the problem, is exponential in n where n is the problem size (= the number of cities). For the Maximum-TSP on the (2, 0)-banded matrices, K=O(λn) where 1.7548 <λ< 1.7549, whereas on the (1, 1)-banded matrices K=O(λn) where 1.6180 <λ< 1.6181. Using recursive equations, we derive a linear-time algorithm that exactly solves the Maximum-TSP on the (2, 0)-banded distance matrices.

Sign in / Sign up

Export Citation Format

Share Document