scholarly journals THE TRAVELING SALESMAN PROBLEM FOR LINES AND RAYS IN THE PLANE

2012 ◽  
Vol 04 (04) ◽  
pp. 1250044 ◽  
Author(s):  
ADRIAN DUMITRESCU
Keyword(s):  
Approximation Algorithms ◽  
Traveling Salesman Problem ◽  
Shortest Path ◽  
Linear Time ◽  
Traveling Salesman ◽  
Tight Bound ◽  
Time Approximation ◽  
Minimum Perimeter ◽  
Open Curve ◽  
The Traveling Salesman Problem

In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of n regions (neighborhoods) and we seek a shortest tour that visits each region. In the path variant, we seek a shortest path that visits each region. We present several linear-time approximation algorithms with improved ratios for these problems for two cases of neighborhoods that are (infinite) lines, and respectively, (half-infinite) rays. Along the way we derive a tight bound on the minimum perimeter of a rectangle enclosing an open curve of length L.

scholarly journals Dynamic Shortest Paths Methods for the Time-Dependent TSP

Algorithms ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 21
Author(s):  
Christoph Hansknecht ◽  
Imke Joormann ◽  
Sebastian Stiller
Keyword(s):  
Column Generation ◽  
Traveling Salesman Problem ◽  
Shortest Path ◽  
Valid Inequalities ◽  
Shortest Paths ◽  
Traveling Salesman ◽  
Time Dependent ◽  
Full Generality ◽  
Branching Rule ◽  
The Traveling Salesman Problem

The time-dependent traveling salesman problem (TDTSP) asks for a shortest Hamiltonian tour in a directed graph where (asymmetric) arc-costs depend on the time the arc is entered. With traffic data abundantly available, methods to optimize routes with respect to time-dependent travel times are widely desired. This holds in particular for the traveling salesman problem, which is a corner stone of logistic planning. In this paper, we devise column-generation-based IP methods to solve the TDTSP in full generality, both for arc- and path-based formulations. The algorithmic key is a time-dependent shortest path problem, which arises from the pricing problem of the column generation and is of independent interest—namely, to find paths in a time-expanded graph that are acyclic in the underlying (non-expanded) graph. As this problem is computationally too costly, we price over the set of paths that contain no cycles of length k. In addition, we devise—tailored for the TDTSP—several families of valid inequalities, primal heuristics, a propagation method, and a branching rule. Combining these with the time-dependent shortest path pricing we provide—to our knowledge—the first elaborate method to solve the TDTSP in general and with fully general time-dependence. We also provide for results on complexity and approximability of the TDTSP. In computational experiments on randomly generated instances, we are able to solve the large majority of small instances (20 nodes) to optimality, while closing about two thirds of the remaining gap of the large instances (40 nodes) after one hour of computation.

TRAVELING SALESMAN PROBLEM OF SEGMENTS

2004 ◽  
Vol 14 (01n02) ◽  
pp. 19-40
Author(s):  
JINHUI XU ◽  
ZHIYONG LIN ◽  
YANG YANG ◽  
RONALD BEREZNEY
Keyword(s):  
Traveling Salesman Problem ◽  
Approximation Scheme ◽  
Dimensional Space ◽  
Traveling Salesman ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Entry Points ◽  
Combinatorial Result ◽  
The Traveling Salesman Problem ◽  
Set Of Points

In this paper, we present a polynomial time approximation scheme (PTAS) for a variant of the traveling salesman problem (called segment TSP) in which a traveling salesman tour is sought to traverse a set of n ∊-separated segments in two dimensional space. Our results are based on an interesting combinatorial result which bounds the total number of entry points in an optimal TSP tour and a generalization of Arora's technique5 for Euclidean TSP (of a set of points). The randomized version of our algorithm takes O(n2( log n)O(1/∊2)) time to compute a (1+∊)-approximation with probability ≥l/2, and can be derandomized with an additional factor of O(n2).

scholarly journals Solving Multiple Traveling Salesman Problem by Meerkat Swarm Optimization Algorithm

2019 ◽  
Vol 54 (3) ◽  
Author(s):  
Belal Al-Khateeb ◽  
Mohammed Yousif
Keyword(s):  
Traveling Salesman Problem ◽  
Shortest Path ◽  
Optimization Algorithm ◽  
Real Life ◽  
Traveling Salesman ◽  
Swarm Optimization ◽  
Total Cost ◽  
Life Problems ◽  
Multiple Traveling Salesman Problem ◽  
The Traveling Salesman Problem

Multiple Traveling Salesman Problem (MTSP) is one of various real-life applications, MTSP is the extension of the Traveling Salesman Problem (TSP). TSP focuses on searching of minimum or shortest path (traveling distance) to visit all cities by salesman, while the primary goal of MTSP is to find shortest path for m paths by n salesmen with minimized total cost. Wherever, total cost means the sum of distances of all salesmen. In this work, we proposed metaheuristic algorithm is called Meerkat Swarm Optimization (MSO) algorithm for solving MTSP and guarantee good quality solution in reasonable time for real-life problems. MSO is a metaheuristic optimization algorithm that is derived from the behavior of Meerkat in finding the shortest path. The implementation is done using many dataset from TSPLIB95. The results demonstrate that MSO in most results is better than another results that compared in average cost that means the MSO superior to other results of MTSP.

scholarly journals A Graph-Based Approach to Optimal Scan Chain Stitching Using RTL Design Descriptions

VLSI Design ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Lilia Zaourar ◽  
Yann Kieffer ◽  
Chouki Aktouf
Keyword(s):  
Approximation Algorithms ◽  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Graph Models ◽  
Rtl Design ◽  
And Performance ◽  
Scan Chain ◽  
The Traveling Salesman Problem ◽  
The Cost

The scan chain insertion problem is one of the mandatory logic insertion design tasks. The scanning of designs is a very efficient way of improving their testability. But it does impact size and performance, depending on the stitching ordering of the scan chain. In this paper, we propose a graph-based approach to a stitching algorithm for automatic and optimal scan chain insertion at the RTL. Our method is divided into two main steps. The first one builds graph models for inferring logical proximity information from the design, and then the second one uses classic approximation algorithms for the traveling salesman problem to determine the best scan-stitching ordering. We show how this algorithm allows the decrease of the cost of both scan analysis and implementation, by measuring total wirelength on placed and routed benchmark designs, both academic and industrial.

scholarly journals Approximation algorithms for the traveling salesman problem

2003 ◽  
Vol 56 (3) ◽  
pp. 387-405 ◽  
Author(s):  
Jérôme Monnot ◽  
Vangelis Th. Paschos ◽  
Sophie Toulouse
Keyword(s):  
Approximation Algorithms ◽  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
The Traveling Salesman Problem
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