scholarly journals The cost-constrained traveling salesman problem

1990 ◽  
Author(s):  
P.R. Sokkappa
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
The Cost

Extrema of a Class of Functions on a Finite Set

1974 ◽  
Vol 26 (4) ◽  
pp. 806-819
Author(s):  
Kenneth W. Lebensold
Keyword(s):  
Positive Integer ◽  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Polygonal Path ◽  
Finite Set ◽  
Vertex Set ◽  
The Traveling Salesman Problem ◽  
The Cost ◽  
Special Case ◽  
Class Of Functions

In this paper, we are concerned with the following problem: Let S be a finite set and Sm* ⊂ 2S a collection of subsets of S each of whose members has m elements (m a positive integer). Let f be a real-valued function on S and, for p ∊ Sm*, define f(P) as Σs∊pf (s). We seek the minimum (or maximum) of the function f on the set Sm*.The Traveling Salesman Problem is to find the cheapest polygonal path through a given set of vertices, given the cost of getting from any vertex to any other. It is easily seen that the Traveling Salesman Problem is a special case of this system, where S is the set of all edges joining pairs of points in the vertex set, Sm* is the set of polygons, each polygon has m elements (m = no. of points in the vertex set = no. of edges per polygon), and f is the cost function.

A Compressed Annealing Approach with Pre-Process for the Asymmetric Traveling Salesman Problem with Time Windows

2011 ◽  
Vol 5 (5) ◽  
pp. 669-678
Author(s):  
Tadanobu Mizogaki ◽  
◽  
Masao Sugi ◽  
Masashi Yamamoto ◽  
Hidetoshi Nagai ◽  
...  
Keyword(s):  
Traveling Salesman Problem ◽  
Feasible Solution ◽  
Time Window ◽  
Time Windows ◽  
Computing Time ◽  
Traveling Salesman ◽  
Asymmetric Traveling Salesman Problem ◽  
Insertion Method ◽  
Time Window Constraints ◽  
The Cost

This paper proposes a method of rapidly finding a feasible solution to the asymmetric traveling salesman problem with time windows (ATSP-TW). ATSP-TW is a problem that involves determining the route with the minimum travel cost for visiting n cities one time each with time window constraints (the period of time in which the city must be visited is constrained). “Asymmetrical” denotes a difference between the cost of outbound and return trips. For such a combinatorial optimization problem with constraints, we propose a method that combines a pre-process based on the insertion method with metaheuristics called “the compressed annealing approach.” In an experiment using a 3-GHz computer, our method derives a feasible solution that satisfies the time window constraints for all of up to about 300 cities at an average of about 1/7 the computing time of existing methods, an average computing time of 0.57 seconds, and a maximum computing time of 9.40 seconds.

Feature Based Costing (FBC) of Welded Assemblies: A Genetic Approach

2002 ◽  
Author(s):  
Gautam Subbarao ◽  
Michael L. Philpott ◽  
R. Sebastian Schrader ◽  
Dale E. Holmes
Keyword(s):  
Genetic Algorithm ◽  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Manufacturing Cost ◽  
Genetic Approach ◽  
Cad System ◽  
Computational Speed ◽  
Feature Based ◽  
Feature Information ◽  
The Cost

A genetic algorithm based welding planner capable of using parametric features to determine the manufacturing cost of welded assemblies has been developed. Parametric weld feature information obtained from a CAD system is translated to a hybrid traveling salesman problem. A genetic algorithm is used to search for a sequence of welds that minimizes the cost of the welded assembly. Emphasis is placed on developing a mechanistic, feature based DFM tool, with the aim of rapidly providing welded assembly cost feedback to the designer in a CAD environment, while maintaining a balance between accuracy and computational speed.

Integrating Task and Motion Planning for Unmanned Aerial Vehicles

2014 ◽  
Vol 02 (01) ◽  
pp. 19-38 ◽  
Author(s):  
Matthew S. Cons ◽  
Tal Shima ◽  
Carmel Domshlak
Keyword(s):  
Motion Planning ◽  
Unmanned Aerial Vehicle ◽  
Traveling Salesman Problem ◽  
Upper Bound ◽  
Search Algorithm ◽  
Integrated Approach ◽  
Traveling Salesman ◽  
Aerial Vehicle ◽  
Path Cost ◽  
The Cost

This paper investigates the problem where a fixed-winged unmanned aerial vehicle is required to find the shortest flyable path to traverse over multiple targets. The unmanned aerial vehicle is modeled as a Dubins vehicle: a vehicle with a minimum turn radius and the inability to go backward. This problem is called the Dubins traveling salesman problem, an extension of the well-known traveling salesman problem. We propose and compare different algorithms that integrate the task planning and the motion planning aspects of the problem, rather than treating the two separately. An upper bound on calculating kinematic satisfying paths for setting costs in the search algorithm is investigated. The proposed integrated algorithms are compared to hierarchical algorithms that solve the search aspect first and then solve the motion planning aspect second. Monte Carlo simulations are performed for a range of vehicle turn radii. The simulations results show the viability of the integrated approach and that using two plausible kinematic satisfying paths as an upper bound to determine the cost-so-far into a search algorithm generally improves performance in terms of the shortest path cost and search complexity.

scholarly journals An Algorithm for Mapping the Asymmetric Multiple Traveling Salesman Problem onto Colored Petri Nets

Algorithms ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 143 ◽  
Author(s):  
Furqan Essani ◽  
Sajjad Haider
Keyword(s):  
Petri Nets ◽  
Traveling Salesman Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Traveling Salesman ◽  
Colored Petri Nets ◽  
Cost Matrix ◽  
Multiple Traveling Salesman Problem ◽  
Hard Problems ◽  
The Cost

The Multiple Traveling Salesman Problem is an extension of the famous Traveling Salesman Problem. Finding an optimal solution to the Multiple Traveling Salesman Problem (mTSP) is a difficult task as it belongs to the class of NP-hard problems. The problem becomes more complicated when the cost matrix is not symmetric. In such cases, finding even a feasible solution to the problem becomes a challenging task. In this paper, an algorithm is presented that uses Colored Petri Nets (CPN)—a mathematical modeling language—to represent the Multiple Traveling Salesman Problem. The proposed algorithm maps any given mTSP onto a CPN. The transformed model in CPN guarantees a feasible solution to the mTSP with asymmetric cost matrix. The model is simulated in CPNTools to measure two optimization objectives: the maximum time a salesman takes in a feasible solution and the collective time taken by all salesmen. The transformed model is also formally verified through reachability analysis to ensure that it is correct and is terminating.

scholarly journals On Tightly Bounding the Dubins Traveling Salesman's Optimum

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Satyanarayana G. Manyam ◽  
Sivakumar Rathinam
Keyword(s):  
Lower Bound ◽  
Traveling Salesman Problem ◽  
Optimal Solution ◽  
Traveling Salesman ◽  
Motion Constraints ◽  
Euclidean Traveling Salesman Problem ◽  
Problem Instances ◽  
Feasible Solutions ◽  
The Cost ◽  
Dubins Traveling Salesman Problem

The Dubins traveling salesman problem (DTSP) has generated significant interest over the last decade due to its occurrence in several civil and military surveillance applications. This problem requires finding a curvature constrained shortest path for a vehicle visiting a set of target locations. Currently, there is no algorithm that can find an optimal solution to the DTSP. In addition, relaxing the motion constraints and solving the resulting Euclidean traveling salesman problem (ETSP) provide the only lower bound available for the DTSP. However, in many problem instances, the lower bound computed by solving the ETSP is far below the cost of the feasible solutions obtained by some well-known algorithms for the DTSP. This paper addresses this fundamental issue and presents the first systematic procedure for developing tight lower bounds for the DTSP.

scholarly journals A Revisiting Method Using a Covariance Traveling Salesman Problem Algorithm for Landmark-Based Simultaneous Localization and Mapping

Sensors ◽  
2019 ◽  
Vol 19 (22) ◽  
pp. 4910 ◽  
Author(s):  
Hyejeong Ryu
Keyword(s):  
Measurement Uncertainty ◽  
Traveling Salesman Problem ◽  
Optimal Path ◽  
Simultaneous Localization And Mapping ◽  
Traveling Salesman ◽  
Localization And Mapping ◽  
Sensor Measurement ◽  
Slam Algorithm ◽  
The Traveling Salesman Problem ◽  
The Cost

This paper presents an efficient revisiting algorithm for landmark-based simultaneous localization and mapping (SLAM). To reduce SLAM uncertainty in terms of a robot’s pose and landmark positions, the method autonomously evaluates valuable landmarks for the data associations in the SLAM algorithm and selects positions to revisit by considering both landmark visibility and sensor measurement uncertainty. The optimal path among the selected positions is obtained by applying the traveling salesman problem (TSP) algorithm. To plan a path that reduces overall uncertainty, the cost matrix associated with the change in covariance between all selected positions of all pairs is applied for the TSP algorithm. From simulations, it is verified that the proposed method efficiently reduces and maintains SLAM uncertainty at the low level compared to the backtracking method.

scholarly journals A Data-Guided Lexisearch Algorithm for the Asymmetric Traveling Salesman Problem

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Zakir Hussain Ahmed
Keyword(s):  
Traveling Salesman Problem ◽  
Optimal Solution ◽  
Traveling Salesman ◽  
Computational Time ◽  
Cost Matrix ◽  
Asymmetric Traveling Salesman Problem ◽  
Path Representation ◽  
Random Instances ◽  
Representation Method ◽  
The Cost

A simple lexisearch algorithm that uses path representation method for the asymmetric traveling salesman problem (ATSP) is proposed, along with an illustrative example, to obtain exact optimal solution to the problem. Then a data-guided lexisearch algorithm is presented. First, the cost matrix of the problem is transposed depending on the variance of rows and columns, and then the simple lexisearch algorithm is applied. It is shown that this minor preprocessing of the data before the simple lexisearch algorithm is applied improves the computational time substantially. The efficiency of our algorithms to the problem against two existing algorithms has been examined for some TSPLIB and random instances of various sizes. The results show remarkably better performance of our algorithms, especially our data-guided algorithm.

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 A generalization of the convex-hull-and-line traveling salesman problem

1998 ◽  
Vol 2 (2) ◽  
pp. 177-191 ◽  
Author(s):  
Md. Fazle Baki ◽  
S. N. Kabadi
Keyword(s):  
Convex Hull ◽  
Traveling Salesman Problem ◽  
Equivalence Relation ◽  
General Class ◽  
Traveling Salesman ◽  
Cost Matrix ◽  
Solvable Case ◽  
Special Cases ◽  
The Traveling Salesman Problem ◽  
The Cost

Two instances of the traveling salesman problem, on the same node set {1,2,…,n} but with different cost matrices C and C′ , are equivalent iff there exist {ai,bi: i=1,…, n} such that for any 1≤i, j≤n,i≠j,C′(i,j)=C(i,j)+ai+bj [7]. One of the well-solved special cases of the traveling salesman problem (TSP) is the convex-hull-and-line TSP. We extend the solution scheme for this class of TSP given in [9] to a more general class which is closed with respect to the above equivalence relation. The cost matrix in our general class is a certain composition of Kalmanson matrices. This gives a new, non-trivial solvable case of TSP.

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