An Approximation Algorithm for a Heterogeneous Traveling Salesman Problem

2011 ◽  
Author(s):  
Jungyun Bae ◽  
Sivakumar Rathinam
Keyword(s):  
Approximation Algorithm ◽  
Traveling Salesman Problem ◽  
Approximation Ratio ◽  
Traveling Salesman ◽  
Dual Algorithm ◽  
Routing Problem ◽  
Primal Dual ◽  
Surveillance Applications

Surveillance applications require a collection of heterogeneous vehicles to visit a set of targets. In this article, we consider a fundamental routing problem that arises in these applications involving two vehicles. Specifically, we consider a routing problem where there are two heterogeneous vehicles that start from distinct initial locations, and a set of targets. The objective is to find a tour for each vehicle such that each of the targets is visited at least once by a vehicle and the sum of the distances traveled by the vehicles is a minimum. We present a novel primal-dual algorithm for the same that provides an approximation ratio of 2.

Escape from solutions stagnation. A Study on Ant System solving TSP

2019 ◽  
Vol 28 (1) ◽  
pp. 77-83
Author(s):  
CAMELIA-M. PINTEA ◽  
◽  
BARNA IANTOVICS ◽  
PETRICA POP ◽  
MATTHIAS DEHMER ◽  
...  
Keyword(s):  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
Current Work ◽  
Ant System ◽  
Routing Problems ◽  
Routing Problem ◽  
The Traveling Salesman Problem ◽  
Exit State

Nowadays, routing problems arise in different contexts of distribution of goods, transportation of commodities and people. Routing problems deals with traveling along a given network in an optimal way. One of the major goals in optimization, including optimization of routing problems, is to reduce the time of stagnation by finding an exit state. The current work is a study about the ability of ants to escape from solution stagnation on a particular routing problem, the Traveling Salesman Problem.

scholarly journals Heuristics for Two Depot Heterogeneous Unmanned Vehicle Path Planning to Minimize Maximum Travel Cost

Sensors ◽  
2019 ◽  
Vol 19 (11) ◽  
pp. 2461 ◽  
Author(s):  
Jungyun Bae ◽  
Woojin Chung
Keyword(s):  
Path Planning ◽  
Traveling Salesman Problem ◽  
Target Location ◽  
Travel Cost ◽  
Unmanned Vehicles ◽  
Traveling Salesman ◽  
Planning Problem ◽  
Travel Costs ◽  
Primal Dual ◽  
Multiple Depot

A solution to the multiple depot heterogeneous traveling salesman problem with a min-max objective is in great demand with many potential applications of unmanned vehicles, as it is highly related to a reduction in the job completion time. As an initial idea for solving the min-max multiple depot heterogeneous traveling salesman problem, new heuristics for path planning problem of two heterogeneous unmanned vehicles are proposed in this article. Specifically, a task allocation and routing problem of two (structurally) heterogeneous unmanned vehicles that are located in distinctive depots and a set of targets to visit is considered. The unmanned vehicles, being heterogeneous, have different travel costs that are determined by their motion constraints. The objective is to find a tour for each vehicle such that each target location is visited at least once by one of the vehicles while the maximum travel cost is minimized. Two heuristics based on a primal-dual technique are proposed to solve the cases where the travel costs are symmetric and asymmetric. The computational results of the implementation have shown that the proposed algorithms produce feasible solutions of good quality within relatively short computation times.

The Traveling Salesman Problem, the Vehicle Routing Problem, and Their Impact on Combinatorial Optimization

2010 ◽  
Vol 1 (2) ◽  
pp. 82-92 ◽  
Author(s):  
Gilbert Laporte
Keyword(s):  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Traveling Salesman Problem ◽  
Vehicle Routing Problem ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman Problem

The Traveling Salesman Problem (TSP) and the Vehicle Routing Problem (VRP) are two of the most popular problems in the field of combinatorial optimization. Due to the study of these two problems, there has been a significant growth in families of exact and heuristic algorithms being used today. The purpose of this paper is to show how their study has fostered developments of the most popular algorithms now applied to the solution of combinatorial optimization problems. These include exact algorithms, classical heuristics and metaheuristics.

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.

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