New heuristic algorithms for the Dubins traveling salesman problem

Abstract

The problem of finding a shortest curvature-constrained closed path through a set of targets in the plane is known as Dubins traveling salesman problem (DTSP). Applications of the DTSP include motion planning for kinematically constrained mobile robots and unmanned fixed-wing aerial vehicles. The difficulty of the DTSP is to simultaneously find an order of the targets and suitable headings (orientation angles) of the vehicle when passing the targets. Since the DTSP is known to be NP-hard there is a need for heuristic algorithms providing good quality solutions in reasonable time. Inspired by standard methods for the TSP we present a collection of such heuristics adapted to the DTSP. The algorithms are based on a technique that optimizes the headings of the targets of an open or closed subtour with given order. This is done by discretizing the headings, constructing an auxiliary network and computing a shortest path in the network. The first algorithm for the DTSP uses the order of the targets obtained from the solution of the Euclidean TSP. A second class of algorithms extends an open subtour by successively adding a new target and closes the tour if all targets have been added. A third class of algorithms starts with a closed subtour consisting of few targets and successively inserts a new target into the tour. The individual algorithms differ by the number of headings to be optimized in each iteration. Extensive simulation results show that the proposed methods are competitive with state-of-the-art methods for the DTSP concerning performance and superior concerning running time, which makes them applicable also to large-scale scenarios. Keywords Dubins traveling salesman problem • Curvature-constrained traveling salesman problem • Dubins vehicle • Heuristic methods B Luitpold Babel

Optimalisasi Pendistribusian Dengan Metode Travelling Salesman Problem Untuk Menentukan Rute Terpendek Di Pt Xyz

“…Traveling salesman problem melibatkan aspek transportasi yang harus mengunjungi ke sejumlah perusahaan dalam mengirim sebuah produk. Perusahaan yang sudah dikunjungi tidak akan dilewati Kembali karena hanya dapat dilewati sekali saja dan kembali ke perusahaan awal (Babel, 2020).…”

Angle Bisector Algorithm and Modified Dynamic Programming Algorithm for Dubins Traveling Salesman Problem

“…We note that the MDPA ensures an upper bound on DTSP tour length as given by the Theorem 4 and is not the case with OHA. OHA is sensitive to number of discretizations and the corresponding discretized angles [2]. So MDPA has an advantage of proven upper bound as compared to OHA.…”

“…However, in applications like an aerial surveillance where an aircraft acts as a salesman has inherent dynamics. For more efficient path planning, in recent years, researchers introduced the system dynamics into TSP [17], [14], [6], [15], [2], [16], [10], [5].…”

“…In simulations, we show that the ABA gives a tour length which is at most 4% more then ETSP tour length for points up to 70 and ρ ∈ {0.1, 0.5, 1} when the Euclidean distance between the given set of points is at least 4ρ. For the same case, ABA also gives shorter tour lengths than AA, SVA and a discreization based algorithm called as Optimized Heading Algorithm (OHA) [2], [13] in which orientation angles at each point are discretized and then the problem is converted to an Asymmetric TSP (ATSP) 1 which is solved using existing techniques. MDPA gives shorter tour lengths compared to AA, SVA and ABA and is competitive with respect to OHA for points up to 13 and ρ ∈ {0.1, 0.5, 1} when there is no constraint on Euclidean distance between the given set of points.…”

A Hybrid Cellular Genetic Algorithm for the Traveling Salesman Problem

“…On the other hand, although using an approximate solution to solve TSP problems cannot guarantee an optimal solution, it can reach a satisfactory solution in a very short time [8]. us, with the development of heuristic algorithms [9][10][11][12][13][14], many experts and scholars have begun to apply heuristic algorithms to solve TSP, which provides new ideas for solving TSP [15][16][17][18][19][20][21].…”