Traveling Salesperson Research Articles

Towards Autonomous, Optimal Water Sampling with Aerial and Surface Vehicles for Rapid Water Quality Assessment

Highlights A practical workflow for optimizing sampling tours for a team of surface and aerial vehicles was developed. Proposed workflow considers unique sensing capabilities of surface vehicles when assigning sampling locations. Likely optimal tours can be found in less than 30 s for practical water quality sampling requirements. Abstract. Most current marine aquaculture operations are located in coastal estuarine areas within one mile of the shoreline, and water quality in these production areas can quickly become unfavorable due to hydrodynamic processes and excessive runoff. The deployment of autonomous, robotic systems can improve the speed and spatiotemporal resolution of water sampling and sensing in mariculture production areas to assess water quality in the context of food safety. Specifically, teams of both aerial and surface vehicles can be deployed simultaneously to capitalize on the benefits of each system; however, a method to optimally design a feasible sampling tour for each robot is needed to maximize sample capacity and ensure efficient water sampling missions. This research brief presents the problem formulation and a solution method to determine optimal tours for a team of aquatic surface and aerial vehicles while considering different vehicle sampling capacities and endurance constraints. This method was implemented to design sampling missions of 15, 20, and 30 samples in both a 0.25 km2 and 3.9 km2 site, using sampling capacity and endurance constraints corresponding to real-world robots used for water sampling in mariculture environments. Results indicate that this optimization problem can be solved in near-real time in the field and yields feasible sampling tours for surface and aerial vehicles under different constraints. This work is a practical step towards developing teams of collaborative robots to persistently monitor adverse mariculture growing conditions so producers can implement data-driven, timely management strategies. Keywords: Mariculture, Robotics, Traveling salesperson problem, Vehicle routing.

Comparative analysis of various Evolutionary Algorithms: Past three decades

INTRODUCTION: The Evolutionary algorithms created back in 1953, have gone through various phases of development over the years. It has been put to use to solve various problems in different domains including complex problems such as the infamous problem of Travelling Salesperson (TSP).OBJECTIVES: The main objective of this research is to find out the advancements in Evolutionary algorithms and to check whether it is still relevant in 2023.METHODS: To give an overview of the related concepts, subdomains, pros, and cons, the historical and recent developments are discussed and critiqued to provide insights into the results and a better conception of the trends in the domain. RESULTS: For a better perception of the development of evolutionary algorithms over the years, decade-wise trend analysis has been done for the past three decades.CONCLUSION: Scope of research in the domain is ever expanding and to name a few EAs for Data mining, Hybrid EAs are still under development.

Multiple traveling salesperson problem with drones: General variable neighborhood search approach

A key factor to consider in the development of new technologies in a number of fields is the use of unmanned aerial vehicles. This rapidly developing technology is used in military, communication, health, mapping, agriculture and transportation fields. The importance of cargo transportation has grown due to the growth of e-commerce. Currently, with advancing technology, and the effect of the pandemic, purchases are increasingly made over the internet. For cargo transporters, this situation leads to an increase in the number of destination points, in distances traveled, and in the delivery frequency, and a decrease in the package sizes. As a result, the planning of transportation has become increasingly complex. One solution is to make greater use of unmanned aerial vehicles in this sector, and to reduce reliance on trucks through appropriate planning. This involves two aspects: the unmanned aerial vehicle delivering to a point, while the cargo truck delivers to a separate point. In this study, we consider a multiple traveling salesperson problem simultaneously using multiple trucks and unmanned aerial vehicles for package delivery. We develop a general variable neighborhood search algorithm, and compare the results with the existing studies in the literature. Computational experiments show that our approach is able to find highly satisfactory solutions in reasonable time, and outperforms the existing methods in terms of best solution, average solution and solution time in majority of the instances.

An Algorithm for Task Allocation and Planning for a Heterogeneous Multi-Robot System to Minimize the Last Task Completion Time.

This paper proposes an algorithm that provides operational strategies for multiple heterogeneous mobile robot systems utilized in many real-world applications, such as deliveries, surveillance, search and rescue, monitoring, and transportation. Specifically, the authors focus on developing an algorithm that solves a min–max multiple depot heterogeneous asymmetric traveling salesperson problem (MDHATSP). The algorithm is designed based on a primal–dual technique to operate given multiple heterogeneous robots located at distinctive depots by finding a tour for each robot such that all the given targets are visited by at least one robot while minimizing the last task completion time. Building on existing work, the newly developed algorithm can solve more generalized problems, including asymmetric cost problems with a min–max objective. Though producing optimal solutions requires high computational loads, the authors aim to find reasonable sub-optimal solutions within a short computation time. The algorithm was repeatedly tested in a simulation with varying problem sizes to verify its effectiveness. The computational results show that the algorithm can produce reliable solutions to apply in real-time operations within a reasonable time.

OPTIMAL POSITION AND PATH PLANNING FOR STOP-AND-GO LASERSCANNING FOR THE ACQUISITION OF 3D BUILDING MODELS

Abstract. Terrestrial laser scanning has become more and more popular in recent years. The according planning of the standpoint network is a crucial issue influencing the overhead and the resulting point cloud. Fully static approaches are both cost and time extensive, whereas fully kinematic approaches cannot produce the same data quality. Stop-and-go scanning, which combines the strengths of both strategies, represents a good alternative solution. In the scanning process, the standpoint planning is by now mostly a manual process based on expert knowledge and relying on the surveyor’s experience. This paper provides a method based on Mixed Integer Linear Programming (MILP) ensuring an optimal placement of scanner standpoints considering all scanner-related constraints (e.g. incidence angle), a full coverage of the scenery, a sufficient overlap for the subsequent registration and an optimal route planning solving a Traveling Salesperson Problem (TSP). This enables the fully automatic application of autonomous systems for providing a complete model while performing a stop-and-go laser scanning, e.g. with the Spot robot from Boston Dynamics. Our pre-computed solution, i.e. standpoints and trajectory, has been evaluated surveying a real-world environment using a 360° panoramic laser scanner and successfully compared with a precise LoD2 building model of the underlying scene. The performed ICP-based registration issued from our fully automatic pipeline turns out to be a very good and safe alternative of the otherwise laborious target-based registration.

On the quadratic random matching problem in two-dimensional domains

We investigate the average minimum cost of a bipartite matching, with respect to the squared Euclidean distance, between two samples of n i.i.d. random points on a bounded Lipschitz domain in the Euclidean plane, whose common law is absolutely continuous with strictly positive Hölder continuous density. We confirm in particular the validity of a conjecture by D. Benedetto and E. Caglioti stating that the asymptotic cost as n grows is given by the logarithm of n multiplied by an explicit constant times the volume of the domain. Our proof relies on a reduction to the optimal transport problem between the associated empirical measures and a Whitney-type decomposition of the domain, together with suitable upper and lower bounds for local and global contributions, both ultimately based on PDE tools. We further show how to extend our results to more general settings, including Riemannian manifolds, and also give an application to the asymptotic cost of the random quadratic bipartite travelling salesperson problem.

Backtracking Algorithms for Constructing the Hamiltonian Decomposition of a 4-regular Multigraph

We consider a Hamiltonian decomposition problem of partitioning a regular graph into edge-disjoint Hamiltonian cycles. It is known that verifying vertex non-adjacency in the 1-skeleton of the symmetric and asymmetric traveling salesperson polytopes is an NP-complete problem. On the other hand, a suffcient condition for two vertices to be non-adjacent can be formulated as a combinatorial problem of finding a Hamiltonian decomposition of a 4-regular multigraph. We present two backtracking algorithms for verifying vertex non-adjacency in the 1-skeleton of the traveling salesperson polytope and constructing a Hamiltonian decomposition: an algorithm based on a simple path extension and an algorithm based on the chain edge fixing procedure. Based on the results of the computational experiments for undirected multigraphs, both backtracking algorithms lost to the known heuristic general variable neighborhood search algorithm. However, for directed multigraphs, the algorithm based on chain fixing of edges showed comparable results with heuristics on instances with existing solutions, and better results on instances of the problem where the Hamiltonian decomposition does not exist.

Travelling on Graphs with Small Highway Dimension

We study the Travelling Salesperson (TSP) and the Steiner Tree problem (STP) in graphs of low highway dimension. This graph parameter roughly measures how many central nodes are visited by all shortest paths of a certain length. It has been shown that transportation networks, on which TSP and STP naturally occur for various applications in logistics, typically have a small highway dimension. While it was previously shown that these problems admit a quasi-polynomial time approximation scheme on graphs of constant highway dimension, we demonstrate that a significant improvement is possible in the special case when the highway dimension is 1. Specifically, we present a fully-polynomial time approximation scheme (FPTAS). We also prove that both TSP and STP are weakly \({\mathsf {NP}}\)-hard for these restricted graphs.

Constraint Programming Algorithms for Route Planning Exploiting Geometrical Information

Problems affecting the transport of people or goods are plentiful in industry and commerce and they also appear to be at the origin of much more complex problems. In recent years, the logistics and transport sector keeps growing supported by technological progress, i.e. companies to be competitive are resorting to innovative technologies aimed at efficiency and effectiveness. This is why companies are increasingly using technologies such as Artificial Intelligence (AI), Blockchain and Internet of Things (IoT). Artificial intelligence, in particular, is often used to solve optimization problems in order to provide users with the most efficient ways to exploit available resources. In this work we present an overview of our current research activities concerning the development of new algorithms, based on CLP techniques, for route planning problems exploiting the geometric information intrinsically present in many of them or in some of their variants. The research so far has focused in particular on the Euclidean Traveling Salesperson Problem (Euclidean TSP) with the aim to exploit the results obtained also to other problems of the same category, such as the Euclidean Vehicle Routing Problem (Euclidean VRP), in the future.

Ground-level Unmanned Aerial System Imagery Coupled with Spatially Balanced Sampling and Route Optimization to Monitor Rangeland Vegetation.

Rangeland ecosystems cover 3.6 billion hectares globally with 239 million hectares located in the United States. These ecosystems are critical for maintaining global ecosystem services. Monitoring vegetation in these ecosystems is required to assess rangeland health, to gauge habitat suitability for wildlife and domestic livestock, to combat invasive weeds, and to elucidate temporal environmental changes. Although rangeland ecosystems cover vast areas, traditional monitoring techniques are often time-consuming and cost-inefficient, subject to high observer bias, and often lack adequate spatial information. Image-based vegetation monitoring is faster, produces permanent records (i.e., images), may result in reduced observer bias, and inherently includes adequate spatial information. Spatially balanced sampling designs are beneficial in monitoring natural resources. A protocol is presented for implementing a spatially balanced sampling design known as balanced acceptance sampling (BAS), with imagery acquired from ground-level cameras and unmanned aerial systems (UAS). A route optimization algorithm is used in addition to solve the 'travelling salesperson problem' (TSP) to increase time and cost efficiency. While UAS images can be acquired 2-3x faster than handheld images, both types of images are similar to each other in terms of accuracy and precision. Lastly, the pros and cons of each method are discussed and examples of potential applications for these methods in other ecosystems are provided.

Improved Filtering for the Euclidean Traveling Salesperson Problem in CLP(FD)

The Traveling Salesperson Problem (TSP) is one of the best-known problems in computer science. The Euclidean TSP is a special case in which each node is identified by its coordinates on the plane and the Euclidean distance is used as cost function.
 Many works in the Constraint Programming (CP) literature addressed the TSP, and use as benchmark Euclidean instances; however the usual approach is to build a distance matrix from the points coordinates, and then address the problem as a TSP, disregarding the information carried by the points coordinates for constraint propagation.
 In this work, we propose to use geometric information, present in Euclidean TSP instances, to improve the filtering power. In order to have a declarative approach, we implemented the filtering algorithms in Constraint Logic Programming on Finite Domains (CLP(FD)).

Medical diagnosis and treatment is NP-complete

ABSTRACT There is great interest in the pursuit of process-driven, algorithmic allocation of health-care resources, including computer-aided medical diagnosis and treatment (MDT). Little is understood regarding the computational complexity of MDT; however, and if determined, how relevant the complexity would be to automating MDT. We approach analysing the computational complexity of MDT in several ways: (1) proving that MDT is computationally intractable (NP-complete, NPC) by reducing the travelling salesperson (TSP) and set-cover (SETCOVER) problems to MDT, (2) showing, in contrast, an example of MDT in tractable form, and (3) showing that, leaving aside TSP and SETCOVER, there are computationally efficient, heuristic-driven search methods based on human diagnostician methods. Calculations show that the sparseness of actual symptom-treatments sets in the space of all possible sets is astronomical (e.g., 10−204,678). While the computational complexity of MDT is interesting theoretically, pragmatically uncovering actual human cognitive practices of MDT will accelerate the development of artificial intelligence to assist and eventually replace physicians.

Collaborative Functioning for Underwater Acoustic Sensor Communication using AURP (AUV-Assisted Underwater Routing Protocol)

Security has become one of the most essential requirements in any application domain of wireless sensor networks. It is highly required so that we can send data to an authenticated person on a secure channel ensuring all the aspects of security features like confidentiality, integrity, authentication, etc. are provided. But it is more essential in a domain like underwater acoustic sensor networks where the bandwidth is severely limited, the energy of sensors is limited and the propagation delay is very high and hence we have limited resources that must be utilized efficiently. In order to address these challenges, the proposed work focuses on a mobile agents based architecture consisting of secure co-operation of AURP (An AUV-aided underwater routing protocol) with the objective of providing maximum data delivery and minimum energy consumption. Further these mobile agents are encrypted and embedded in the AUV’s in their buffer for the data capturing process as these mobile agents can travel throughout the network via controlled AUV's. This work uniquely contributes a mobile agent based periodic approach for collecting data from various gateway nodes (cluster heads) of different clusters as specified in its itinerary using travelling sales person so that it covers all of them using an optimal amount of energy & processing them one by one and completing its itinerary and depositing the data to a sink and then repeating the same process again periodically when these AUV’s gets charged exploiting a solar energy. Each cluster has some members within one hop distance that have sensed some data which needs to be sent to a gateway node using encrypted mobile agents and only when some AUV's services are provided to that particular gateway node.

Unmanned Aerial Vehicle Surveillance Under Visibility and Dwell-Time Constraints

A framework is introduced for planning unmanned aerial vehicle (UAV) flight paths for visual surveillance of ground targets, each having particular viewing requirements. Specifically, the framework is designed for instances in which each target is associated with a set of imaging parameters, including a desired: (i) tilt angle, (ii) azimuth, with the option of a 360 deg view, and (iii) dwell-time. Tours are sought to image the targets, while minimizing both the total mission time and the time required to reach the initial target. An ϵ-constraint scalarization is used to pose the multi-objective problem as a constrained optimization, which, through careful discretization, can be approximated as a discrete graph-search. It is shown that, in many cases, this approximation is equivalent to a generalized traveling salesperson problem (GTSP). A heuristic procedure for solving the discrete approximation and recovering solutions to the full routing problem is presented and illustrated through numerical studies.

Experimental analysis of design elements of scalarizing function-based multiobjective evolutionary algorithms

In this paper, we systematically study the influence of the main design elements of scalarizing function-based multiobjective evolutionary algorithms (MOEAs) on the performance of these algorithms. Such algorithms proved to be very successful in multiple computational experiments and practical applications. Well-known examples of this class of MOEAs are Jaszkiewicz’s multiobjecitve genetic local search and multiobjective evolutionary algorithm based on decomposition (MOEA/D). The two algorithms share the same common structure and differ in two aspects, i.e., the selection of parents for recombination and the selection of weight vectors of scalarizing functions. Using three different multiobjective combinatorial optimization problems, i.e., the multiobjective symmetric traveling salesperson problem, the traveling salesperson problem with profits, and the multiobjective set covering problem, we show that the design element with the highest influence on the performance is the choice of a mechanism for parents selection, while the selection of weight vectors, either random or evenly distributed, has practically negligible influence if the number of evenly distributed weight vectors is sufficiently large.

How intermittent breaks in interaction improve collective intelligence

People influence each other when they interact to solve problems. Such social influence introduces both benefits (higher average solution quality due to exploitation of existing answers through social learning) and costs (lower maximum solution quality due to a reduction in individual exploration for novel answers) relative to independent problem solving. In contrast to prior work, which has focused on how the presence and network structure of social influence affect performance, here we investigate the effects of time. We show that when social influence is intermittent it provides the benefits of constant social influence without the costs. Human subjects solved the canonical traveling salesperson problem in groups of three, randomized into treatments with constant social influence, intermittent social influence, or no social influence. Groups in the intermittent social-influence treatment found the optimum solution frequently (like groups without influence) but had a high mean performance (like groups with constant influence); they learned from each other, while maintaining a high level of exploration. Solutions improved most on rounds with social influence after a period of separation. We also show that storing subjects' best solutions so that they could be reloaded and possibly modified in subsequent rounds-a ubiquitous feature of personal productivity software-is similar to constant social influence: It increases mean performance but decreases exploration.

Human behaviour in the Euclidean Travelling Salesperson Problem: Computational modelling of heuristics and figural effects

The Travelling Salesperson Problem (TSP) describes a situation where an imaginary individual wishes to visit multiple cities once before returning to his/her own city. This type of problem is known as a nondeterministic polynomial (NP) hard problem, since the factorial number of solutions results in it being impractical to solve using exhaustive processing. Interestingly, when presented as a Euclidean graph (i.e., ETSP), humans identify near optimal solutions almost effortlessly, despite billions of possible tours. In this study, we consider human processing of the ETSP, and introduce the reader to a number of factors that literature proposes as impacting human performance. We hypothesise that: (i) human ETSP activity may be modelled by considering the quotient relationship between node-to-node and node-to-centroid distances; and (ii) consideration of figural effects can optimise automated TSP solution generation. In this paper human processing based heuristics are developed, i.e. replacing the cost function within the nearest neighbour algorithm, to guide node selection. Results showed that the quotient relationship between node-to-node and node-to-centroid distances can be used to closely model average human performance, across a range of ETSP graphs. Interestingly, however, additional consideration of graph figural effects (e.g. distance between boundary points in the convex hull, standard deviation of distances between nodes that make up the convex hull, and number of nodes in the convex hull) results in significantly improved tour costs.

Theoretical Analysis of Local Search and Simple Evolutionary Algorithms for the Generalized Travelling Salesperson Problem.

The generalized travelling salesperson problem is an important NP-hard combinatorial optimization problem for which metaheuristics, such as local search and evolutionary algorithms, have been used very successfully. Two hierarchical approaches with different neighbourhood structures, namely a cluster-based approach and a node-based approach, have been proposed by Hu and Raidl (2008) for solving this problem. In this article, local search algorithms and simple evolutionary algorithms based on these approaches are investigated from a theoretical perspective. For local search algorithms, we point out the complementary abilities of the two approaches by presenting instances where they mutually outperform each other. Afterwards, we introduce an instance which is hard for both approaches when initialized on a particular point of the search space, but where a variable neighbourhood search combining them finds the optimal solution in polynomial time. Then we turn our attention to analysing the behaviour of simple evolutionary algorithms that use these approaches. We show that the node-based approach solves the hard instance of the cluster-based approach presented in Corus et al. (2016) in polynomial time. Furthermore, we prove an exponential lower bound on the optimization time of the node-based approach for a class of Euclidean instances.

A Bi-Modal Routing Problem with Cyclical and One-Way Trips: Formulation and Heuristic Solution

A bi-modal routing problem is solved using a heuristic approach. Motivated by a recreational hiking application, the problem is similar to routing problems in business with two transport modes. The problem decomposes into a set covering problem (SCP) and an asymmetric traveling salesperson problem (ATSP), corresponding to a hiking time objective and a driving distance objective. The solution algorithm considers hiking time first, but finds all alternate optimal solutions, as inputs to the driving distance problem. Results show the trade-offs between the two objectives.

Convex Hull Based Trajectory Design for Mobile Sink in Wireless Sensor Networks

Data collection through mobile sink (MS) is an efficient solution to solve hotspot or sinkhole problem which is usually caused by data collection using a static sink. In this paper, we propose an algorithm for designing a delay bound path for MS which is based on convex hull and therefore we refer it a concentric convex hull (CCH) algorithm. For a given set of sensor nodes, the CCH generates a set of convex hull as the potential paths and selects one of them as the final path for MS fulfilling certain optimising criteria. Unlike other existing techniques, the proposed technique does not use travelling sales person (TSP) tour. This, in turn, reduces the hop count and restricts the time complexity of the proposed technique to O(n2) for n sensor nodes. We simulate the proposed algorithm, compare and analyse the results with some of the existing algorithms over diverse network performance metrics.