Traveling Salesman Algorithm Research Articles

Time complexity of the analyst's traveling salesman algorithm

The Analyst's Traveling Salesman Problem asks for conditions under which a (finite or infinite) subset of $\R^N$ is contained on a curve of finite length. We show that for finite sets, the algorithm constructed in \cite{Schul-Hilbert,BNV} that solves the Analyst's Traveling Salesman Problem has polynomial time complexity and we determine the sharp exponent.

Real-time Fast Selection System with Object Recognition and TSP algorithms

The stage before the conversion of agricultural products into post-harvest consumer products is the process of separating the raw products into appropriate classes. Today, this difficult manual separating process is a process in which a large number of workers work at an intense pace on the product line and the workforce is intensively spent. Disruptions in separating as a result of carelessness cause product loss, loss of time and cost increases. In this study, as an alternative to manual separating processes, a real-time separating system, which detects the products in the factory band with object recognition methods and enables fast positioning of the separating tool on the products, works simultaneously with object recognition and traveling salesman problem algorithms has been created. In this way, a low-budget separating system is recommended for large selecting processes with a time- and cost-effective selecting model. In the study, the creation of a real-time fast separating system with the support of the traveling salesman algorithm, performance evaluation and research and findings on the fast separating model are presented.

Cooperative survey of seabed ROIs using multiple USVs with coverage path planning

A fine-grained offshore seabed map is critical to the site selection and construction for offshore wind farms, which can be obtained by the cooperative survey with multiple unmanned surface vehicles (USVs). To accomplish the mission of surveying multiple regions of interest (ROIs) by cooperative coverage path planning of USVs, a sequential algorithm is proposed to facilitate the generating the ROIs’ boundary, decomposing concave polygons, and planning coverage path for multiple USVs. First, in order to extract the multiple ROIs and generate accurate polygon boundaries, the grid clustering method and the α -shapes method are adopted with a prior seabed distribution map information. Second, an improved Bayazit decomposition algorithm is presented to reduce the number of sub-regions and turnings by USVs during the coverage planning. Third, aiming at routing the traveling order of every sub-region, a novel discrete group teaching optimization algorithm with an adaptive neighborhood radius model is proposed, which performs robustly compared with five classical multiple traveling salesman algorithms. Finally, numerical simulation results show that the proposed algorithm integrating the ROIs determination and coverage path planning methods is effective for cooperative surveying of multiple USVs.

Adriatic Sea Hub Ports Feeder Service Optimization Using Multi-Criteria Decision-Making Methods

From a scientific viewpoint, as well as from the perspective of navigation practice, it is clear that the Adriatic Sea feeder service is relatively underdeveloped. Hence, the objective of this study is to suggest a model for selecting the hub port and to optimize the network of seaports engaged in the feeder service. Accordingly, an appropriate hub port has been identified through the methods of multi-criteria decision making and expert assessment, and the optimum shipping route has been calculated by applying the travelling salesman algorithm (TSA). In order to analyze whether there is a possibility of obtaining better optimization results, an integration of a sub-hub port system is suggested. Optimization has been achieved by applying a minimum spanning tree algorithm (MST) and a combination of these algorithms. The proposed methodology for selecting the hub port, sub-hub port and optimizing the feeder network can be implemented globally. The practical application of the achieved model would result in cost minimization, owing to shorter shipping routes or a combination of different transportation means (feeders).

Distributed and incremental travelling salesman algorithm on time-evolving graphs

Travelling salesman problem (TSP) is a graph problem that has been widely used in many applications, especially for transportation and logistics. Because TSP is a NP hard problem, minimizing the complexity of TSP algorithms is an important problem. Many heuristic algorithms have been proposed to compute the TSP tours of a given static graph. But limited studies have been done on time-evolving graph (TEG) where the graph can change over time due to update events, such as weight changes on edges or vertices. It is a more challenging problem because the speed of TSP computations must be high enough to catch up the graph update frequency. In this paper, we make the very first attempt to minimize the computation time of solving TSP on time-evolving graphs. By exploring parallel computing power and reusing previous computing results, we proposed a distributed and incremental TSP algorithm which can be implemented on vertex-centric parallel graph computing frameworks to efficiently find TSP tours on large changing graphs. Our incremental algorithm can maintain shortest TSP tour with minimum amount of recomputation. Through our experimental evaluation, we have shown incremental TSP algorithm is 98% faster than distributed algorithm.

Traveling Salesman Algorithms Complexity

Traveling Salesman Algorithms Complexity

Facility Location Problem Approach for Distributed Drones

Currently, industry and academia are undergoing an evolution in developing the next generation of drone applications. Including the development of autonomous drones that can carry out tasks without the assistance of a human operator. In spite of this, there are still problems left unanswered related to the placement of drone take-off, landing and charging areas. Future policies by governments and aviation agencies are inevitably going to restrict the operational area where drones can take-off and land. Hence, there is a need to develop a system to manage landing and take-off areas for drones. Additionally, we proposed this approach due to the lack of justification for the initial location of drones in current research. Therefore, to provide a foundation for future research, we give a justified reason that allows predetermined location of drones with the use of drone ports. Furthermore, we propose an algorithm to optimally place these drone ports to minimize the average distance drones must travel based on a set of potential drone port locations and tasks generated in a given area. Our approach is derived from the Facility Location problem which produces an efficient near optimal solution to place drone ports that reduces the overall drone energy consumption. Secondly, we apply various traveling salesman algorithms to determine the shortest route the drone must travel to visit all the tasks.

The effect of mass mosquito trapping on malaria transmission and disease burden (SolarMal): a stepped-wedge cluster-randomised trial

Odour baits can attract host-seeking Anopheles mosquitoes indoors and outdoors. We assessed the effects of mass deployment of odour-baited traps on malaria transmission and disease burden. We installed solar-powered odour-baited mosquito trapping systems (SMoTS) to households on Rusinga Island, Lake Victoria, western Kenya (mean population 24 879), in a stepped-wedge cluster-randomised trial. All residents in the completed health and demographic surveillance system were eligible to participate. We used the travelling salesman algorithm to assign all households to a cluster (50 or 51 geographically contiguous households); nine contiguous clusters formed a metacluster. Initially, no cluster had SMoTS (non-intervened). During the course of the intervention roll-out SMoTS were gradually installed cluster by cluster until all clusters had SMoTS installed (intervened). We generated 27 cluster randomisations, with the cluster as unit of randomisation, to establish the order to install the traps in the clusters until all had a SMoTS installed. Field workers and participants were not masked to group allocation. The primary outcome of clinical malaria was monitored through repeated household visits covering the entire population, once before roll-out (baseline) and five times throughout the 2-year roll-out. We measured clinical malaria as fever plus a positive result with a rapid diagnostic test. The SolarMal project was registered on the Dutch Trial Register (NTR 3496). We enrolled 34 041 participants between April 25, 2012, and March 23, 2015, to 81 clusters and nine metaclusters. 4358 households were provided with SMoTS during roll-out between June 3, 2013, and May 16, 2015. 23 clinical malaria episodes were recorded in intervened clusters and 33 episodes in non-intervened clusters (adjusted effectiveness 40·8% [95% CI -172·8 to 87·1], p=0·5) during the roll-out. Malaria prevalence measured by rapid diagnostic test was 29·8% (95% CI 20·9-38·0) lower in SMoTS clusters (prevalence 23·7%; 1552 of 6550 people) than in non-intervened clusters (prevalence 34·5%; 2002 of 5795 people). The unexpectedly low clinical incidence of malaria during roll-out led to an imprecise estimate of effectiveness from the clinical incidence data. The substantial effect on malaria prevalence is explained by reduction in densities of Anopheles funestus. Odour-baited traps might be an effective malaria intervention. COmON Foundation.

Spatially variable risk factors for malaria in a geographically heterogeneous landscape, western Kenya: an explorative study

BackgroundLarge reductions in malaria transmission and mortality have been achieved over the last decade, and this has mainly been attributed to the scale-up of long-lasting insecticidal bed nets and indoor residual spraying with insecticides. Despite these gains considerable residual, spatially heterogeneous, transmission remains. To reduce transmission in these foci, researchers need to consider the local demographical, environmental and social context, and design an appropriate set of interventions. Exploring spatially variable risk factors for malaria can give insight into which human and environmental characteristics play important roles in sustaining malaria transmission.MethodsOn Rusinga Island, western Kenya, malaria infection was tested by rapid diagnostic tests during two cross-sectional surveys conducted 3 months apart in 3632 individuals from 790 households. For all households demographic data were collected by means of questionnaires. Environmental variables were derived using Quickbird satellite images. Analyses were performed on 81 project clusters constructed by a traveling salesman algorithm, each containing 50–51 households. A standard linear regression model was fitted containing multiple variables to determine how much of the spatial variation in malaria prevalence could be explained by the demographic and environmental data. Subsequently, a geographically-weighted regression (GWR) was performed assuming non-stationarity of risk factors. Special attention was taken to investigate the effect of residual spatial autocorrelation and local multicollinearity.ResultsCombining the data from both surveys, overall malaria prevalence was 24 %. Scan statistics revealed two clusters which had significantly elevated numbers of malaria cases compared to the background prevalence across the rest of the study area. A multivariable linear model including environmental and household factors revealed that higher socioeconomic status, outdoor occupation and population density were associated with increased malaria risk. The local GWR model improved the model fit considerably and the relationship of malaria with risk factors was found to vary spatially over the island; in different areas of the island socio-economic status, outdoor occupation and population density were found to be positively or negatively associated with malaria prevalence.DiscussionIdentification of risk factors for malaria that vary geographically can provide insight into the local epidemiology of malaria. Examining spatially variable relationships can be a helpful tool in exploring which set of targeted interventions could locally be implemented. Supplementary malaria control may be directed at areas, which are identified as at risk. For instance, areas with many people that work outdoors at night may need more focus in terms of vector control.Trial registration: Trialregister.nl NTR3496—SolarMal, registered on 20 June 2012

The distributed parallel genetic algorithm on the ad hoc network

Today, mobile computing is one of the important issues in computer and network sciences. Using the processing power of mobile devices purposefully for solving complex issues is one of the research fields for researchers. One of the important issues in the optimization which needs a high processing power for finding the best possible answer is travelling salesman problem. In this paper, by providing a method based on the distributed parallel genetic algorithm on a number of mobile nodes in the Ad Hoc network, it was attempted to increase the speed of finding the best answer for the travelling salesman algorithm.

Smart Tourism in 1-Click

The use and application of technology is the challenge of tourism for the XXI century. Thus, a novel application for mobile devices is deployed. Our application allows you to browse all points of interest to the user such as hotels, restaurants, attractions, etc. Our application incorporates at first instance the city of Mexico, one of the cities most visited by tourists. With respect to Mexico city we added three important features to our application. First, the user can indicate whether traveling by car or walks. Second, user can choose city area to visit, as well as the maximum distance at which he want to move. Third, our application will generate the shortest route to follow. Secondly but no less important, our application incorporates the city of Puebla, a city declared World Heritage. It support the efficiently tourists in planning their stay in Puebla City showing user a set of tourist places and services, both useful for tourists, of which user chooses those who want to know. From this set of selected places our application determines the shortest path using the traveling salesman algorithm. Also, emergency services information about all local points is available. Generation of custom path is integrated, allowing user to have Google maps with all places to visit with a true an accurate location. Finally, our application allows the user to display maps of tourist places in real time without the GPS service, instead we use GPRS via Wireless Application Protocol with the Google Maps API.

BLIND ordering of large-scale transcriptomic developmental timecourses

RNA-Seq enables the efficient transcriptome sequencing of many samples from small amounts of material, but the analysis of these data remains challenging. In particular, in developmental studies, RNA-Seq is challenged by the morphological staging of samples, such as embryos, since these often lack clear markers at any particular stage. In such cases, the automatic identification of the stage of a sample would enable previously infeasible experimental designs. Here we present the 'basic linear index determination of transcriptomes' (BLIND) method for ordering samples comprising different developmental stages. The method is an implementation of a traveling salesman algorithm to order the transcriptomes according to their inter-relationships as defined by principal components analysis. To establish the direction of the ordered samples, we show that an appropriate indicator is the entropy of transcriptomic gene expression levels, which increases over developmental time. Using BLIND, we correctly recover the annotated order of previously published embryonic transcriptomic timecourses for frog, mosquito, fly and zebrafish. We further demonstrate the efficacy of BLIND by collecting 59 embryos of the sponge Amphimedon queenslandica and ordering their transcriptomes according to developmental stage. BLIND is thus useful in establishing the temporal order of samples within large datasets and is of particular relevance to the study of organisms with asynchronous development and when morphological staging is difficult.

System automation for a bacterial colony detection and identification instrument via forward scattering

A system design and automation of a microbiological instrument that locates bacterial colonies and captures the forward-scattering signatures are presented. The proposed instrument integrates three major components: a colony locator, a forward scatterometer and a motion controller. The colony locator utilizes an off-axis light source to illuminate a Petri dish and an IEEE1394 camera to capture the diffusively scattered light to provide the number of bacterial colonies and two-dimensional coordinate information of the bacterial colonies with the help of a segmentation algorithm with region-growing. Then the Petri dish is automatically aligned with the respective centroid coordinate with a trajectory optimization method, such as the Traveling Salesman Algorithm. The forward scatterometer automatically computes the scattered laser beam from a monochromatic image sensor via quadrant intensity balancing and quantitatively determines the centeredness of the forward-scattering pattern. The final scattering signatures are stored to be analyzed to provide rapid identification and classification of the bacterial samples.

A TSP-GA multi-objective algorithm for flow-shop scheduling

A multi-objective evolutionary search algorithm using a travelling salesman algorithm and genetic algorithm for flow-shop scheduling is proposed in this paper. The initial sequence is obtained by solving the TSP. The initial population of the genetic algorithm is created with the help of a neighbourhood creation scheme known as a random insertion perturbation scheme, which uses the sequence obtained from TSP. The proposed algorithm uses a weighted sum of multiple objectives as a fitness function. The weights are randomly generated for each generation to enable a multi-directional search. The performance measures considered include minimising makespan, mean flow time and machine idle time. The performance of the proposed algorithm is demonstrated by applying it to benchmark problems available in the OR-Library.

Comparison of shortest sailing distance through random and regular sampling points

Abstract The shortest sailing distance through n sampling points is calculated for simple theoretical sampling domains (square and circle) as well as for a rather irregular and concavely shaped real sampling domain in the Barents Sea. The sampling sites are either located at the nodes of a square grid (regular sampling) or they are randomly distributed. For n less than ten, the exact shortest sailing distance is derived. For larger n, a traveling salesman algorithm (simulated annealing) was applied, and its bias (distance from true minimum) was estimated based on a case where the true minimum distance was known. In general, the average minimum sailing distance based on random sampling was considerably shorter than for regular sampling, and the difference increased with sample size until an asymptotic value was reached at about n=60 for a square domain. For the sampling domain in the Barents Sea used for shrimp (Pandalus borealis) abundance surveys (n=118 stations), the cruise-track lengths based on random sampling were approximately normally distributed. The mean sailing distance was 18% shorter than the cruise track for regular sampling and the standard deviation equalled 2.6%.

Approximation algorithms for the traveling salesman problem

We first prove that the minimum and maximum traveling salesman problems, their metric versions as well as some versions defined on parameterized triangle inequalities (called sharpened and relaxed metric traveling salesman) are all equi-approximable under an approximation measure, called differential-approximation ratio, that measures how the value of an approximate solution is placed in the interval between the worst- and the best-value solutions of an instance. We next show that the 2OPT, one of the most-known traveling salesman algorithms, approximately solves all these problems within differential-approximation ratio bounded above by 1/2. We analyze the approximation behavior of 2OPT when used to approximately solve traveling salesman problem in bipartite graphs and prove that it achieves differential-approximation ratio bounded above by 1/2 also in this case. We also prove that, for any e>0, it is NP-hard to differentially approximate metric traveling salesman within better than 649/650 + e and traveling salesman with distances 1 and 2 within better than 741/742 + e. Finally, we study the standard approximation of the maximum sharpened and relaxed metric traveling salesman problems. These are versions of maximum metric traveling salesman defined on parameterized triangle inequalities and, to our knowledge, they have not been studied until now.

Synchronisation and Load Balancing for Parallel Hierarchical Radiosity of Complex Scenes on a Heterogeneous Computer Network

In this paper we propose a SPMD parallel hierarchical radiosity algorithm relying on a novel partitioning method which may apply to any kind of architectural scene. This algorithm is based on MPI (Message Passing Interface), a communication library which allows the use of either a heterogeneous set of concurrent computers or a parallel computer or both. The database is stored on a common directory and accessed by all the processors (through NFS in case of a network of computers). As the objective is to handle complex scenes such as building interiors, to cope with the problem of memory size, only a subset of the database resides in memory of each processor. This subset is determined with the help of a partitioning into 3D cells, clustering and visibility calculations. A graph expressing visibility between the resulting clusters is determined, partitioned (with a new method based on classification of K‐means type) and distributed amongst all the processors. Each processor is responsible for gathering energy (using the Gauss‐Seidel method) only for its subset of clusters. In order to reduce the disk transfers due to downloading these subsets of clusters, we use an ordering strategy based on the traveling salesman algorithm. Dynamic load balancing relies on a task stealing approach while termination is detected by configuring the processors into a ring and moving a token around this ring. The parallel iterative resolution is of group iterative type. Its mathematical convergence is proven in the appendix.

The application of inverse kinematics in the optimum sequencing of robot tasks†

SUMMARY This paper addresses one of the operational problems associated with the application of robots to industrial systems: the optimum sequencing of robotic task performance. The application of inverse kinematics in determining the sequence that minimizes the cycle time in a robot cell is described. An extension of the Travelling Salesman Algorithm is found to be suitable for obtaining the optimum sequence and cycle time.

An algorithm for the design of mailbox collection routes in urban areas

Mailbox collection is a complex and costly operation in most postal services. The authors recently undertook a study aimed at improving this operation at the Canada Post Corporation (CPC). This paper describes an improvement to the clustering and routing algorithm currently in use. Various traffic and union rules affecting mailbox collection in an urban context are first described and their effect on shortest distance computations is explained. This is followed by a description of the clustering and routing algorithm currently used at CPC. A model and a generalized travelling salesman algorithm that take the various rules into account are then presented. It is then shown how the CPC routes can sometimes be improved by using the proposed algorithm as a postoptimizer.

Effects of a computer-based process planning system on an ‘intercompany transport’ work system

Abstract A computer based disposition system for the organisation of interfactory transport is presented. Based on a travelling salesman algorithm and further modules, it reduces the distances between following transport orders significantly. The effects on the work and in particular on stress and strain of the employees in this system are compared with other results in the literature and field studies by work analysis and their clusters. The manual transshipment (better stowing) of cargo is identified as critical in the sense of a possible violation of tolerable boundaries. Using an approach for the determination of marginal values, first it is shown, that the increase of heart rate during work depends on the mass of transshipped cargo as well as on the handling rate and can be predicted according to these stressors. Possibilities for the determination of required relaxation allowances are shown. On the basis of the results of these studies an ergonomic work area is defined, in which the demand for maxim...