Minimum Cost Path Research Articles

Occlusion Resistant Spatio-Temporal Hybrid Cue Network for Indian Sign Language Recognition and Translation

Objective: To tackle the issues of occlusion in human skeleton extraction and simplify the pixel matching related to the human skeleton structure for efficient Indian Sign Language (ISL) recognition and translation. Methods: This paper presents Occlusion-Resistant STHCN (OSTHCN) to tackle the occlusion problem in human skeleton extraction for effective ISL recognition and translation. This model incorporates Skeleton Occupancy Likelihood Map estimation using B-Spline curves to enhance the skeleton extraction. Due to occlusions caused by fingers and hands, the extracted skeleton is composed of disconnected skeletal subgraphs. Consequently, each observed skeleton is represented as a probability distribution along an ellipsoidal contour, originating from the central points of the skeleton. A heuristic technique estimates occluded skeletons using 3D probability map with an occupancy grid where each voxel indicates skeleton likelihood. The occupancy distribution is updated using observed branch clusters across image sequences, detecting occluded skeletons by finding minimum-cost paths. Finally, Maximally connected subgraphs are merged into a main graph by finding minimum-cost paths in the 3D likelihood map, enabling the prediction of occluded skeleton parts for ISL recognition and translation. Findings: OSTHCN model achieved an accuracy of 96.74% on the ISL Continuous Sign Language Translation Recognition (ISL-CSLTR) dataset outperforming existing prediction models. Novelty: This model employs a unique occlusion-handling strategy for skeleton extraction, estimating occluded part, integrating connected subgraphs via minimal cost path searches for more precise skeleton parts and enhancing accuracy for ISL recognition and translation. Keywords: Sign Language, Graph Convolutional Neural Network, Ellipsoidal Contour, 3D Likelihood Map, Occupancy Probability

Travel Time Estimation for Optimal Planning in Internal Transportation

Optimal planning depends on precise and exact estimation of the operation costs of mobile robots. Unfortunately, determining the current and future state of a vehicle implies identifying all the parameters in its model. Rather than broadening the number of factors, in this work we adopt the approach of using a higher-level abstraction model to identify only a few cost parameters. Based on the observation that arc travel times accurately reflect the effect of physical states, this work proposes using them as the key parameters to compute accurate path traversal costs in the context of indoor transportation. This approach eliminates the need to model all factors in order to derive the cost for every robot. The resulting model organizes those parameters in a bilinear state-space form and includes the evolution of actual travel times with changing states. We show that the proposed model accurately estimates arc travel times with respect to actual observations gathered from real robots traversing a few arcs of a traffic network until battery exhaustion. We experimentally obtained minimum-cost paths from random origin and destination nodes when using heuristics and the “closer-to-reality” (bilinear-state version of our model) path costs, finding that it can save an average of 15% in transportation time compared to conventional methods.

Brazilian maritime containerized cabotage competitiveness assessment based on a multimodal super network

This study evaluates the competitiveness of Brazilian maritime container cabotage within a multimodal transportation super network, employing an adapted All Pairs Shortest Path (APSP) algorithm to solve the All Pairs Minimum Cost Path problem. The research analyzes cost structures, environmental impacts, and operational efficiencies across 637 cities, 18 container terminals, 8 barge terminals, and 301 maritime routes. Key metrics, including freight rates, in-transit inventory costs, and CO2 equivalent emissions, are incorporated into the network's impedance values, enabling a comprehensive comparison between maritime cabotage and road transportations modes. Results indicate that maritime cabotage holds a significant cost advantage over road transportation mode for long-haul routes, particularly when distances exceed 1.800 km. Additionally, maritime cabotage offers substantial environmental benefits, with CO2 equivalent emission reductions of up to 41,3 %, depending on the route and cabotage shipping company.

Bus Network Adjustment Pre-Evaluation Based on Biometric Recognition and Travel Spatio-Temporal Deduction

A critical component of bus network adjustment is the accurate prediction of potential risks, such as the likelihood of complaints from passengers. Traditional simulation methods, however, face limitations in identifying passengers and understanding how their travel patterns may change. To address this issue, a pre-evaluation method has been developed, leveraging the spatial distribution of bus networks and the spatio-temporal behavior of passengers. The method includes stage of travel demand analysis, accessible path set calculation, passenger assignment, and evaluation of key indicators. First, we explore the actual passengers’ origin and destination (OD) stop from bus card (or passenger Code) payment data and biometric recognition data, with the OD as one of the main input parameters. Second, a digital bus network model is constructed to represent the logical and spatial relationships between routes and stops. Upon inputting bus line adjustment parameters, these relationships allow for the precise and automatic identification of the affected areas, as well as the calculation of accessible paths of each OD pair. Third, the factors influencing passengers’ path selection are analyzed, and a predictive model is built to estimate post-adjustment path choices. A genetic algorithm is employed to optimize the model’s weights. Finally, various metrics, such as changes in travel routes and ride times, are analyzed by integrating passenger profiles. The proposed method was tested on the case of the Guangzhou 543 route adjustment. Results show that the accuracy of the number of predicted trips after adjustment is 89.6%, and the predicted flow of each associated bus line is also consistent with the actual situation. The main reason for the error is that the path selection has a certain level of irrationality, which stems from the fact that the proportion of passengers who choose the minimum cost path for direct travel is about 65%, while the proportion of one-transfer passengers is only about 50%. Overall, the proposed algorithm can quantitatively analyze the impact of rigid travel groups, occasional travel groups, elderly groups, and other groups that are prone to making complaints in response to bus line adjustment.

Reproducibility of a single-volume dynamic CT myocardial blood flow measurement technique: validation in a swine model

BackgroundWe prospectively assessed the reproducibility of a novel low-dose single-volume dynamic computed tomography (CT) myocardial blood flow measurement technique.MethodsThirty-four pairs of measurements were made under rest and stress conditions in 13 swine (54.3 ± 12.3 kg). One or two acquisition pairs were acquired in each animal with a 10-min delay between each pair. Contrast (370 mgI/mL; 0.5 mL/kg) and a diluted contrast/saline chaser (0.5 mL/kg; 30:70 contrast/saline) were injected peripherally at 5 mL/s, followed by bolus tracking and acquisition of a single volume scan (100 kVp; 200 mA) with a 320-slice CT scanner. Bolus tracking and single volume scan data were used to derive perfusion in mL/min/g using a first-pass analysis model; the coronary perfusion territories of the left anterior descending (LAD), left circumflex (LCx), and right coronary artery (RCA) were automatically assigned using a previously validated minimum-cost path technique. The reproducibility of CT myocardial perfusion measurement within the LAD, LCx, RCA, and the whole myocardium was assessed via regression analysis. The average CT dose index (CTDI) of perfusion measurement was recorded.ResultsThe repeated first (Pmyo1) and second (Pmyo2) single-volume CT perfusion measurements were related by Pmyo2 = 1.01Pmyo1 − 0.03(ρ = 0.96; RMSE = 0.08 mL/min/g; RMSE = 0.07 mL/min/g) for the whole myocardium, and by Preg2 = 0.86Preg1 + 0.13(ρ = 0.87; RMSE = 0.31 mL/min/g; RMSE = 0.29 mL/min/g) for the LAD, LCx, and RCA perfusion territories. The average CTDI of the single-volume CT perfusion measurement was 10.5 mGy.ConclusionThe single-volume CT blood flow measurement technique provides reproducible low-dose myocardial perfusion measurement using only bolus tracking data and a single whole-heart volume scan.Relevance statementThe single-volume CT blood flow measurement technique is a noninvasive tool that reproducibly measures myocardial perfusion and provides coronary CT angiograms, allowing for simultaneous anatomic-physiologic assessment of myocardial ischemia.Key PointsA low-dose single-volume dynamic CT myocardial blood flow measurement technique is reproducible.Motion misregistration artifacts are eliminated using a single-volume CT perfusion technique.This technique enables combined anatomic-physiologic assessment of coronary artery disease.Graphical

Minimum Cost Pathfinding Algorithm for the Determination of Optimal Paths under Airflow Constraints

Pathfinding algorithms allow for the numerical determination of optimal paths of travel across many applications. These algorithms remain poorly defined for additional consideration of outside parameters, such as fluid flow, while considering contaminant transport problems. We have developed a pathfinding algorithm based on the A* search algorithm which considers the effect of fluid flow behaviors in two dimensions. This search algorithm returns the optimal path between two points in a setting containing impermeable boundaries, allowing for a computational approach to the determination of the most likely path of travel for contaminants or hazards of concern due to fluid flow. This modified A* search algorithm has applications in the statistical modeling of airborne contamination distributions, providing a relative estimate of the statistical relationship between two points in an underground mine’s ventilation system. This method provides a significant improvement to the spatial resolution of minimum-cost path methods currently in use in mine ventilation network software.

Reproducibility of a semiautomatic lobar lung tissue assignment technique on noncontrast CT scans: a study on swine animal model

BackgroundTo evaluate the reproducibility of a vessel-specific minimum cost path (MCP) technique used for lobar segmentation on noncontrast computed tomography (CT).MethodsSixteen Yorkshire swine (49.9 ± 4.7 kg, mean ± standard deviation) underwent a total of 46 noncontrast helical CT scans from November 2020 to May 2022 using a 320-slice scanner. A semiautomatic algorithm was employed by three readers to segment the lung tissue and pulmonary arterial tree. The centerline of the arterial tree was extracted and partitioned into six subtrees for lobar assignment. The MCP technique was implemented to assign lobar territories by assigning lung tissue voxels to the nearest arterial tree segment. MCP-derived lobar mass and volume were then compared between two acquisitions, using linear regression, root mean square error (RMSE), and paired sample t-tests. An interobserver and intraobserver analysis of the lobar measurements was also performed.ResultsThe average whole lung mass and volume was 663.7 ± 103.7 g and 1,444.22 ± 309.1 mL, respectively. The lobar mass measurements from the initial (MLobe1) and subsequent (MLobe2) acquisitions were correlated by MLobe1 = 0.99 MLobe2 + 1.76 (r = 0.99, p = 0.120, RMSE = 7.99 g). The lobar volume measurements from the initial (VLobe1) and subsequent (VLobe2) acquisitions were correlated by VLobe1 = 0.98VLobe2 + 2.66 (r = 0.99, p = 0.160, RSME = 15.26 mL).ConclusionsThe lobar mass and volume measurements showed excellent reproducibility through a vessel-specific assignment technique. This technique may serve for automated lung lobar segmentation, facilitating clinical regional pulmonary analysis.Relevance statementAssessment of lobar mass or volume in the lung lobes using noncontrast CT may allow for efficient region-specific treatment strategies for diseases such as pulmonary embolism and chronic thromboembolic pulmonary hypertension.Key points• Lobar segmentation is essential for precise disease assessment and treatment planning.• Current methods for segmentation using fissure lines are problematic.• The minimum-cost-path technique here is proposed and a swine model showed excellent reproducibility for lobar mass measurements.• Interobserver agreement was excellent, with intraclass correlation coefficients greater than 0.90.Graphical

A Segmentation-Based Optimal Seamline Generation Method for SAR Image Mosaic

In the mosaic creation of multiple high-resolution synthetic aperture radar (SAR) images, achieving an optimal seamline in overlapping areas is crucial for seamless and visually satisfactory results. Many existing seamline generation methods are designed primarily for optical remote sensing images, but due to the differing characteristics of SAR images and optical images, applying these methods directly to SAR images poses challenges in finding the optimal seamline. In response, this paper proposes a segmentation-based optimal seamline generation (SOSG) method for SAR image mosaics. The SOSG method involves a multi-step process. First, SAR image joint segmentation is performed within the overlapping areas. Subsequently, homogeneous areas are identified based on the segmentation results. Following this, a pixel cost matrix is constructed, incorporating homogeneous areas and intensity differences. Finally, the minimum path cost from the starting pixel to the end pixel is computed using the Dijkstra algorithm to determine the optimal path. To assess the feasibility and effectiveness of the proposed method, experiments are conducted using multiple SAR images from the Chinese Gaofen-3 01 satellite as datasets. The experimental results demonstrate that the proposed method yields seamless mosaic images when compared to other methods, while delivering satisfactory outcomes. This indicates the potential of the proposed method in addressing the unique challenges posed by SAR images and enhancing the quality of SAR image mosaics.

Resource allocation on periotity based schuduling and improve the security using DSSHA-256

Cloud computing has gained popularity with advancements in virtualization technology and the deployment of 5G. However, scheduling workload in a heterogeneous multi-cloud environment is a complicated process. Users of cloud services want to ensure that their data is secure and private, especially sensitive or proprietary information. Several research works have been proposed to solve the challenges associated with cloud computing. The proposed Adaptive Priority based scheduling (PBS) focuses on reducing data access completion time and computation expense for task scheduling in cloud computing. PBS assigns tasks depending on its size and selects the minimum cost path for data access. It contains a task register, scheduler, and task execution components for efficient task execution. The proposed system also executes a double signature mechanism for data privacy and security in data storage. This study correlates the performance of three algorithms, PBS, (Task Requirement Degree) TRD and (recommended a Risk adaptive Access Control) RADAC, in terms of task execution time and makespan time. The experimental results demonstrate that PBS outperforms TRD and RADAC in both metrics, as the number of tasks increases. PBS has a minimum task execution time and a lower makespan time than the other two algorithms

Path Planning in a Weighted Planar Subdivision Under the Manhattan Metric

In this paper, we consider the problem of path planning in a weighted polygonal planar subdivision. Each polygon has an associated positive weight which shows the cost of path per unit distance of movement in that polygon. The goal is to find a minimum cost path under the Manhattan metric for two given start and destination points. First, we propose an O(n2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n^2)$$\\end{document} time and space algorithm to solve this problem, where n is the total number of vertices in the subdivision. Then, we improve the time and space complexity of the algorithm to O(nlog2n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n \\log ^2 n)$$\\end{document} and O(nlogn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n \\log n)$$\\end{document}, respectively, by applying a divide and conquer approach. We also study the case of rectilinear regions in three dimensions and show that the minimum cost path under the Manhattan metric is obtained in O(n2log3n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ O(n^2 \\log ^3 n) $$\\end{document} time and O(n2log2n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ O(n^2 \\log ^2 n) $$\\end{document} space.

Minimum Cost Path on Grid Road Network Considering Right Turn Cost

Minimum Cost Path on Grid Road Network Considering Right Turn Cost

Facies conditional simulation based on VAE-GAN model and image quilting algorithm

Characterization of complex reservoir structures by using limited observations is challenging in geosciences because it requires to reproduce geological realism. We propose a novel method to reconstruct complex structures by combining variational autoencoder and generative adversarial networks (VAE-GAN) with conditional image quilting algorithm. It improves the stability of traditional GAN-based simulation method without decreasing the quality of patterns. Firstly, we construct a VAE-GAN model to extract the high-dimensional features of facies patterns and to create abundant new patterns. The VAE-GAN-based learning method has a good ability in feature learning from training patches and accurately reproduce new facies patterns. Finally, these new patterns are spliced together to reconstruct a complex geological structure by employing the conditional image quilting algorithm, in which patterns are pasted to the simulated areas based on the calculated minimum cost path. During this process, conditioning is also considered. Since the pattern is generated by using the deep learning method rather than directly extracted from the training image, the diversity of realizations is enhanced without losing reproducibility. Based on synthetic training image, several examples are described and analyzed in detail, demonstrating the effectiveness and reliability of the present method. In addition, the new method is applied to a real training image. The complex heterogeneous structures are well reproduced by our method, indicating its practicability.

Time-Varying Topology Formation Reconfiguration Control of the Multi-Agent System Based on the Improved Hungarian Algorithm

Distributed time-varying formation technology for multi-agent systems is recently become a research hotspot in formation control field. However, the formation reconfiguration control technology for agents that randomly appeared to fail during maneuvers is rarely studied. In this paper, the topological relations between intelligence are designed by graph theory to simplify the cooperative interaction between multi-agent systems. Moreover, this paper constructs the time-varying configuration of the target formation based on the rigidity graph theory and leader–follower strategy. Drawing on the establishment of the expert experience database in a collaborative process, we innovatively propose the establishment of a graphic library to help the multi-agent system quickly form an affine transformation as soon as it is disabled. Secondly, the improved Hungarian algorithm is adopted to allocate the target point when the first failure occurs. This algorithm incorporates a gradient weighting factor from the auction algorithm to improve the speed of system reconfiguration with minimum path cost. On this basis, a distributed multi-agent control law based on consistency theory is established, and the system’s stability can be guaranteed via Lyapunov functions. Finally, the simulation results demonstrate the feasibility and effectiveness of the proposed formation reconfiguration control algorithm in a collaborative environment.

Automated astronaut traverses with minimum metabolic workload: Accessing permanently shadowed regions near the lunar south pole

The Artemis exploration zone is a topographically complex impact-cratered terrain. Steep undulating slopes pose a challenge for walking extravehicular activities (EVAs) anticipated for the Artemis III and subsequent missions. Using 5 m/pixel Lunar Orbiter Laser Altimeter (LOLA) measurements of the surface, an automated Python pipeline was developed to calculate traverse paths that minimize metabolic workload. The tool combines a Monte Carlo method with a minimum-cost path algorithm that assesses cumulative slope over distances between a lander and stations, as well as between stations. To illustrate the functionality of the tool, optimized paths to permanently shadowed regions (PSRs) are calculated around potential landing sites 001, nearby location 001(6), and 004, all within the Artemis III ‘Connecting Ridge’ candidate landing region. We identified 521 PSRs and computed (1) traverse paths to accessible PSRs within 2 km of the landing sites, and (2) optimized descents from host crater rims into each PSR. Slopes are limited to 15° and previously identified boulders are avoided. Surface temperature, astronaut body illumination, regolith bearing capacity, and astronaut-to-lander direct view are simultaneously evaluated. Travel times are estimated using Apollo 12 and 14 walking EVA data. A total of 20 and 19 PSRs are accessible from sites 001 and 001(6), respectively, four of which maintain slopes <10°. Site 004 provides access to 11 PSRs, albeit with higher EVA workloads. From the crater rims, 94 % of PSRs can be accessed. All round-trip traverses from potential landing sites can be performed in under 2 h with a constant walk. Traverses and descents to PSRs are compiled in an atlas to support Artemis mission planning.

Adaptive Manipulability-Based Path Planning Strategy for Industrial Robot Manipulators

In this article, a novel manipulability-based optimal rapidly exploring random tree (RRT*) path planning strategy is proposed for industrial robot manipulators. When sampling in the search space, two constraints, namely, path length and manipulability measure, are imposed to find a minimal-cost path connecting the start and goal points. By tracking the generated path, a robot manipulator's end-effector can traverse the workspace with a shorter length and, meanwhile, avoid configuration singularities. A constrained closed-loop inverse kinematics technique is utilized to exploit the kinematic redundancy to assign a higher manipulability to an end-effector position. Additionally, the metrics of path length and manipulability measure are used to determine the adaptive step size for the RRT* planner. This helps the space-filling tree to grow efficiently toward unsearched areas and find an optimal path. Simulation analysis and experimental results of a six-degree-of-freedom FANUC-M-20iA industrial robot illustrate the efficiency of the proposed path planning methods.

Identification of Urban Clusters Based on Multisource Data—An Example of Three Major Urban Agglomerations in China

Accurately identifying the boundary of urban clusters is a crucial aspect of studying the development of urban agglomerations. This process is essential for comprehending and optimizing smart and compact urban development. Existing studies often rely on a single category of data, which can result in coarse identification boundaries, insufficient detail accuracy, and slight discrepancies between the coverage and the actual conditions. To accurately identify the extent of urban clusters, this study proposes and compares the results of three methods for identifying dense urban areas of three major agglomerations in China: Beijing–Tianjin–Hebei, the Yangtze River Delta, and the Guangdong–Hong Kong–Macao Greater Bay Area. The study then integrates the results of these methods to obtain a more effective identification approach. The social economic method involved extracting a density threshold based on the fused nuclear density of socio-economic vitality data, including population, GDP, and POI, while the remote sensing method evaluated feature indices based on remote sensing images, including the density index, continuity index, gradient index, and development index. The traffic network method utilizes land transportation networks and travelling speeds to identify the minimum cost path and delineate the boundary by 20–30 min isochronous circles. The results obtained from the three methods were combined, and hotspots were identified using GIS overlay analysis and spatial autocorrelation analysis. This method integrates the multi-layered information from the previous three methods, which more comprehensively reflects the characteristics and morphology of urban clusters. Finally, the accuracy of each identification result is verified and compared. The results reveal that the average overall accuracy (OA) of the three areas delineated by the first three methods are 57.49%, 30.88%, and 33.74%, respectively. Furthermore, the average Kappa coefficients of these areas are 0.4795, 0.2609, and 0.2770, respectively. After performing data fusion, the resulting average overall accuracy (OA) was 85.34%, and the average Kappa coefficient was 0.7394. These findings suggest that the data fusion method can effectively delineate dense urban areas with greater accuracy than the previous three methods. Additionally, this method can accurately reflect the scope of urban clusters by depicting their overall boundary contour and the distribution of internal details in a more scientific manner. The study proposes a feasible method and path for the identification of urban clusters. It can serve as a starting point for formulating spatial planning policies for urban agglomerations, aiding in precise and scientific control of boundary growth. This can promote the rational allocation of resources and optimization of spatial structure by providing a reliable reference for the optimization of urban agglomeration space and the development of regional spatial policies.

Construction and pattern optimization of ecological network in Zhengzhou metropolitan area.

The rapid urbanization process has led to the increasingly prominent problems of ecological environment protection and optimization. The construction of ecological network system, planning to guide ecological values, and efficiently utilizing landscape effects are of great significance for regional regulation of ecological space and promotion of local sustainable development. Taking Zhengzhou metropolitan area as an example, based on land use data at eight time points from 1980 to 2020, using ArcGIS, Guidos Toolbox, Conefor and other tools, we outlined the ecological network with a high structural integrity in the study area. We used future land use simulation to predict future land pattern, morphological spatial pattern analysis to identify landscape elements, minimum cumulative resistance to construct comprehensive resistance surface, gravity model to calculate ecological gravity, hydrologic analysis to create resistance paths, and network structure evaluation, etc. The results showed that, among the nine source sites in the study area, the ecological sources in the Yellow River Basin connected the large-scale centralized source areas in the east and west of the network. The rest sources were located in the northeast, southeast, and southwest of the study area, which were distributed in a semi-circumferential manner around the main urban area of Zhengzhou. There were a total of 163 minimum cost paths and 58 ecological corridors, of which 10, 19 and 29 were primary, secondary and tertiary corridors, respectively, in the form of "three horizontals and three verticals" and "point-axis" along the Yellow River Basin distribution was dominant. A total of 70 ecological nodes were recored in the study area, which were divided into strategic points (10), natural ecological points (27) and artificial environment points (33). Those ecological nodes were distributed in key nodes such as the core of each source area and the intersection of corridors location. The ecological network included all the landscape elements in the study area and connected the main ecological substrates in a horizontal "C" shape. The overall performance was a semi-enclosed network structure of "one horizontal, two verticals and four groups".

A 3/2-Approximation for the Metric Many-Visits Path TSP

In the Many-visits Path TSP, we are given a set of $n$ cities along with their pairwise distances (or costs) $c(uv)$, and moreover each city $v$ comes with an associated positive integer request $r(v)$. The goal is to find a minimum-cost path, starting at city $s$ and ending at city $t$, that visits each city $v$ exactly $r(v)$ times. We present a $3/2$-approximation algorithm for the metric Many-visits Path TSP that runs in time polynomial in $n$ and polylogarithmic in the requests $r(v)$. Our algorithm can be seen as a generalization of the $3/2$-approximation algorithm for Path TSP by Zenklusen [Proceedings of SODA, 2019, pp. 1539--1549], which answered a long-standing open problem by providing an efficient algorithm which matches the approximation guarantee of Christofides' algorithm from 1976 for metric TSP. One of the key components of our approach is a polynomial-time algorithm to compute a connected, degree-bounded multigraph of minimum cost in an undirected graph with edge costs. We tackle this problem by generalizing a fundamental result of Király, Lau, and Singh [Combinatorica, 32 (2012), pp. 705--720] on the Minimum Bounded Degree Matroid Basis problem, and devise such an algorithm for generalized polymatroids, even allowing element multiplicities. Our result directly yields a $3/2$-approximation to the metric Many-visits TSP, as well as a $3/2$-approximation for the problem of scheduling classes of jobs with sequence-dependent setup times on a single machine so as to minimize the makespan.

An optimal trajectory planning for automated on‐ramp merging

AbstractThis paper proposes an optimal trajectory planning model for automated on‐ramp merging. The minimum cost path based on the optimal control theory is selected as the optimal trajectory of the on‐ramp merging vehicle, which could avoid potential collisions and satisfy the kinematic constraints on the vehicle motion. Moreover, an optimal control strategy is presented to solve the trajectory planning problem of the facilitating vehicle. An analytical closed‐form solution is derived by using the Hamiltonian analysis and the path information of the merging vehicle. Particularly, the proposed planning process also considers the lateral movement of the on‐ramp merging, which is more efficient in the application. Owing to the location and time that the on‐ramp vehicle merges into the mainline can be obtained endogenously by its planning process, the model has high adaptation to various on‐ramp environments. Solutions to the above two optimal methods are implemented in a model predictive control framework to cope with possible external disturbances. Several numerical simulations and PreScan‐Simulink Co‐Simulation illustrate the effectiveness of the proposed model. Furthermore, this methodology is compared with a typical CACC strategy to demonstrate its potential to reduce fuel consumption, as well as improve passenger comfort.

Multiobjective Order Promising for Outsourcing Supply Network of IC Design Houses

To decide which orders to be accepted for an IC design house, besides wafers and capacity, several factors also need to be considered, including product flexibility, minimal cost path, order delay cost, and the fairness of order fulfillment rate between customers. This research focuses on a multi-objective order promising problem for the hybrid MTS-MTO outsourcing supply network of an IC design house. The objectives are to maximize total profit, minimize total delay cost of accepted orders, and minimize the discrepancy of order fulfillment rate between customers. The multi-stage and multi-site outsourcing supply network, technical capacity constraints, product flexibility and multi-chip module are considered. This problem is modeled with a multi-objective mixed integer programming model. A heuristic algorithm, called the fairness-based multi-objective order promising algorithm (FMOPA) with four modes is developed to solve the problem. Moreover, experimental design is conducted to evaluate the efficiency of the proposed model with various factors and levels. Analysis of variance (ANOVA) is used to evaluate the factors in accordance to the objectives. The optimal algorithm mode under thirty-two combinations of different environment factors are also evaluated. This can assist decision makers to use the optimal algorithm mode to generate the best favorable result under different environment factors.