Sum Of Arrival Times Research Articles

Exact Anytime Multi-Agent Path Finding Using Branch-and-Cut-and-Price and Large Neighborhood Search

Given a set of agents on a grid, the multi-agent path finding problem aims to find a path that moves each agent from its given start location to its target location such that they do not collide and that the sum of arrival times is minimized. LNS2 is a state-of-the-art algorithm for anytime, suboptimal solving. It is an upper-bounding algorithm that repeatedly adjusts an existing solution and, being a local search, is oblivious to optimality. BCP is a state-of-the-art algorithm for exact solving. It is a lower-bounding tree search that attempts to tighten the lower bound until a solution appears. As BCP operates on the lower bound, the first solution it finds is optimal or nearly optimal, and therefore has poor anytime behavior. This paper proposes to tightly couple LNS2 and BCP to achieve better anytime, suboptimal solving while retaining the optimality guarantee of BCP. Experiments indicate that the combination achieves better anytime behavior than BCP in general and better suboptimal performance than LNS2 on congested maps.

Robust Multistatic Target Localization in the Presence of NLOS Errors and Outliers

In this letter, we address the problem of multistatic target localization using time-sum-of-arrival (TSOA) measurements in the presence of errors due to non-line-of-sight (NLOS) propagation and outliers. To handle the effect of bias errors induced due to NLOS/outliers, an additional balancing parameter is incorporated in the data model. Then, a non-linear weighted least squares (NLWLS) based design objective is formulated for the joint estimation of source position and the balancing parameter. We then propose a simple iterative algorithm, which enjoys closed-form updates for the source position and the balancing parameter, based on the majorization-minimization (MM) technique to arrive at a minimizer of the NLWLS objective. Various numerical simulations are presented in the letter to demonstrate the accuracy of the proposed algorithm when compared to other existing algorithms in the literature.

Data-Selective Least Squares Methods for Elliptic Localization With NLOS Mitigation

In this letter, we consider the problem of 2-D elliptic localization, where multiple spatially separated sensors, including the transmitters and receivers, are exploited to locate the signal reflecting/relaying target in the mixed line-of-sight/nonline-of-sight (NLOS) environments. We begin by revisiting a plain closed-form linear least squares (LS) solution. As it is vulnerable to the existence of erroneous time-sum-of-arrival (TSOA) measurements under the NLOS conditions, we then devise two new data-selective LS methods, by which the outliers can be identified and mitigated and a higher level of resistance to the NLOS bias errors can be provided. To conduct data selection, the first algorithm combines the use of the traditional linear LS estimator and an additional cost function, whereas the second relies on the parameterization of the TSOA-defined ellipses and follows a nonlinear LS estimation criterion. Based on the simulations, we demonstrate the effectiveness of the proposed methods in NLOS error mitigation at acceptable computational costs.

A three-stage supply chain scheduling problem based on the nursing assistants’ daily work in a hospital

In a hospital, the nursing assistants in wards are always responsible for delivering patients to do some medical examinations, and the nursing assistants in the medical departments need take these patients back to the corresponding wards after examinations. We transform this actual problem about nursing assistants’ daily work into a three-stage supply chain scheduling problem if patients are regarded as jobs, the ward as the customer, the nursing assistants as vehicles and the medical department as the processing machine in the factory. The capacity of each vehicle is limited because the nursing assistant only can deliver several patients once. And the transportation schedule back and forth between the customer and the factory are the same in view of the actual arrangement. In order to reduce the average consumption time of patients, the objective is to minimize the total flowtime, that is, the sum of arrival time of every completed job back to the customer. We show that the problem is NP-hard in the strong sense, and provide an approximation algorithm with the performance ratio of 2. Moreover, we study some polynomially solvable cases of the problem.

A hybrid large-neighborhood search algorithm for the cumulative capacitated vehicle routing problem with time-window constraints

This paper introduces a special vehicle routing problem, i.e. the cumulative capacitated vehicle routing problem with time-window constraints (Cum-CVRPTW). The problem can be defined as designing least-cost delivery routes from a depot to a set of geographically-scattered customers, subject to the constraint that each customer has to be served within a time window; accordingly, the objective costs are computed as the sum of arrival times at all the customers. The Cum-CVRPTW finds practical utility in many situations, e.g. the provision of humanitarian aids in the context of natural disasters. The Cum-CVRPTW can be viewed as a combination of two NP-hard problems, i.e. the vehicle routing problem with time windows and the cumulative vehicle routing problem. To effectively address this problem, an effective algorithm is designed, which is based on the frameworks of Large Neighborhood Search Algorithm and hybridizes with Genetic Algorithm. The proposed algorithm adopts a constraint-relaxation scheme to extend the search space, enabling the iterative exploration of both the feasible and infeasible neighborhood solutions of an incumbent solution. Furthermore, some speed-up techniques are designed to reduce the computational complexity. To elucidate its effectiveness, the proposed algorithm is examined on the benchmark instances from the literature. The resultant numerical findings show that the algorithm is able to improve and obtain some best-known solutions found by existing state-of-the-art methods.

Positioning performance analysis of the time sum of arrival algorithm with error features

The theoretical positioning accuracy of multilateration (MLAT) with the time difference of arrival (TDOA) algorithm is very high. However, there are some problems in practical applications. Here we analyze the location performance of the time sum of arrival (TSOA) algorithm from the root mean square error (RMSE) and geometric dilution of precision (GDOP) in additive white Gaussian noise (AWGN) environment. The TSOA localization model is constructed. Using it, the distribution of location ambiguity region is presented with 4-base stations. And then, the location performance analysis is started from the 4-base stations with calculating the RMSE and GDOP variation. Subsequently, when the location parameters are changed in number of base stations, base station layout and so on, the performance changing patterns of the TSOA location algorithm are shown. So, the TSOA location characteristics and performance are revealed. From the RMSE and GDOP state changing trend, the anti-noise performance and robustness of the TSOA localization algorithm are proved. The TSOA anti-noise performance will be used for reducing the blind-zone and the false location rate of MLAT systems.

Mathematical formulations and exact algorithm for the multitrip cumulative capacitated single-vehicle routing problem

This paper addresses the multitrip Cumulative Capacitated Single-Vehicle Routing Problem (mt-CCSVRP). In this problem inspired by disaster logistics, a single vehicle can perform successive trips to serve a set of affected sites and minimize an emergency criterion, the sum of arrival times. Two mixed integer linear programs, a flow-based model and a set partitioning model, are proposed for small instances with 20 sites. An exact algorithm for larger cases transforms the mt-CCSVRP into a resource-constrained shortest path problem where each node corresponds to one trip and the sites to visit become resources. The resulting problem can be solved via an adaptation of Bellman–Ford algorithm to a directed acyclic graph with resource constraints and a cumulative objective function. Seven dominance rules, two upper bounds and five lower bounds speed up the procedure. Computational results on instances derived from classical benchmark problems for the capacitated VRP indicate that the exact algorithm outperforms a commercial MIP solver on small instances and can solve cases with 40 sites to optimality.

Supply Chain Scheduling on a Single Machine with Availability Constraint

In the actual industrial engineering, the machine may be checked to ensure that they can work efficiently. Thus, the machine has an unavailable interval so that the job could be interrupted. When the machine becomes available again, the job can be resumed processing. When the job is completed, it can be delivered in batches to one customer by vehicles with capacity constraint. Our goal is to minimize the sum of arrival time of batches and the total delivery cost. We develop an optimal polynomial time algorithm and give an instance to verify the algorithm.

Mobile Positioning and Tracking Based on TOA/TSOA/TDOA/AOA with NLOS-Reduced Distance Measurements

In this paper, we address the issue of mobile positioning and tracking after measurements have been made on the distances and possibly directions between an MS (mobile station) and its nearby base stations (BS's). The measurements can come from the time of arrival (TOA), the time sum of arrival (TSOA), the time difference of arrival (TDOA), and the angle of arrival (AOA). They are in general corrupted with measurement noise and NLOS (non-line-of-sight) error. The NLOS error is the dominant factor that degrades the accuracy of mobile positioning. Assuming specific statistic models for the NLOS error, however, we propose a scheme that significantly reduces its effect. Regardless of which of the first three measurement types (i.e. TOA, TSOA, or TDOA) is used, the proposed scheme computes the MS location in a mathematically unified way. We also propose a method to identify the TOA measurements that are not or only slightly corrupted with NLOS errors. We call them nearly NLOS-error-free TOA measurements. From the signals associated with TOA measurements, AOA information can be obtained and used to aid the MS positioning. Finally, by combining the proposed MS positioning method with Kalman filtering, we propose a scheme to track the movement of the MS.