Minimum Path Research Articles

MDHO: Mayfly Deer Hunting Optimization Algorithm for Optimal Obstacle Avoidance Based Path Planning Using Mobile Robots

Mobile robot becomes more significant in human life and industry, whereas navigation of robot in the dynamic environment results a challenging problem and it need to be solved in an efficient way. Path planning gained more attention in recent decades and puts its practical usage in different industries. Path planning for the mobile robot is to determine feasible path to reach target location in workspace. A more challenging problem with mobile robot is solving path planning issue by avoiding obstacles in an optimize way. Various methods are designed to perform path planning mechanism, but it faced complexity in finding the solution to reach the target. Hence, an efficient Mayfly Deer Hunting Optimization (MDHO) algorithm is designed in this research to move the mobile robots to reach target location in the environment using multi-objective function. However, multi-objective function is designed by considering the factors, like path length, path smoothness, and the obstacle avoidance. The path that satisfies the objective constraints is selected as optimal path to reach the target of mobile robot. The proposed model attains minimum path length, maximal path smoothness, and maximum fitness as 1159.0 m, 0.913, and 3.5418 by considering fixed obstacles and multiple targets.

Minimal Exposure Paths in Time-Varying Fields: A Semi-Lagrangian Approach

In the context of Wireless Sensor Networks (WSNs), the Minimal Exposure Path (MEP) represents an important metric to evaluate the quality of network services. Most of the current literature is concentrated on stationary sensors, while few works have addressed the existence of moving nodes. Mobile Wireless Sensor Networks (MWSNs) present a great potential for detecting invaders compared to static ones, but dealing with dynamic sensors significantly increases the coverage complexity since the overall exposure of the sensor field depends on time. Therefore, in this letter, we propose an approach to compute Minimal Exposure Paths in time-varying fields based on a control optimization method called semi-Lagrangian (SL) scheme, in such a way that an intruder will be able to penetrate the dynamic field with the lowest exposure. The SL has already been proven to reach the optimal Minimal Exposure Path (MEP) on static WSNs, but concerning dynamic nodes, the proof is much more complicated. Then, we propose a heuristics that provides convergence of the SL algorithm to a result we conjecture to be the optimal one. Results with different time-varying sensor models in obstacle-free and cluttered environments have been presented and discussed.

Reliability assessment of a stochastic-flow distribution network with carbon emission constraint

• Emission is incorporated into reliability analysis of a distribution network • A new performance indicator is proposed to assess a distribution network • An MP based algorithm is developed to compute the new indicator • A real case study of a fruit distribution network is presented This paper proposes a new reliability assessment for a distribution network with carbon emission constraint where a node represents a supplier, a distribution center, or a market, and an arc connecting a pair of nodes represents a carrier. The available capacity of each carrier (e.g., number of vehicles) is stochastic due to unexpected events. In this sense, such a distribution network is considered to be a stochastic-flow distribution network (SFDN). In addition, transportation emissions that have direct hazardous effects on environment and human health are becoming the major concern in the process of commodity distribution. Thus, SFDN reliability with carbon emission constraint, defined as the probability that the network can successfully deliver a specified quantity of goods from the source to the destination with the total transportation emissions no more than a given limitation, is taken as a key performance indicator for distribution activity. Grounded on minimal paths (MPs), an algorithm is proposed to calculate the new indicator. A simple example is provided to illustrate the procedure, and then, a real fruit distribution network is adopted to demonstrate the utility of the proposed algorithm.

Analysis of transition path ensemble in the exactly solvable models via overdamped langevin equation

Transition of a system between two states is an important but difficult problem in natural science. In this article we study the transition problem in the framework of transition path ensemble. Using the overdamped Langevin method, we introduce the path integral formulation of the transition probability and obtain the equation for the minimum action path in the transition path space. For the effective sampling in the transition path ensemble, we derive a conditional overdamped Langevin equation. In two exactly solvable models, the free particle system and the harmonic system, we present the expression of the conditional probability density and the explicit solutions for the conditional Langevin equation and the minimum action path. The analytic results demonstrate the consistence of the conditional Langevin equation with the desired probability distribution in the transition. It is confirmed that the conditional Langevin equation is an effective tool to sample the transition path ensemble, and the stationary action principle actually leads to the most probable path.

Low energy fold paths in multistable origami structures

Origami design concepts are finding pervasive utility in engineering applications due to their ability to map complex shape transformations into a series of folding actions. The interplay between stretching, folding, and facet bending modes in origami structures also generates a complex energy landscape of multistable states to leverage for engineering applications. However, identifying rigid and deformable folding paths in this high-dimensional and non-convex energy landscape remains a challenge. To help address this challenge, we first introduce a global, constraint-based approach to modeling origami that uses a redundant kinematic description of the facets and nodes, and treats the kinematic compatibility between these redundant descriptors as a constraint. This approach allows for complex facet shapes without increasing the dimensionality of the system, as would be necessary in truss-based and other node-based formulations in order to stiffen the facet. Secondly, we adopt the nudged elastic band method, that is widely used in computational chemistry, to identify minimum energy folding paths. This strategy addresses, from a global perspective, the difficulty of piecing together sequences of local folding steps in order to connect two different points in configuration space. We implement this path finding approach on both the kinematic constraint formulation and a truss-based model, and compare their behaviors on a series of folding and multistable origami examples.

Coverage Optimization for Directional Sensor Networks: A Novel Sensor Redeployment Scheme

The ever-growing Internet of Things (IoT) provides a powerful means for complex and changeable environmental monitoring. Directional sensor networks (DSNs), as a typical architecture of IoT, can efficiently facilitate various digital and intelligent IoT applications. In the DSNs, due to the asymmetry in coverage focus and diversity in detection angle of the directional IoT sensors, how to enhance the coverage performance with the limited sensors becomes a new challenge. To this end, we develop a novel sensor redeployment scheme based on the minimum exposure path (MEP) to optimize the coverage performance of the DSNs. Specifically, we first propose a minimum exposure path searching algorithm based on the particle swarm optimization (MEP-PSO) algorithm with the target of obtaining the MEP in the DSNs. With this algorithm, the traditional MEP problem can be analyzed and simplified by conducting the grid discretization and building the weighted undirected graph. Then, an MEP-based coverage optimization (MEP-CO) algorithm is proposed to determine the optimal deployment locations and the dispatch sensors so that the IoT sensors can be dynamically redeployed to achieve the coverage optimization. After that, we derive the formula for the coverage upper bound (CUB) and develop a CUB algorithm to provide a benchmark for evaluating the effectiveness of different coverage optimization algorithms. Simulation results demonstrate that the proposed coverage optimization scheme can significantly promote the minimum exposure value (MEV) and coverage ratio of the monitoring area compared with the existing algorithms.

Weighted distances in the Cairo pattern

The Cairo Pattern is an interesting tiling of the plane. It consists of pentagons which completely cover the plane without overlapping. The Cairo Pattern is the dual of a semi-regular grid. It is assumed that one can walk on the pentagons such that it is possible to step only two neighboring pentagons. Different types of steps have different weights. The distance of two pentagons is the length of the minimal path between them. All distances are based on a linear programming model. The main tool of the analysis is the simplex method of linear programming. The analysis also uses the special properties of the model of minimal path. All minimal paths are given explicitly. Therefore, the complexity of our final result is O(1) inspite of the fact that the general simplex method is thought to be exponential.

Distributed Motion Planning for Multiple Quadrotors in Presence of Wind Gusts

This work demonstrates distributed motion planning for multi-rotor unmanned aerial vehicle in a windy outdoor environment. The motion planning is modeled as a receding horizon mixed integer nonlinear programming (RH-MINLP) problem. Each quadrotor solves an RH-MINLP to generate its time-optimal speed profile along a minimum snap spline path while satisfying constraints on kinematics, dynamics, communication connectivity, and collision avoidance. The presence of wind disturbances causes the motion planner to continuously regenerate new motion plans, thereby significantly increasing the computational time and possibly leading to safety violations. Control Barrier Functions (CBFs) are used for assist in collision avoidance in the face of wind disturbances while alleviating the need to recalculate the motion plans continually. The RH-MINLPs are solved using a novel combination of heuristic and optimal methods, namely Simulated Annealing and interior-point methods, respectively, to handle discrete variables and nonlinearities in real-time feasibly. The framework is validated in simulations featuring up to 50 quadrotors and Hardware-in-the-loop (HWIL) experiments, followed by outdoor field tests featuring up to 6 DJI M100 quadrotors. Results demonstrate (1) fast online motion planning for outdoor communication-centric multi-quadrotor operations and (2) the utility of CBFs in providing effective motion plans.

Two-point resistances of symmetric polyhedral networks

A random walk along the edges of a polyhedron consists of starting at a particular vertex, choosing one of its adjacent neighbors at random, stepping to that neighbor, and then repeating the process until a specified vertex is reached. The average number of steps it takes to get from a given vertex to another is called the hitting time. For polyhedra with some degree of symmetry, there are groups of vertices that have the same hitting time from a given starting vertex. These groups form symmetrically equivalent layers within the polyhedron. This paper explores a number of novel approaches to calculating these layers based on Euclidean distance, minimum length paths, and the number of edges of each face of the polyhedron. After the hitting times have been found, the equivalent resistance between any two vertices of the network is easily calculated. The physical relevance of this problem is discussed, a comparison with other approaches to solving it is made and some open questions are mentioned.

NOMA and UAV Scheduling for Ultra-Reliable and Low-Latency Communications

Ultra-reliable and low-latency communications (uRLLC) has received great attention in the study of wireless communication for it can provide high network performance in terms of reliability and latency. However, the reliability requirements of uRLLC require further investigation due to the inherent openness of the wireless channel. Different from the previous reliable contributions that focused on the retransmission mechanism, in this paper, we consider scenarios with the interference of multiple UAVs. We establish an analytical framework of the packet error rate (PER) for an air-to-ground (A2G) channel. In this framework, the cellular users are allocated to different UAVs according to their minimum path loss with the aim of minimizing the PER. Furthermore, a wireless link scheduling algorithm is proposed to enhance the reliability between the UAV and cellular user. Simulated results show that, under the same power and channel block length level, our proposed non-orthogonal multiple access (NOMA) scheduling scheme has the best performance.

On the status of component failures in a working coherent system when the lifetimes are DNID random variables

In this paper, we investigate the number of failed components in a coherent system with possibly dependent and not necessarily identically distributed component lifetimes. Based on two different partial information about the status of component failures, obtained either with a single inspection or under double monitoring of the system, we compute the probability of the given number of failures in a working coherent system. In the computations, we use the concept of minimal path sets of the system. These results enable us to establish explicit expressions for survival functions of two types of residual lifetimes of a used system. For illustration, we provide numerical examples of coherent systems composed of discretely or continuously distributed component lifetimes.

A Time Impulse Neural Network Framework for Solving the Minimum Path Pair Problems of the Time-Varying Network

The minimum path pair (MPP) query problem is to find the optimal meeting point of two minimum paths for two users in a network, where each user's minimum path has its own departure and destination nodes. However, the MPP query problem on a time-varying network that generally exists in the world remains open. In this study, we investigate the time-varying minimum path pair (TMPP) query problem, where the arcs of the network are time dependent. We first model the TMPP and then propose a time impulse neural network (TINN) to solve the TMPP. In the design of the TINN, the entire network topology is considered as the architecture of the neural network, and each node is viewed as a neuron. The core of an impulse-based neuron consists of six parts: input, impulse receiver, time window selector, neuron storage, impulse sender, and output. Unlike the traditional neural network, the whole neural network does not require a training process but is implemented through an impulse mechanism. The TINN consists of two stages; the first stage is to find the two minimum paths of two users, while the second stage is to calculate the distance between these two minimum paths. The underlying idea of the TINN is to find the minimum path using an impulse mechanism. The minimum path relies on the earliest time impulse stemming from the depart node that arrives at the destination node. With this mechanism, both the minimum path of the network and the distance between two paths can be addressed. Furthermore, theoretical analysis demonstrates the correctness and provides the complexity of the TINN. Experiments of the TINN are carried out based on the well-known New York City Map. A comparative study illustrates the effectiveness of the TINN.

Зависимость уровня искажений выходного сигнала передатчика современных телекоммуникационных сигналов с разделением составляющих от параметров фильтра тракта огибающей

The article investigates the dependence of the envelope elimination and restoration (EER) transmitter out-of-band emissions on the parameters of its envelope path LPF. LPFs of the sixth order with the Cauer structure, having the same degree of clock frequency unwanted products suppression, unilaterally and bilaterally loaded, and optimized LPFs with a smooth transition of the frequency response from the passband to the stopband are considered. It is shown that when the transmitter is operating at a nominal load (broadband antenna), a sharp transition from the passband to the stopband in the envelope path LPF leads to an increase in out-of-band emissions that are separated from the center frequency of the transmitter by the LPF cutoff frequency. The minimum envelope path allowable bandwidth is at least 5 transmitted signal bandwidths when using a Cauer-type LPF with a standard approximation and at least 3.5 bandwidths for an optimized LPF with a smooth transition. For the case of a transmitter operating on a resonant antenna with a limited bandwidth, the dependences of the minimum envelope path filter required bandwidth on the antenna bandwidth and the VSWR value at the edges of the amplified signal band are revealed. It is shown that the use of two-sided loaded filters in the envelope path allows the transmitter to work on antennas with half the bandwidth and reduce the antenna SWR requirements from 1.03 to 1.07. The use of smooth transition filters allows you to reduce the minimum required bandwidth of the LPF by 20% compared to standard filters. The most preferable is the use of a two-sided loaded LPF of the 6th order with a smooth transition, which ensures the operation of the transmitter to the antenna with VSWR = 1.07 at the edges of the transmitted signal band with a minimum LPF bandwidth equal to 5.8 signal bands.

Simple method to extract minimal cut sets of a direct network

System planning, design, and control, network reliability validation, and evaluation are critical. The enumeration of minimal cut sets (MCs) in a network is usually more complicated than the search for minimal path sets (MPs). The purpose of this research is to offer an efficient accurate approach for enumerating directed networks’ MCs. The method is concerned with determining the MCs depending on the set of minimal path nodes.

A short proof of the bijection between minimal feedback arc sets and Hamiltonian paths in tournaments

A short proof of the bijection between minimal feedback arc sets and Hamiltonian paths in tournaments

Approximate solution of the shortest path problem with resource constraints and applications to vehicle routing problems

<abstract><p>Vehicle routing problem (VRP) is a fundamental combinatorial optimization and integer programming problem with several important applications. The VRP is usually solved by using branch-and-bound techniques requiring solving a shortest path problem with resource constraints (SPPRC) and the determination of a lower bound, which can be computed by using column generation. The SPPRC entails finding the minimum cost elementary path in a valuated graph that is subject to constraints on resource consumption. The proposed exact solutions to this hard NP-hard problem require an excessive computation time which increases with the number of resources. In this paper, we propose a new approximate resolution of the SPPRC for acyclic and cyclic graphs. Our method is based on a Lagrangian relaxation of a subset of the constraints and using dominance only on a subset of the resources. This reduces the search space and allows users to efficiently compute solutions used to improve the column generation procedure. Extensive evaluation and comparison to the classical exact method show that the proposed algorithm achieves a good compromise between efficiency and quality of the SPPRC and the VRP solutions. Thus, our method can be used for practical large-scale VRP applications.</p></abstract>

THE PROCEDURE OF SELECTING THE VALUES OF THE WORK CONDITION PARAMETERS OF THE BALL-CRATERING METHOD FOR THE ASSESSMENT OF RESISTANCE TO ABRASIVE WEAR

In the example of the CrN coating deposited by the cathodic arc evaporation (CAE) method on two differently prepared substrates, the procedure for selecting the values of the work condition parameters of the ballcratering method was presented. The procedure was developed thanks to applying an individual experiment design from Taguchi's approach and has not been used to determine the values of the parameters of the operating conditions of the test friction node for tribological tests. The procedure, according to Taguchi, allowed us to determine the values of the parameters for assessing the abrasion resistance of anti-wear coatings, with the use of a much smaller number of tests, compared to the methods used so far and a repetitive wear mechanism. The starting point of the presented procedure was selecting the area of the permissible values of the operating parameters, in the ball-cratering method, in which optimal values were searched for to minimise the relative error in determining the diameters of wear marks craters. After determining the area of limit values, an experiment plan was generated in which the variables were: load, rotational speed, minimum friction path, and maximum friction path. The results of abrasive wear tests performed with the ball-cratering method, in accordance with the developed test procedure for the CrN coating – were deposited on the substrate after heat treatment and the substrate after the nitriding process had been successfully verified.

Unsupervised Reaction Pathways Search for the Oxidation of Hypergolic Ionic Liquids: 1-Ethyl-3-methylimidazolium Cyanoborohydride (EMIM+/CBH–) as a Case Study

Hypergolic ionic liquids have come under increased study for having several desirable properties as a fuel source. One particular ionic liquid, 1-ethyl-3-methylimidazolium/cyanoborohydride (EMIM+/CBH-), and oxidant, nitric acid (HNO3), has been reported to be hypergolic experimentally, but its mechanism is not well-understood at a mechanistic level. In this computational study, the reaction is first probed with ab initio molecular dynamics simulations to confirm that anion-oxidant interactions likely are the first step in the mechanism. Second, the potential energy surface of the anion-oxidant system is studied with an in-depth search over possible isomerizations, and a network of possible intermediates are found. The critical point search is unsupervised and thus has the potential of identifying structures that deviate from chemical intuition. Molecular graphs are employed for analyzing 3000+ intermediates found, and nudged elastic band calculations are employed to identify transition states between them. Finally, the reactivity of the system is discussed through examination of minimal energy paths connecting the reactant to various common products from hypergolic ionic liquid oxidation. Eight products are reported for this system: NO, N2O, NO2, HNO, HONO, HNO2, HCN, and H2O. All reaction paths leading to these exothermic products have overall reaction barriers of 6-7 kcal/mol.

Optimal Path Generation with Obstacle Avoidance and Subfield Connection for an Autonomous Tractor

As autonomous tractors become more common crop harvesting applications, the need to optimize the global servicing path becomes crucial for maximizing efficiency and crop yield. In recent years, several methods of path generation have been researched, but very few have studied their applications on complex field shapes. In this study, a method of creating the optimal servicing path for simple and complex field shapes is proposed. The proposed algorithm creates subfields for a target land, optimizes the track direction for several subfields individually, merges subfields that result in overall increased efficiency, and finds the minimum non-operating paths to travel from subfield to subfield while selecting the respective optimal subfield starting locations. Additionally, it is required that this process must be done within 3 seconds to meet performance requirements. Results from 3 separate field shapes show that the field traversal efficiency can range from 68.0% to 94.4%, and the coverage ratio can range from 98.8% to 99.9% for several different conditions. In comparison with previous studies using the same field shape, the proposed methods demonstrate an increase of 5.5% in field traversal efficiency.

Reliability Calculation Method of Shipborne Vehicles' Sortie Mission for Dynamic Network Structure.

To provide decision support to the commander, it is necessary to calculate shipborne vehicles' sortie mission reliability during the formulation of the layout plan. Therefore, this paper presents the sortie mission network model and reliability calculation method for shipborne vehicles. Firstly, the shipborne vehicle layout and sortie task characteristics are used to establish the sortie mission network model. The shipborne vehicles' sortie mission reliability problem is transformed into a two-terminal network reliability problem. Secondly, the minimal path set method is used to calculate the two-terminal network reliability. An improved tabu search algorithm based on a strategy of breaking up the whole into parts is proposed to search for the minimal path set that matches the length. Finally, the sum of disjoint products is used to process the minimal path set to obtain the shipborne vehicles' sortie mission reliability calculation formula. A numerical analysis of two simplified shipborne vehicles' layouts is given to illustrate the calculation process of the method. This study provides a new evaluation index and an effective quantitative basis for the evaluation system of shipborne vehicles' layout. It also provides theoretical support for the development of decision-making related to the sortie mission of shipborne vehicles.