Minimum Path Length Research Articles

A Multi-Objective Coverage Path Planning Algorithm for UAVs to Cover Spatially Distributed Regions in Urban Environments

This paper presents a multi-objective coverage flight path planning algorithm that finds minimum length, collision-free, and flyable paths for unmanned aerial vehicles (UAV) in three-dimensional (3D) urban environments inhabiting multiple obstacles for covering spatially distributed regions. In many practical applications, UAVs are often required to fully cover multiple spatially distributed regions located in the 3D urban environments while avoiding obstacles. This problem is relatively complex since it requires the optimization of both inter (e.g., traveling from one region/city to another) and intra-regional (e.g., within a region/city) paths. To solve this complex problem, we find the traversal order of each area of interest (AOI) in the form of a coarse tour (i.e., graph) with the help of an ant colony optimization (ACO) algorithm by formulating it as a traveling salesman problem (TSP) from the center of each AOI, which is subsequently optimized. The intra-regional path finding problem is solved with the integration of fitting sensors’ footprints sweeps (SFS) and sparse waypoint graphs (SWG) in the AOI. To find a path that covers all accessible points of an AOI, we fit fewer, longest, and smooth SFSs in such a way that most parts of an AOI can be covered with fewer sweeps. Furthermore, the low-cost traversal order of each SFS is computed, and SWG is constructed by connecting the SFSs while respecting the global and local constraints. It finds a global solution (i.e., inter + intra-regional path) without sacrificing the guarantees on computing time, number of turning maneuvers, perfect coverage, path overlapping, and path length. The results obtained from various representative scenarios show that proposed algorithm is able to compute low-cost coverage paths for UAV navigation in urban environments.

Better tired than lost: Turtle ant trail networks favor coherence over short edges.

Creating a routing backbone is a fundamental problem in both biology and engineering. The routing backbone of the trail networks of arboreal turtle ants (Cephalotes goniodontus) connects many nests and food sources using trail pheromone deposited by ants as they walk. Unlike species that forage on the ground, the trail networks of arboreal ants are constrained by the vegetation. We examined what objectives the trail networks meet by comparing the observed ant trail networks with networks of random, hypothetical trail networks in the same surrounding vegetation and with trails optimized for four objectives: minimizing path length, minimizing average edge length, minimizing number of nodes, and minimizing opportunities to get lost. The ants’ trails minimized path length by minimizing the number of nodes traversed rather than choosing short edges. In addition, the ants’ trails reduced the opportunity for ants to get lost at each node, favoring nodes with 3D configurations most likely to be reinforced by pheromone. Thus, rather than finding the shortest edges, turtle ant trail networks take advantage of natural variation in the environment to favor coherence, keeping the ants together on the trails.

Dual-Objective Collision-Free Path Optimization of Arc Welding Robot

In order to solve the dual-objective path optimization problem of arc welding robot, a complete and novel methodology is proposed, including modeling, collision-free path search and global path optimization. First of all, the grid method is utilized to accurately model the welding workpieces and surrounding environment. Afterwards, an adaptive extension bidirectional RRT* algorithm (AB-RRT*) is used to search for collision-free paths between any two weld seams. Finally, aiming to minimize path length and energy consumption, the global path is optimized through the improved discrete NSGA-III algorithm (IDNSGA-III). Simulation results show that the AB-RRT* algorithm can search for optimal or sub-optimal solutions with higher efficiency. The IDNSGA-III algorithm can properly maintain the trade-off between convergence and distribution. Furthermore, it can obtain satisfactory solutions in a shorter time and provide effective guidance and help for engineers to plan the actual path.

Tonal harmony and the topology of dynamical score networks

I introduce the concept of dynamical score networks for the representation and analysis of tonal compositions: a score is interpreted as a dynamical network where every chord is a node and each progression links successive chords. This network can be viewed as a time series of a non-stationary signal, and as such, it can be partitioned for the automatic identification of tonal regions using time series analysis and change point detection without relying on comparisons with pre-determined reference sets or extensive corpora. I demonstrate that the essential features of tonal harmony, centricity, referentiality, directedness and hierarchy, emerge naturally from the network topology and its scale-free properties. Finally, solving for the minimal length path through a route optimization algorithm on these graphs provides an abstraction of harmonic sequences that can be generalized for the conception of generative models of tonal compositional design.

Optimal Design of Ship Branch Pipe Route by a Cooperative Co-Evolutionary Improved Particle Swarm Genetic Algorithm

Abstract This paper proposes a cooperative co-evolutionary improved particle swarm genetic (CCIPSG) algorithm for ship branch pipe route design (SBPRD) based on the strategy of first decomposition and then reconstruction. SBPRD is a common type of ship pipe route design connecting one start point and several end points with various performance constraints in 3-D space. The traditional optimization method of SBPRD needs to select the laying sequence of branch pipelines, determine the branch points, and finally conduct the pipeline layout, which is full of uncertainty. The CCIPSG algorithm proposed in this paper aims to avoid the uncertainty of laying sequence and branch points by using the strategy of decomposition before reconstruction. The branch pipe route is deemed as a system; through the process of decomposing, the branch pipe route is decomposed as several single pipe routes with a common start point and different end points. After obtaining the optimal solutions of each single pipe route by using the improved particle swarm genetic algorithm, the co-evolutionary mechanism and overlapped potential energy value method are used to reconstruct the branch pipeline with the minimum total path length and elbows. Compared with the conventional method, the CCIPSG algorithm could not only automatically determinate the laying sequence and branch points but also improve the convergence speed and the quality of the solution. Finally, the simulation result demonstrates the feasibility and efficiency of the proposed method.

Recursive Constraint Manifold Subsearch for Multirobot Path Planning with Cooperative Tasks

The Cooperative Path Planning (CPP) problem seeks to determine a path for a group of robots which form temporary teams to perform tasks. The multi-scale effects of simultaneously coordinating many robots distributed across the workspace while also tightly coordinating the members of teams increases the difficulty of planning. Previous research produced the Constraint Manifold Subsearch (CMS) algorithm that can find minimal length paths to the CPP problem. However, CMS as currently formulated cannot handle more general cost functions, such as minimizing energy expenditure, and cannot handle task schedules that require multiple input teams to merge to form a set of multiple output teams. Furthermore, as CMS must couple planning for all interacting teams, it does not scale well to very large environments. In this paper, we rederive the CMS algorithm using a task graph to reason about inter-team dependencies, allowing the use of more general cost functions and task schedules. We then introduce the recursive CMS (rCMS) algorithm that exploits the reformulation to split the CPP into independent subproblems, significantly reducing computational complexity. Simulation studies show that rCMS can solve substantially larger problems than CMS.

Word Sense Disambiguation Method Based on Graph Model and Word Vector

As a basic research of natural language processing, word sense disambiguation (WSD) has a very important influence on machine translation, classification tasks, retrieval tasks, etc. In order to solve the problem that existing disambiguation methods rely too much on knowledge base, a disambiguation method combining graph model and word vector is proposed in this paper. Firstly, in this method, the text data are preprocessed by removing punctuation marks and segmenting words. Secondly, the dependency relation is extracted by using the tool of PYLTP for dependency parsing, the words of dependency parent node are matched and the undirected graph is built, and the context knowledge of ambiguous words is selected according to the minimum path length set by the graph model. Finally, Word2Vec model is used to train Wikipedia corpus to obtain word vectors containing ambiguous words and contextual knowledge, and calculate the cross similarity of the word vector, the high mean similarity is regarded as the correct meaning of the ambiguous word. The effectiveness of the proposed method is verified by comparative experiments on the SEVAL-2007 Task# 5 dataset.

Multi-Target Search in Euclidean Space with Ray Shooting

The shortest path problem (SPP) asks us to find a minimum length path between two points, usually on a graph. In a Euclidean environment the points are in a 2D plane and here the path must avoid a set of polygonal obstacles. Solution methods for this Euclidean SPP (ESPP) typically convert the continuous 2D map into a discretised representation, like a graph or navigation mesh. RayScan is a recent and fast ESPP algorithm which avoids the preprocessing step by using a combination of "ray shooting" and polygon scanning. In this paper we improve the performance of RayScan using spatial reasoning and ray caching techniques. We also extend the algorithm, from single-target search to a multi-target setting. Comparative game map experiments show a substantial speedup.

Evaluation of Transmission Properties of Networks Described with Reference Graphs Using Unevenness Coefficients

This paper discusses an evaluation method of transmission properties of networks described with regular graphs (Reference Graphs) using unevenness coefficients. The first part of the paper offers generic information about describing network topology via graphs. The terms ‘chord graph’ and ‘Reference Graph’, which is a special form of a regular graph, are defined. The operating principle of a basic tool used for testing the network’s transmission properties is discussed. The next part consists of a description of the searching procedure of the shortest paths connecting any two nodes of a graph and the method determining the number of uses of individual graph edges. The analysis shows that using particular edges of a graph depends on two factors: their total number in minimum length paths and their total number in parallel paths connecting the graph nodes. The latter makes it possible to define an unevenness coefficient. The calculated values of the unevenness coefficients can be used to evaluate the transmission properties of networks and to control the distribution of transmission resources.

Smoothing of digital elevation models and the alteration of overland flow path length distributions

AbstractDEM smoothing is a common pre‐processing technique used to remove undesirable roughness from a DEM. However, it is hypothesized that smoothing straightens and reduces the length of overland flow paths, which is an important factor controlling modelled time‐to‐peak flow. Currently, there is a lack of research comparing how different smoothing techniques alter the distribution of overland flow path length. Four low‐pass filtering techniques were applied to three fine‐resolution LiDAR DEMs of varying relief: the mean filter, the median filter, the Gaussian filter, and the feature‐preserving DEM smoothing (FPDEMS) filter, each with different degrees of smoothing. Downslope‐distance‐to‐stream distributions were then derived using D8 and D∞ flow directions and statistically compared to distributions derived from the unsmoothed DEM for each study site. The results indicate that the alteration of flow path length distributions as a result of smoothing is complex. Mean flow path lengths may decrease or increase in response to smoothing, depending on landscape relief and the derivation of flow directions, and generalized flow paths may become longer. The largest increase in mean flow path lengths was 19.2 m using the 21 × 21 median filter and D8 flow directions in the high‐relief study site, relative to an unsmoothed mean length of 138.6 m in this site. The largest decrease in mean flow path length was 48.9 m using the 21 × 21 mean filter and D∞ flow directions in the low‐relief study site, relative to an unsmoothed mean length of 290.9 m in this site. Furthermore, minimal flow path length alterations were achieved with the Gaussian filter when gentle smoothing is required, and with the FPDEMS filter when moderate to aggressive smoothing is required. These results suggest that an appropriate smoothing method should be chosen based on the relief of the landscape and the degree of smoothing required.

The Method of Determining the Optimal Transmission Resources Distribution of ICT Networks Modelled by Graphs

Abstract The paper discusses the method of improvement of transmission properties of ICT networks by setting the correct distribution of transmission resources in order that it is possible to increase the resulting global probability of supporting the calls generated in the nodes included in the network. The method uses some parts of the graph theory. A minimum length path searching algorithm was used which made it possible to calculate the volume of movement transferred by individual edges of the graph describing the network. The coefficient of the distribution of transmission resources was determined and used to calculate the value of the resources in reference to a particular link, both in the case of equal and diverse movement generated in individual network nodes. A piece of software was developed which uses the results of applying the above-mentioned algorithm to prepare the files describing the analyzed structures in order to carry out simulation tests. The views and analyses are illustrated by examples, and the resulting effects of the influence of the introduction of the method of dividing network resources into transmission properties of a network modelled by graphs are shown in the charts included.

UAVs Path Planning under a Bi-Objective Optimization Framework for Smart Cities

Unmanned aerial vehicles (UAVs) have been used extensively for search and rescue operations, surveillance, disaster monitoring, attacking terrorists, etc. due to their growing advantages of low-cost, high maneuverability, and easy deployability. This study proposes a mixed-integer programming model under a multi-objective optimization framework to design trajectories that enable a set of UAVs to execute surveillance tasks. The first objective maximizes the cumulative probability of target detection to aim for mission planning success. The second objective ensures minimization of cumulative path length to provide a higher resource utilization goal. A two-step variable neighborhood search (VNS) algorithm is offered, which addresses the combinatorial optimization issue for determining the near-optimal sequence for cell visiting to reach the target. Numerical experiments and simulation results are evaluated in numerous benchmark instances. Results demonstrate that the proposed approach can favorably support practical deployability purposes.

Compressive strength, dynamic, and static modulus of cement-lime laying mortars obtained from samples of various geometries

Correlations between compressive strength and modulus of elasticity resulted from cement-based materials of different geometries can help researchers to compare experimental data of studies that applied procedures described by different characterization standards. Due to the absence of systematic studies about the correlation between compressive strength, dynamic, and static modulus of cement-lime masonry mortars, this experimental program was carried out to determine empirical relationships between these mechanical properties, based on tests of 108 samples of shapes and sizes used in quality control of structural masonry: (4 × 4 × 16) cm prisms, 10 cm cubes, (5 × 10) cm cylinders, and (10 × 20) cm cylinders. Different cement-lime masonry mortar compositions with 28-days compressive strength between 3 and 21 MPa were evaluated. The 45 new empirical models developed in this work define the relationships between mechanical properties resulted from the various sample types. Comparisons with correlations reported in previous literature for different mortars types were also made. The compressive strength of cement-lime masonry mortars is directly related to the mutual influence of restraining effects of loading platens and the volume of the mortar specimen, since larger size specimens were more likely to contain portions with lower strength. Size and shape of samples significantly affected the dynamic modulus of cement-lime masonry mortars. Differently from concrete, the minimum wave path length of 10 cm was not enough to disregard size and shape effects on the ultrasonic pulse velocity measured in mortars. Static modulus results of small and large cylinders were different due to the higher concentration of cement paste close to the lateral surface of the reduced specimens. The results provided important information for characterization and technological control of cement-lime masonry mortars.

Resilient Control Plane Design for Virtual Software Defined Networks

Control plane survivability in virtual software-defined networks (vSDN) – where multiple tenants share the same physical infrastructure – is even more critical than in normal SDN networks. A reliable communication channel from the switches through the network hypervisor to the virtual controller is inevitable in order to avoid state inconsistencies, tenant isolation and security issues on the virtual switches. Although reliable controller placement and control plane design was thoroughly investigated in SDNs, there was a lack of attention for resilient hypervisor placement and control path design for vSDNs. Therefore, in this paper we make a two-fold contribution towards a survivable vSDN control plane. First, we propose an approximation algorithm for (hypervisor) placement which – in contrast with traditional approaches which minimize the average latency to the hypervisors as an objective function – focuses on finding the appropriate number of hypervisor instances to satisfy the control path length constraints declared in the service level agreements, leaving enough options open for self-driving network designs and intelligent algorithms. Second, we propose a general dynamic program that calculates minimum length paths traversing specific type of nodes in a given order, and apply it to find control paths from the virtual controller of the slice to the virtual switches traversing the corresponding hypervisor location. We conduct thorough simulations on real-world topologies to demonstrate the effectiveness of our approaches in no failure and single link failure scenarios.

Medians are Below Joins in Semimodular Lattices of Breadth 2

Let L be a lattice of finite length and let d denote the minimum path length metric on the covering graph of L. For any xi =(x_{1},dots ,x_{k})in L^{k}, an element y belonging to L is called a median of ξ if the sum d(y,x1) + ⋯ + d(y,xk) is minimal. The lattice L satisfies the c1-median property if, for any xi =(x_{1},dots ,x_{k})in L^{k} and for any median y of ξ, yleq x_{1}vee dots vee x_{k}. Our main theorem asserts that if L is an upper semimodular lattice of finite length and the breadth of L is less than or equal to 2, then L satisfies the c1-median property. Also, we give a construction that yields semimodular lattices, and we use a particular case of this construction to prove that our theorem is sharp in the sense that 2 cannot be replaced by 3.

Computational Design of Compositionally Graded Alloys for Property Monotonicity

Abstract Functionally graded materials (FGMs) exhibit spatial gradients in properties that can be exploited to satisfy multiple conflicting performance objectives in the same part. Compositionally graded alloys are a subclass of FGMs that have received increased attention with the development of metal additive manufacturing. However, the formation of secondary phases can often lead to cracks or deleterious properties in these materials. In prior work, a computational methodology was presented that can design compositional gradients to avoid these phases at any temperature without the need to visualize phase diagrams (Kirk et al., 2018, “Computational Design of Gradient Paths in Additively Manufactured Functionally Graded Materials,” ASME J. Mech. Des., 140(11), p. 111410). The methodology optimizes gradient paths through composition space for a specified cost function, but prior work only considered minimizing path length or maximizing the distance from undesirable phases. In this work, a new cost function is presented to produce compositional paths with optimal property gradients. Specifically, monotonicity is presented as the optimal quality of a pathwise property gradient because monotonic property gradients can be transformed to nearly any form on the part by controlling deposition rate. The proposed cost function uses a metric for non-monotonicity to find the shortest path with monotonic properties and is shown to be compatible with optimal path planners. A synthetic case study examines the effect of a cost function parameter on the trade-off between length and monotonicity. The cost function is also demonstrated in the Fe-Co-Cr system to find a compositional path with monotonic gradients in coefficient of thermal expansion (CTE). The deposition of the path on a hypothetical part is then planned subject to a maximum deposition rate and CTE gradient. Future work is proposed to extend the framework to optimize multiple properties at once and to incorporate multi-material topology optimization (MMTO) techniques into a complete design methodology for functionally graded metal parts.

Solving routing and spectrum allocation problems in flexgrid optical networks using pre-computing strategies

Flexible optical network architectures are considered a very promising solution where spectrum resources are allocated within flexible frequency grids. This paper presents a minimum spectrum utilization (SU) and average path length (APL) approach to solve the (off-line) routing and spectrum allocation problem (RSA) based on combining a simple ordering pre-computation strategy, namely most subcarriers first (MSF) with three nature-inspired algorithms. These algorithms are ant colony optimization, differential evolution based relative position indexing (DE-RPI), and differential evolution general combinatorial (DE-GC). We begin by showing that MSF is the most effective ordering pre-computation strategy when compared to other well-known typical heuristics in the literature, such as first-fit, and longest path first. Then, we apply MSF in combination with the three nature-inspired algorithms to simultaneously optimize the SU and APL. The usefulness of MSF ordering pre-computation strategy is presented via a comparison of results obtained when using and not using MSF under the same scenarios. The algorithms are evaluated in benchmark optical networks, such as the NSFNet, the European optical network, and the 40-node USA network. We show that DE-RPI with MSF ordering pre-computation is the best option to solve the RSA problem, obtaining an average improvement percentage in the range of 0.9772–4.4086% on the SU and from $$-0.1668$$ to 0.8511% on the APL when compared to other meta-heuristics, either with or without the MSF ordering policy.

Toward monochromated sub-nanometer UEM and femtosecond UED

A preliminary design of a mega-electron-volt (MeV) monochromator with 10−5 energy spread for ultrafast electron diffraction (UED) and ultrafast electron microscopy (UEM) is presented. Such a narrow energy spread is advantageous in both the single shot mode, where the momentum resolution in diffraction is improved, and the accumulation mode, where shot-to-shot energy jitter is reduced. In the single-shot mode, we numerically optimized the monochromator efficiency up to 13% achieving 1.3 million electrons per pulse. In the accumulation mode, to mitigate the efficiency degradation caused by the shot-to-shot energy jitter, an optimized gun phase yields only a mild reduction of the single-shot efficiency, therefore the number of accumulated electrons nearly proportional to the repetition rate. Inspired by the recent work of Qi et al. (Phys Rev Lett 124:134803, 2020), a novel concept of applying reverse bending magnets to adjust the energy-dependent path length difference has been successfully realized in designing a MeV monochromator to achieve the minimum energy-dependent path length difference between cathode and sample. Thanks to the achromat design, the pulse length of the electron bunches and the energy-dependent timing jitter can be greatly reduced to the 10 fs level. The introduction of such a monochromator provides a major step forward, towards constructing a UEM with sub-nm resolution and a UED with ten-femtosecond temporal resolution. The one-to-one mapping between the electron beam parameter and the diffraction peak broadening enables a real-time nondestructive diagnosis of the beam energy spread and divergence. The tunable electric–magnetic monochromator allows the scanning of the electron beam energy with a 10−5 precision, enabling online energy matching for the UEM, on-momentum flux maximizing for the UED and real-time energy measuring for energy-loss spectroscopy. A combination of the monochromator and a downstream chicane enables “two-color” double pulses with femtosecond duration and the tunable delay in the range of 10 to 160 fs, which can potentially provide an unprecedented femtosecond time resolution for time resolved UED.

A descent method for the Dubins traveling salesman problem with neighborhoods

In this study, we focus mainly on the problem of finding the minimum-length path through a set of circular regions by a fixed-wing unmanned aerial vehicle. Such a problem is referred to as the Dubins traveling salesman problem with neighborhoods (DTSPN). Algorithms developed in the literature for solving DTSPN either are computationally demanding or generate low-quality solutions. To achieve a better trade-off between solution quality and computational cost, an efficient gradient-free descent method is designed. The core idea of the descent method is to decompose DTSPN into a series of subproblems, each of which consists of finding the minimum-length path of a Dubins vehicle from a configuration to another configuration via an intermediate circular region. By analyzing the geometric properties of the subproblems, we use a bisection method to solve the subproblems. As a result, the descent method can efficiently address DTSPN by successively solving a series of subproblems. Finally, several numerical experiments are carried out to demonstrate the descent method in comparison with several existing algorithms.

HPDST: Holding pathlength domain scheduled traffic strategy for multi-domain optical networks

In this paper, we proposed a resources allocation strategy for Routing and Wavelength Assignment (RWA) problem in Multi-Domain Optical Networks (MDONs). In the proposed Holding Pathlength Domain Scheduled Traffic (HPDST) strategy, the selection of candidate route is based on the three network parameters: holding time of request, pathlength of the route, and the number of domains across the route. On the basis of these parameters, order of the arrived connection requests is decided. The HPDST strategy is compared with two existing strategies: Minimum Holding Time (MinHoldTime) and Minimum Path Length (MinPathLen). In MinHoldTime scheduling strategy, connections with lowest holding time is given priority. Whereas, shortest route connections are considered first, in MinPathLen strategy. The performance of the proposed HPDST strategy is evaluated with three different network parameters. These are blocking probability, network capacity utilization, and resources utilization ratio. Simulation is performed under three different ratios of the intra and inter-domain scheduled traffic requests, as well as for the consideration of all inter-domain requests. Simulation of the proposed HPDST strategy shows better results as compared to the existing strategies under the investigated network parameters.