Enhancing Critical Path Problem in Neutrosophic Environment Using Python

In the real world,one of the most common problems in project management is the unpredictability of resources and timelines.An efficient way to resolve uncertainty problems and overcome such obstacles is through an extended fuzzy approach,often known as neutrosophic logic.Our rigorous proposed model has led to the creation of an advanced technique for computing the triangular single-valued neutrosophic number.This innovative approach evaluates the inherent uncertainty in project durations of the planning phase,which enhances the potential significance of the decision-making process in the project.Our proposed method,for the first time in the neutrosophic set literature,not only solves existing problems but also introduces a new set of problems not yet explored in previous research.A comparative study using Python programming was conducted to examine the effectiveness of responsive and adaptive planning,as well as their differences from other existing models such as the classical critical path problem and the fuzzy critical path problem.The study highlights the use of neutrosophic logic in handling complex projects by illustrating an innovative dynamic programming framework that is robust and flexible,according to the derived results,and sets the stage for future discussions on its scalability and application across different industries.

Optimal search path planning of UUV in battlefeld ambush scene

Aiming at the practical application of Unmanned Underwater Vehicle(UUV)in underwater combat,this paper proposes a battlefield ambush scene with UUV considering ocean current.Firstly,by establishing these mathematical models of ocean current environment,target movement,and sonar detection,the probability calculation methods of single UUV searching target and multiple UUV cooperatively searching target are given respectively.Then,based on the Hybrid Quantum-behaved Particle Swarm Optimization(HQPSO)algorithm,the path with the highest target search probability is found.Finally,through simulation calculations,the influence of different UUV parameters and target parameters on the target search probability is analyzed,and the minimum number of UUVs that need to be deployed to complete the ambush task is demonstrated,and the optimal search path scheme is obtained.The method proposed in this paper provides a theoretical basis for the practical application of UUV in the future combat.

An Improved Bounded Conflict-Based Search for Multi-AGV Pathfinding in Automated Container Terminals

As the number of automated guided vehicles(AGVs)within automated container terminals(ACT)continues to rise,conflicts have becomemore frequent.Addressing point and edge conflicts ofAGVs,amulti-AGVconflict-free path planning model has been formulated to minimize the total path length of AGVs between shore bridges and yards.For larger terminalmaps and complex environments,the grid method is employed to model AGVs’road networks.An improved bounded conflict-based search(IBCBS)algorithmtailored to ACT is proposed,leveraging the binary tree principle to resolve conflicts and employing focal search to expand the search range.Comparative experiments involving 60 AGVs indicate a reduction in computing time by 37.397%to 64.06%while maintaining the over cost within 1.019%.Numerical experiments validate the proposed algorithm’s efficacy in enhancing efficiency and ensuring solution quality.

Impact of Sky Conditions on Net Ecosystem Productivity over a “Floating Blanket” Wetland in Southwest China

Based on eddy covariance(EC) measurements during 2016–20, the effects of sky conditions on the net ecosystem productivity(NEP) over a subtropical “floating blanket ” wetland were investigated. Sky conditions were divided into overcast, cloudy, and sunny conditions. On the half-hourly timescale, the daytime NEP responded more rapidly to the changes in the total photosynthetic active radiation(PARt) under overcast and cloudy skies than that under sunny skies. The increase in the apparent quantum yield under overcast and cloudy conditions was the greatest in spring and the least in summer. Additionally, lower atmospheric vapor pressure deficit(VPD) and moderate air temperature were more conducive to enhancing the apparent quantum yield under cloudy skies. On the daily timescale, NEP and the gross primary production(GPP) were higher under cloudy or sunny conditions than those under overcast conditions across seasons. The daily NEP and GPP during the wet season peaked under cloudy skies. The daily ecosystem light use efficiency(LUE) and water use efficiency(WUE) during the wet season also changed with sky conditions and reached their maximum under overcast and cloudy skies, respectively. The diffuse photosynthetic active radiation(PAR_d) and air temperature were primarily responsible for the variation of daily NEP from half-hourly to monthly timescales, and the direct photosynthetic active radiation(PAR_b) had a secondary effect on NEP. Under sunny conditions, PAR_b and air temperature were the dominant factors controlling daily NEP. While daily NEP was mainly controlled by PAR_d under cloudy and overcast conditions.

Mechanical response and dilatancy characteristics of deep marble under different stress paths:A sight from energy dissipation

Dilatancy is a fundamental volumetric growth behavior observed during loading and serves as a key index to comprehending the intricate nonlinear behavior and constitutive equation structure of rock.This study focuses on Jinping marble obtained from the Jinping Underground Laboratory in China at a depth of 2400 m.Various uniaxial and triaxial tests at different strain rates,along with constant confining pressure tests and reduced confining pressure tests under different confining pressures were conducted to analyze the mechanical response and dilatancy characteristics of the marble under four stress paths.Subsequently,a new empirical dilatancy coefficient is proposed based on the energy dissipation method.The results show that brittle failure characteristics of marble under uniaxial compression are more obvious with the strain rate increasing,and plastic failure characteristics of marble under triaxial compression are gradually strengthened.Furthermore,compared to the constant confining pressure,the volume expansion is relatively lower under unloading condition.The energy dissipation is closely linked to the process of dilatancy,with a rapid increase of dissipated energy coinciding with the beginning of dilatancy.A new empirical dilatancy coefficient is defined according to the change trend of energy dissipation rate curve,of which change trend is consistent with the actual dilatancy response in marble under different stress paths.The existing empirical and theoretical dilatancy models are analyzed,which shows that the empirical dilatancy coefficient based on the energy background is more universal.

Extended Lorenz majorization and frequencies of distances in an undirected network

Purpose:To contribute to the study of networks and graphs.Design/methodology/approach:We apply standard mathematical thinking.Findings:We show that the distance distribution in an undirected network Lorenz majorizes the one of a chain.As a consequence,the average and median distances in any such network are smaller than or equal to those of a chain.Research limitations:We restricted our investigations to undirected,unweighted networks.Practical implications:We are convinced that these results are useful in the study of small worlds and the so-called six degrees of separation property.Originality/value:To the best of our knowledge our research contains new network results,especially those related to frequencies of distances.

Lower Continental Crusts Involved in the Alpine Orogeny:New Insight from the Santa Lucia Nappe Metasediments(Corsica,France)

In the Alpine Corsica(France),the Santa Lucia Nappe represents a peculiar unit preserving the unique relicts of Paleozoic lower to medium continental crust.It consists of composite basement affected by Permian granulite facies metamorphic conditions unconformably covered by a Late Cretaceous clastic sequence(Tomboni Conglomerate and Tralonca Flysch)affected by polyphase deformation and low-grade-metamorphism.In this work,we present a new reconstruction of the deformation events registered by the Tralonca Flysch during the Alpine orogeny.The D1 phase was testified by rare isoclinal folds.The D2 phase produced a continuous foliation and a map-scale sheath-fold with a top-to-W sense of shear.The D3 phase produced E-verging non-cylindrical folds and S3 crenulation cleavage that is not associated to metamorphic blastesis.We present the first temperature-pressure-deformation(P-T-d)path for the Tralonca Flysch,demonstrating that the Santa Lucia Nappe underwent accretion and then first stage exhumation in the Alpine wedge during the D1 phase with pressure and temperature peaks both occurred under blueschist metamorphic conditions.The D2 phase occurred at lower pressure-temperature conditions during a second stage exhumation.This pressure-temperaturedeformation path is comparable with those of the Lower Units(i.e.,the subducted continental units of Alpine Corsica)suggesting a common geodynamic history.

Heuristic Expanding Disconnected Graph:A Rapid Path Planning Method for Mobile Robots

Existing mobile robots mostly use graph search algorithms for path planning,which suffer from relatively low planning efficiency owing to high redundancy and large computational complexity.Due to the limitations of the neighborhood search strategy,the robots could hardly obtain the most optimal global path.A global path planning algorithm,denoted as EDG*,is proposed by expanding nodes using a well-designed expanding disconnected graph operator(EDG)in this paper.Firstly,all obstacles are marked and their corners are located through the map pre-processing.Then,the EDG operator is designed to find points in non-obstruction areas to complete the rapid expansion of disconnected nodes.Finally,the EDG*heuristic iterative algorithm is proposed.It selects the candidate node through a specific valuation function and realizes the node expansion while avoiding collision with a minimum offset.Path planning experiments were conducted in a typical indoor environment and on the public dataset CSM.The result shows that the proposed EDG*reduced the planning time by more than 90%and total length of paths reduced by more than 4.6%.Compared to A*,Dijkstra and JPS,EDG*does not show an exponential explosion effect in map size.The EDG*showed better performance in terms of path smoothness,and collision avoidance.This shows that the EDG*algorithm proposed in this paper can improve the efficiency of path planning and enhance path quality.

Experimental observations on the nonproportional multiaxial ratchetting of cast AZ91 magnesium alloy at room temperature

The nonproportional multiaxial ratchetting of cast AZ91 magnesium (Mg) alloy was examined by performing a sequence of axial-torsional cyclic tests controlled by stress with various loading paths at room temperature (RT).The evolutionary characteristics and path dependence of multiaxial ratchetting were discussed.Results illustrate that the cast AZ91 Mg alloy exhibits considerable nonproportional additional softening during cyclic loading with multiple nonproportional multiaxial loading paths;multiaxial ratchetting presents strong path dependence,and axial ratchetting strains are larger under nonproportional loading paths than under uniaxial and proportional45°linear loading paths;multiaxial ratchetting becomes increasingly pronounced as the applied stress amplitude and axial mean stress increase.Moreover,stress-strain curves show a convex and symmetrical shape in axial/torsional directions.Multiaxial ratchetting exhibits quasi-shakedown after certain loading cycles.The abundant experimental data obtained in this work can be used to develop a cyclic plasticity model of cast Mg alloys.

Effect of non-uniform swelling on coal multiphysics during gas injection: The triangle approach

In current dual porosity/permeability models,there exists a fundamental assumption that the adsorption-induced swelling is distributed uniformly within the representative elementary volume (REV),irrespective of its internal structures and transient processes.However,both internal structures and transient processes can lead to the non-uniform swelling.In this study,we hypothesize that the non-uniform swelling is responsible for why coal permeability in experimental measurements is not only controlled by the effective stress but also is affected by the adsorption-induced swelling.We propose a concept of the swelling triangle composed of swelling paths to characterize the evolution of the non-uniform swelling and serve as a core link in coupled multiphysics.A swelling path is determined by a dimensionless volumetric ratio and a dimensionless swelling ratio.Different swelling paths have the same start and end point,and each swelling path represents a unique swelling case.The swelling path as the diagonal of the triangle represents the case of the uniform swelling while that as the two perpendicular boundaries represents the case of the localized swelling.The paths of all intermediate cases populate inside the triangle.The corresponding relations between the swelling path and the response of coal multiphysics are established by a non-uniform swelling coefficient.We define this method as the triangle approach and corresponding models as swelling path-based ones.The proposed concept and models are verified against a long-term experimental measurement of permeability and strains under constant effective stress.Our results demonstrate that during gas injection,coal multiphysics responses have a close dependence on the swelling path,and that in both future experiments and field predictions,this dependence must be considered.

Ground threat prediction-based path planning of unmanned autonomous helicopter using hybrid enhanced artificial bee colony algorithm

Unmanned autonomous helicopter(UAH)path planning problem is an important component of the UAH mission planning system.Aiming to reduce the influence of non-complete ground threat information on UAH path planning,a ground threat prediction-based path planning method is proposed based on artificial bee colony(ABC)algorithm by collaborative thinking strategy.Firstly,a dynamic threat distribution probability model is developed based on the characteristics of typical ground threats.The dynamic no-fly zone of the UAH is simulated and established by calculating the distribution probability of ground threats in real time.Then,a dynamic path planning method for UAH is designed in complex environment based on the real-time prediction of ground threats.By adding the collision warning mechanism to the path planning model,the flight path could be dynamically adjusted according to changing no-fly zones.Furthermore,a hybrid enhanced ABC algorithm is proposed based on collaborative thinking strategy.The proposed algorithm applies the leader-member thinking mechanism to guide the direction of population evolution,and reduces the negative impact of local optimal solutions caused by collaborative learning update strategy,which makes the optimization performance of ABC algorithm more controllable and efficient.Finally,simulation results verify the feasibility and effectiveness of the proposed ground threat prediction path planning method.

A Multi-Constraint Path Optimization Scheme Based on Information Fusion in Software Defined Network

The existingmultipath routing in Software Defined Network (SDN) is relatively blind and inefficient, and there is alack of cooperation between the terminal and network sides, making it difficult to achieve dynamic adaptationof service requirements and network resources. To address these issues, we propose a multi-constraint pathoptimization scheme based on information fusion in SDN. The proposed scheme collects network topology andnetwork state information on the network side and computes disjoint paths between end hosts. It uses the FuzzyAnalytic Hierarchy Process (FAHP) to calculate the weight coefficients of multiple constrained parameters andconstructs a composite quality evaluation function for the paths to determine the priority of the disjoint paths. TheSDN controller extracts the service attributes by analyzing the packet header and selects the optimal path for flowrule forwarding. Furthermore, the service attributes are fed back to the path composite quality evaluation function,and the path priority is dynamically adjusted to achieve dynamic adaptation between service requirements andnetwork status. By continuously monitoring and analyzing the service attributes, the scheme can ensure optimalrouting decisions in response to varying network conditions and evolving service demands. The experimentalresults demonstrated that the proposed scheme can effectively improve average throughput and link utilizationwhile meeting the Quality of Service (QoS) requirements of various applications.

Depth First:Optimal Path Discovery Between Designated Nodes in Random Ring-Based Graphs

This paper focuses on optimally determining the existence of connected paths between some given nodes in random ring-based graphs.Serving as a fundamental underlying structure in network modeling,ring topology appears as commonplace in many realistic scenarios.Regarding this,we consider graphs composed of rings,with some possible connected paths between them.Without prior knowledge of the exact node permutations on rings,the existence of each edge can be unraveled through edge testing at a unit cost in one step.The problem examined is that of determining whether the given nodes are connected by a path or separated by a cut,with the minimum expected costs involved.Dividing the problem into different cases based on different topologies of the ring-based networks,we propose the corresponding policies that aim to quickly seek the paths between nodes.A common feature shared by all those policies is that we stick to going in the same direction during edge searching,with edge testing in each step only involving the test between the source and the node that has been tested most.The simple searching rule,interestingly,can be interpreted as a delightful property stemming from the neat structure of ring-based networks,which makes the searching process not rely on any sophisticated behaviors.We prove the optimality of the proposed policies by calculating the expected cost incurred and making a comparison with the other class of strategies.The effectiveness of the proposed policies is also verified through extensive simulations,from which we even disclose three extra intriguing findings:i)in a onering network,the cost will grow drastically with the number of designated nodes when the number is small and will grow slightly when that number is large;ii)in ring-based network,Depth First is optimal in detecting the connectivity between designated nodes;iii)the problem of multi-ring networks shares large similarity with that of two-ring networks,and a larger number of ties between rings will not influence the expected cost.

A robust triaxial localization method of AE source using refraction path

Acoustic emission(AE)localization algorithms based on homogeneous media or single-velocity are less accurate when applied to the triaxial localization experiments.To the end,a robust triaxial localization method of AE source using refraction path is proposed.Firstly,the control equation of the refraction path is established according to the sensor coordinates and arrival times.Secondly,considering the influence of time-difference-of-arrival(TDOA)errors,the residual of the governing equation is calculated to estimate the equation weight.Thirdly,the refraction points in different directions are solved using Snell’s law and orthogonal constraints.Finally,the source coordinates are iteratively solved by weighted correction terms.The feasibility and accuracy of the proposed method are verified by pencil-lead breaking experiments.The simulation results show that the new method is almost unaffected by the refraction ratio,and always holds more stable and accurate positioning performance than the traditional method under different ratios and scales of TDOA outliers.

Phenology of different types of vegetation and their response to climate change in the Qilian Mountains,China

The Qilian Mountains(QM)possess a delicate vegetation ecosystem,amplifying the evident response of vegetation phenology to climate change.The relationship between changes in vegetation growth and climate remains complex.To this end,we used MODIS NDVI data to extract the phenological parameters of the vegetation including meadow(MDW),grassland(GSD),and alpine vegetation(ALV))in the QM from 2002 to 2021.Then,we employed path analysis to reveal the direct and indirect impacts of seasonal climate change on vegetation phenology.Additionally,we decomposed the vegetation phenology in a time series using the trigonometric seasonality,Box-Cox transformation,ARMA errors,and Trend Seasonal components model(TBATS).The findings showed a distinct pattern in the vegetation phenology of the QM,characterized by a progressive shift towards an earlier start of the growing season(SOS),a delayed end of the growing season(EOS),and an extended length of the growing season(LOS).The growth cycle of MDW,GSD,and ALV in the QM species is clearly defined.The SOS for MDW and GSD occurred earlier,mainly between late April and August,while the SOS for ALVs occurred between mid-May and mid-August,a one-month delay compared to the other vegetation.The EOS in MDW and GSD were concentrated between late August and April and early September and early January,respectively.Vegetation phenology exhibits distinct responses to seasonal temperature and precipitation patterns.The advancement and delay of SOS were mainly influenced by the direct effect of spring temperatures and precipitation,which affected 19.59%and 22.17%of the study area,respectively.The advancement and delay of EOS were mainly influenced by the direct effect of fall temperatures and precipitation,which affected 30.18%and 21.17%of the area,respectively.On the contrary,the direct effects of temperature and precipitation in summer and winter on vegetation phenology seem less noticeable and were mainly influenced by indirect effects.The indirect effect of winter precipitation is the main factor affecting the advance or delay of SOS,and the area proportions were 16.29%and 23.42%,respectively.The indirect effects of fall temperatures and precipitation were the main factors affecting the delay and advancement of EOS,respectively,with an area share of 15.80%and 21.60%.This study provides valuable insight into the relationship between vegetation phenology and climate change,which can be of great practical value for the ecological protection of the Qinghai-Tibetan Plateau as well as for the development of GSD ecological animal husbandry in the QM alpine pastoral area.

Multi-circular formation control with reinforced transient profiles for nonholonomic vehicles:A path-following framework

This article investigates a multi-circular path-following formation control with reinforced transient profiles for nonholonomic vehicles connected by a digraph.A multi-circular formation controller endowed with the feature of spatial-temporal decoupling is devised for a group of vehicles guided by a virtual leader evolving along an implicit path,which allows for a circumnavigation on multiple circles with an anticipant angular spacing.In addition,notice that it typically imposes a stringent time constraint on time-sensitive enclosing scenarios,hence an improved prescribed performance control(IPPC)using novel tighter behavior boundaries is presented to enhance transient capabilities with an ensured appointed-time convergence free from any overshoots.The significant merits are that coordinated circumnavigation along different circles can be realized via executing geometric and dynamic assignments independently with modified transient profiles.Furthermore,all variables existing in the entire system are analyzed to be convergent.Simulation and experimental results are provided to validate the utility of suggested solution.

A Path Planning Algorithm Based on Improved RRT Sampling Region

For the problem of slow search and tortuous paths in the Rapidly Exploring Random Tree(RRT)algorithm,a feedback-biased sampling RRT,called FS-RRT,is proposedbasedon RRT.Firstly,toimprove the samplingefficiency of RRT to shorten the search time,the search area of the randomtree is restricted to improve the sampling efficiency.Secondly,to obtain better information about obstacles to shorten the path length,a feedback-biased sampling strategy is used instead of the traditional random sampling,the collision of the expanding node with an obstacle generates feedback information so that the next expanding node avoids expanding within a specific angle range.Thirdly,this paper proposes using the inverse optimization strategy to remove redundancy points from the initial path,making the path shorter and more accurate.Finally,to satisfy the smooth operation of the robot in practice,auxiliary points are used to optimize the cubic Bezier curve to avoid path-crossing obstacles when using the Bezier curve optimization.The experimental results demonstrate that,compared to the traditional RRT algorithm,the proposed FS-RRT algorithm performs favorably against mainstream algorithms regarding running time,number of search iterations,and path length.Moreover,the improved algorithm also performs well in a narrow obstacle environment,and its effectiveness is further confirmed by experimental verification.

Effects of cold rolling path on recrystallization behavior and mechanical properties of pure copper during annealing

The recrystallization behavior,grain boundary characteristic distribution,and mechanical properties of pure Cu sheets that were subjected to different cold rolling paths,and then annealed at 400°C for 10,30,60,and 420 min,were investigated.Different rolling paths changed the grain boundary orientations of cold-rolled copper,causing recrystallized grains to nucleate and grow in an oriented manner.However,the evolution of the texture indicated that cold-rolled copper with different rolling paths did not show an obvious preferred orientation after annealing.The RD-60 specimen exhibited the smallest grain size(6.6μm).The results indicated that the grain size and low-ΣCSL grain boundaries worked together to provide RD-60 samples with appropriate mechanical properties and high plasticity.The yield strength,ultimate tensile strength,and elongation of RD-60 sample were 81 MPa,230 MPa,and 49%,respectively.These results could provide guidance for tuning the microstructures and properties of pure Cu foils,as well as designing fabrication routes for pure Cu foils through processes such as rolling and drawing.

A Reverse Path Planning Approach for Enhanced Performance of Multi-Degree-of-Freedom Industrial Manipulators

In the domain of autonomous industrial manipulators,precise positioning and appropriate posture selection in path planning are pivotal for tasks involving obstacle avoidance,such as handling,heat sealing,and stacking.While Multi-Degree-of-Freedom(MDOF)manipulators offer kinematic redundancy,aiding in the derivation of optimal inverse kinematic solutions to meet position and posture requisites,their path planning entails intricate multiobjective optimization,encompassing path,posture,and joint motion optimization.Achieving satisfactory results in practical scenarios remains challenging.In response,this study introduces a novel Reverse Path Planning(RPP)methodology tailored for industrial manipulators.The approach commences by conceptualizing the manipulator’s end-effector as an agent within a reinforcement learning(RL)framework,wherein the state space,action set,and reward function are precisely defined to expedite the search for an initial collision-free path.To enhance convergence speed,the Q-learning algorithm in RL is augmented with Dyna-Q.Additionally,we formulate the cylindrical bounding box of the manipulator based on its Denavit-Hartenberg(DH)parameters and propose a swift collision detection technique.Furthermore,the motion performance of the end-effector is refined through a bidirectional search,and joint weighting coefficients are introduced to mitigate motion in high-power joints.The efficacy of the proposed RPP methodology is rigorously examined through extensive simulations conducted on a six-degree-of-freedom(6-DOF)manipulator encountering two distinct obstacle configurations and target positions.Experimental results substantiate that the RPP method adeptly orchestrates the computation of the shortest collision-free path while adhering to specific posture constraints at the target point.Moreover,itminimizes both posture angle deviations and joint motion,showcasing its prowess in enhancing the operational performance of MDOF industrial manipulators.

On traceable iterated line graph and hamiltonian path index

Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characterization of G for which L^(n)(G)has a hamiltonian path.As applications,we use this characterization to give several upper bounds on the hamiltonian path index of a graph.