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.

Original optimal method to solve the all-pairs shortest path problem: Dhouib-matrix-ALL-SPP

The All-pairs shortest path problem(ALL-SPP)aims to find the shortest path joining all the vertices in a given graph.This study proposed a new optimal method,Dhouib-matrix-ALL-SPP(DM-ALL-SPP)to solve the ALL-SPP based on column-row navigation through the adjacency matrix.DM-ALL-SPP is designed to generate in a single execution the shortest path with details among all-pairs of vertices for a graph with positive and negative weighted edges.Even for graphs with a negative cycle,DM-ALL-SPP reported a negative cycle.In addition,DM-ALL-SPP continues to work for directed,undirected and mixed graphs.Furthermore,it is characterized by two phases:the first phase consists of adding by column repeated(n)iterations(where n is the number of vertices),and the second phase resides in adding by row executed in the worst case(n∗log(n))iterations.The first phase,focused on improving the elements of each column by adding their values to each row and modifying them with the smallest value.The second phase is emphasized by rows only for the elements modified in the first phase.Different instances from the literature were used to test the performance of the proposed DM-ALL-SPP method,which was developed using the Python programming language and the results were compared to those obtained by the Floyd-Warshall algorithm.

AN INVERSE MAXIMUM CAPACITY PATH PROBLEM WITH LOWER BOUND CONSTRAINTS

The computational complexity of inverse mimimum capacity path problem with lower bound on capacity of maximum capacity path is examined, and it is proved that solution of this problem is NP-complete. A strong polynomial algorithm for a local optimal solution is provided.

Output-threshold coupled neural network for solving the shortest path problems

This paper presents a coupled neural network, called output-threshold coupled neural network (OTCNN), which can mimic the autowaves in the present pulsed coupled neural networks (PCNNs), by the construction of mutual coupling between neuron outputs and the threshold of a neuron. Based on its autowaves, this paper presents a method for finding the shortest path in shortest time with OTCNNs. The method presented here features much fewer neurons needed, simplicity of the structure of the neurons and the networks, and large scale of parallel computation. It is shown that OTCNN is very effective in finding the shortest paths from a single start node to multiple destination nodes for asymmetric weighted graph, with a number of iterations proportional only to the length of the shortest paths, but independent of the complexity of the graph and the total number of existing paths in the graph. Finally, examples for finding the shortest path are presented.

PATH PROBLEM SIMPLIFICATION WITH DESIRED BOUNDED LENGTHS IN ACYCLIC NETWORKS

Path determination is a fundamental problem of operations research. Current solutions mainly focus on the shortest and longest paths. We consider a more generalized problem; specifically, we consider the path problem with desired bounded lengths （DBL path problem）. This problem has extensive applications; however, this problem is much harder, especially for large-scale problems. An effective approach to this problem is equivalent simplification. We focus on simplifying the problem in acyclic networks and creating a path length model that simplifies relationships between various path lengths. Based on this model, we design polynomial algorithms to compute the shortest, longest, second shortest, and second longest paths that traverse any arc. Furthermore, we design a polynomial algorithm for the equivalent simplification of the is O（m）, where m is the number of arcs. DBL path problem. The complexity of the algorithm

Optimal paths planning in dynamic transportation networks with random link travel times

A theoretical study was conducted on finding optimal paths in transportation networks where link travel times were stochastic and time-dependent(STD). The methodology of relative robust optimization was applied as measures for comparing time-varying, random path travel times for a priori optimization. In accordance with the situation in real world, a stochastic consistent condition was provided for the STD networks and under this condition, a mathematical proof was given that the STD robust optimal path problem can be simplified into a minimum problem in specific time-dependent networks. A label setting algorithm was designed and tested to find travelers' robust optimal path in a sampled STD network with computation complexity of O(n2+n·m). The validity of the robust approach and the designed algorithm were confirmed in the computational tests. Compared with conventional probability approach, the proposed approach is simple and efficient, and also has a good application prospect in navigation system.

Improved ant colony optimization algorithm for the traveling salesman problems

Ant colony optimization （ACO） is a new heuristic algo- rithm which has been proven a successful technique and applied to a number of combinatorial optimization problems. The traveling salesman problem （TSP） is among the most important combinato- rial problems. An ACO algorithm based on scout characteristic is proposed for solving the stagnation behavior and premature con- vergence problem of the basic ACO algorithm on TSP. The main idea is to partition artificial ants into two groups： scout ants and common ants. The common ants work according to the search manner of basic ant colony algorithm, but scout ants have some differences from common ants, they calculate each route＇s muta- tion probability of the current optimal solution using path evaluation model and search around the optimal solution according to the mutation probability. Simulation on TSP shows that the improved algorithm has high efficiency and robustness.

Niche pseudo-parallel genetic algorithms for path optimization of autonomous mobile robot

A new genetic algorithm named niche pseudo-parallel genetic algorithm （NPPGA） is presented for path evolution and genetic optimization of autonomous mobile robot. The NPPGA is an effective improvement to maintain the population diversity as well for the sake of avoiding premature and strengthen parallelism of the population to accelerate the search process combined with niche genetic algorithms and pseudo-parallel genetic algorithms. The proposed approach is evaluated by robotic path optimization, which is a specific application of traveler salesman problem （TSP）. Experimental results indicated that a shortest path could be obtained in the practical traveling salesman problem named ＂Robot tour around Pekin＂, and the performance conducted by NPPGA is better than simple genetic algorithm （SGA） and distributed paralell genetic algorithms （DPGA）.

Applying the Method for Solving Traveling Salesman Problem Based on Backtracking Algorithm to Order Picking

In the distribution center, the way of order picking personnel to pick goods has two kinds: single picking and batch picking. Based on the way of the single picking and assumed warehouse model, in order to reduce the walking path of order picking, the order picking problem is transformed into the traveling salesman problem in this paper. Based on backtracking algorithm, the order picking path gets optimized. Finally verifing the optimization method under the environment of VC++6.0, order picking path in the warehouse model get optimized, and compared with the traditional order picking walking paths. The results show that in small and medium-sized warehouse, the optimization method proposed in this paper can reduce order picking walking path and improve the work efficiency as well as reduce the time cost.

关于Knight’s Tour Problem的图论解法

通过分析欧拉所给出Knight’s Tour Problem的解法,结合哈密尔顿路和哈密尔顿圈的相关知识,得出其解法对应着二部图中的一条哈密尔顿圈.由此再充分利用8×8棋盘所对应的8×8表格的对称性及同格图的特性,对欧拉所给出的Knight’s Tour Problem的解法作了进一步的探讨,得出了以欧拉的解法为基础的以任一棋格为骑士周游起点的另外一系列解法.最后,把Knight’sTour Problem推广到m×n棋盘上,考虑到移动规则的特殊性,利用图论的相关知识,得到3×4,8×16和16×16棋盘上的Knight’s Tour Problem的解法,同时给出8m×8n(m>2,n>2)棋盘上Knight’s Tour Problem的猜想.

中国技能型社会建设的问题背景、结构设计与路径规划

“技能型社会建设”课题的提出是我国职业教育发展具有历史转折意义的重要事件,它使职业教育发展从系统建设内部要素,转向了系统建设外部社会条件,核心任务是通过建设技能型社会为职业教育发展创造条件,解决职业教育发展中的深层社会问题,满足产业发展对技能人才的需求。技能形成过程包括四个关键环节,即理性的教育选择、丰富的技能训练机会供给、有效的技能配置与合理的技能劳动成果认定,它们构成了技能型社会的基本结构。合理的教育选择观念是技能型社会建设的逻辑起点,对教育选择观念产生关键性影响的因素存在于技能训练机会供给、技能配置、技能劳动成果认定这三个环节。技能型社会建设,要根据各因素相互作用关系聚焦问题解决关键点,根据各因素问题解决的难易程度规划建设进程,根据各因素的职能归属规划技能型社会建设任务落实主体,根据各因素作用的性质设计有针对性的解决策略。

Complete Path of Rural Poverty Alleviation System in Guizhou Province Based on Empirical Investigation and Analysis of 4 Typical Counties in Guizhou Province

Guizhou Province has the highest incidence and severity of poverty throughout the country.The investigation on its poverty alleviation is of typical significance for the poverty relief and development of concentrated and continuous destitute areas in the new time.On the basis of in-depth research,the 4 typical counties on poverty relief and development in Guizhou Province- Changshun,Yinjiang,Qinglong and Weining have been studied intensively.In the meanwhile,their common successful experiences and existing problems have been summarized.With regard to the complete path for the next stage of poverty alleviation system in Guizho Province,the following recommendations have been proposed: establish a multi-level system for sending agricultural technicians down to the countryside; improve the autonomy of primary-level organizations,especially the anti-poverty organizations at the county level; standardize the allocation of welfare projects; promote agricultural insurance; and improve the sustainable development capacity and market competition ability of farmer specialized cooperative economy organizations.

Reduction and Analysis of a Max-Plus Linear System to a Constraint Satisfaction Problem for Mixed Integer Programming

This research develops a solution method for project scheduling represented by a max-plus-linear (MPL) form. Max-plus-linear representation is an approach to model and analyze a class of discrete-event systems, in which the behavior of a target system is represented by linear equations in max-plus algebra. Several types of MPL equations can be reduced to a constraint satisfaction problem (CSP) for mixed integer programming. The resulting formulation is flexible and easy-to-use for project scheduling;for example, we can obtain the earliest output times, latest task-starting times, and latest input times using an MPL form. We also develop a key method for identifying critical tasks under the framework of CSP. The developed methods are validated through a numerical example.

Finding Solutions to the Picard Boundary Value Problem via Homotopy Method

This paper deals with the problem of finding solutions to the Picard boundary problem. In our approacn, by means of the homotopy method, the equation considered is linked to a simpler equation by introducing a parameter. We first find the solutions of the simpler equation, and give a priori estimates of the equation we considered, and then one can obtain the solutions of Picard boundary problem by following the path of solutions of Cauchy problem.

考虑鲁棒成本与绝对后悔的最短路径问题研究

为克服鲁棒偏差方法在处理区间路网时所求鲁棒最短路径的保守性问题,通过分析鲁棒成本的定义以及鲁棒最短路径过于保守的原因,结合算例分析提出了绝对后悔值的概念,并以鲁棒成本和绝对后悔值为目标函数建立了区间路网的多目标最短路径模型;根据最短路径模型的特点设计了分离路径决策变量与连续变量的Benders分解算法,同时基于传统有效路径的判断依据重新定义了符合该最短路径模型的有效路径,并在分解后的主问题模型中引入了有效路径约束以加快算法收敛速度;利用MATLAB生成了一个包含29个节点、70条双向通行路段的区间路网对模型与算法进行仿真测试。结果表明:考虑鲁棒成本和绝对后悔值的最短路径模型能在区间路网中找到不保守,且同时兼具鲁棒性的最短路径,能够有效克服鲁棒偏差方法的缺陷。

新型农业保险政策激励粮食生产:逻辑、问题与路径

新型农业保险政策激励粮食生产是现阶段我国确保粮食安全的重要手段。从制度变迁来看,政府职能从“越位”到“缺位”再到“归位”;从内在逻辑来看,新型农业保险政策激励粮食生产蕴含了深刻的经济逻辑、社会逻辑及制度逻辑;从面临问题来看,新型农业保险政策激励粮食生产还存在政府引导不到位与市场主体运行不规范并存、短期效应较为明显但实现长期目标任务艰巨、三大主粮部分险种有待推进与其他粮食作物保险亟待开发等突出问题。因此,要进一步发挥政府调控作用与市场机制在资源配置中的决定性作用,明确粮食作物保险发展目标及完善支持政策,优化粮食作物保险的供给方式并提升服务能力。

公安院校大学生提出问题能力培养:不足、成因与改进路径

提出问题能力是大学生应该具备的重要能力。通过考察教学活动各环节并访谈师生发现,大学生在提出问题能力方面存在不足,具体表现为:主动思考和发现问题能力不足;准确表述和界定问题的能力有待提升;不能将已有知识与实践情境建立联系。究其原因,主要包括:学习动力不足,学生知识储备不够,知识建构能力较弱;教师教学观念方法落后,学生主体地位未能落实;学校培养制度不完善,培养环境有待优化。培养大学生提出问题能力的改革路径包括:加强思想教育,引导学生树立正确学习观;修订培养方案,重视提出问题能力培养;深化教育教学改革,突出学生主体地位;推进制度创新,完善大学生提出问题能力培养机制。

当前成人在线教学的问题审视与优化策略及其远程教育学阐释

当前成人在线教学的教师没有明确转换教师角色与任务,常常只是将传统课堂搬迁到网络上,在线主体的心理距离因时空分离不断扩大,教师对在线教学的认知、行为与情感投入不够,强烈影响了学员的学习投入感、师生疏离感与教学成效。从远程教育学看,成人远程教育的关键是设计优秀在线课程并提供学习支持服务以实现三种交互,所以,成教的直播课、录播课、仿真技能课的有效实施都需利用对应的社交平台与工具平台设计课前课中课后的支持服务,依据布鲁姆教学目标的分类区别化设计成人在线教学策略,根据内容特征与学员情感需要设计多种混合式教学,利用平台记录的学习大数据及其画像,从交互距离与远程学员自治两个维度让师生获得动态、整全的及时诊断与警示。

高等职业教育高质量发展的基础、问题与趋向研究

高等职业教育是我国高等人才培养的重要一环,对于完善高等教育多位一体育人机制有着深远影响,可以充分填补新兴产业及高精尖产业技术人才空缺。基于此,重点针对高等职业教育高质量发展基础、问题与趋向进行分析,并结合新时代职业教育发展新需求,提出高等职业教育高质量发展的路径,明确新时代职业教育发展方向,细化各个层面职业院校与高职院校教育工作决策,以期为部分职业院校提供多元化的教育内容参考。