Path Problem Research Articles

Convertible Bonds: A Supplementary Exit Path for Private Equity Funds

With the rapid development of China's economy, private equity funds have become an important force to help unlisted small and medium-sized startups quickly become bigger and stronger. As an important financing channel for enterprises, private equity funds can provide a large amount of financial support for target enterprises, and in all aspects of their investment operations, the choice of exit method is particularly important as the core link that directly affects returns. Therefore, this paper takes the case study as the research method, and selects SoftBank Group's gradual reduction of Alibaba shares through the issuance of convertible trust bonds as a case study, and studies the use of convertible bonds as a supplement to the IPO exit method of private equity funds. The study finds that convertible bonds, as a supplement to the IPO exit method, have more efficient, lower risk and low cost financing capabilities, effectively solve the problem of single exit path, improve the speed of private equity fund exit liquidation, and reduce the loss range while retaining the profit growth space.

EMOA*: A framework for search-based multi-objective path planning

In the Multi-Objective Shortest Path Problem (MO-SPP), one has to find paths on a graph that simultaneously minimize multiple objectives. It is not guaranteed that there exists a path that minimizes all objectives, and the problem thus aims to find the set of Pareto-optimal paths from the start to the goal vertex. A variety of multi-objective A*-based search approaches have been developed for this purpose. Typically, these approaches maintain a front set at each vertex during the search process to keep track of the Pareto-optimal paths that reach that vertex. Maintaining these front sets becomes burdensome and often slows down the search when there are many Pareto-optimal paths. In this article, we first introduce a framework for MO-SPP with the key procedures related to the front sets abstracted and highlighted, which provides a novel perspective for understanding the existing multi-objective A*-based search algorithms. Within this framework, we develop two different, yet closely related approaches to maintain these front sets efficiently during the search. We show that our approaches can find all cost-unique Pareto-optimal paths, and analyze their runtime complexity. We implement the approaches and compare them against baselines using instances with three, four and five objectives. Our experimental results show that our approaches run up to an order of magnitude faster than the baselines.

Load asymptotics and dynamic speed optimization for the greenest path problem: a comprehensive analysis

Load asymptotics and dynamic speed optimization for the greenest path problem: a comprehensive analysis

A Fuzzy Variable H Strategy Based Ripple-Spreading Algorithm to Find the k Shortest Paths

Ripple-spreading Algorithm (RSA) is a relatively new, nature-inspired, multi-agent based method for path optimization. This paper demonstrates that by modifying the micro-level behaviors of nodes and ripples, RSA achieves good scalability for solving the k shortest paths problem (k–SPP). Initially, each node may generate k or more ripples to guarantee optimality. To improve computational efficiency for large-scale problems, we propose an approximate RSA (ARSA), where nodes generate no more than h ripples (1≤h<k). While this reduces optimality, it significantly improves efficiency. Further, we introduce a fuzzy variable H strategy, FVHSRSA, to strike a better balance between optimality and efficiency. The optimality/efficiency of ARSA may still suffer if it uses a constant h too small/large. This strategy allows nodes closer to the destination to generate more ripples, while nodes farther away use fewer ripples. By dynamically adjusting h, FVHSRSA achieves a better trade-off between optimality and efficiency. Comprehensive experiments on 4 common network categories validate the effectiveness and efficiency of FVHSRSA in solving the k–SPP.

Dynamic clustering optimization for energy efficient IoT Network: A simple constrastive graph approach

The growing demand for IoT spans sectors includes industrial automation, home control, healthcare, military, and surveillance. Optimal Wireless Sensor Networks (WSNs), consisting of thousands of sensor nodes (SN) play an essential role in randomly distributing and transmitting environmental data like, temperature, pressure, humidity, light, sound. Energy efficiency is significant for these sensor nodes to prompt research and the development of various design techniques and protocols, especially for IoT applications. Thus, achieving energy-optimized WSNs with dynamic functionality and automatic self-configuration of sensor nodes is an essential research objective. In this work, Dynamic Clustering Optimization for Energy Efficient IoT Network: A Simple Constrastive Graph Approach (DCO-EEN-SCGA) is proposed. The Mean Standard Deviation Shortest Path Problem (MSDSPP) is used in multiple parameters for detecting the shortest valid path. Simple Constrastive Graph Clustering (SCGC) is used to decrease the transmission overhead and energy consumption. Finally, the performance of proposed DCO-EEN-SCGA method provides 15.17%, 17.42%, and 19.25% higher energy consumption, 16.35%, 18.62% and 20.11% higher throughput and 17.45%, 18.72%, and 19.19% higher end to end delay. When comparing with existing techniques like An Opportunistic Energy‐effective Dynamic Self‐Configuration Clustering Algorithm in WSN‐based IoT Networks (OEDSCC-WSNN), Clustering at the Edge: Load Balancing with Energy Efficiency for IoT (CE-LBEE-IOT) and An Energy-effective Hybrid Clustering Technique for IoT-based Multilevel Heterogeneous WSN (EEHT-IOT-MHWN) methods respectively.

Efficient online sensitivity analysis for the injective bottleneck path problem

Efficient online sensitivity analysis for the injective bottleneck path problem

Dynamic evolution analysis and parameter optimization design of data-driven network infectious disease model

Background and Objective:globalization and population mobility have increased the spread of infectious diseases and challenged public health security. This paper proposes a complex network epidemic model with nonlinear incidence rate and quadratic transmission. The Turing pattern, sensitivity analysis and parameter identification of the epidemic model under different network structures are studied; Methods:this paper discusses the Turing pattern of the model under different network structures, and identifies the key parameters of the model through sensitivity analysis. The influence of network dimension on the spread of infectious diseases on random networks is also explored, and the problems of minimum path and minimum cover set of random networks are further discussed. We also carry out parameter identification experiments, adopt gradient descent algorithm to realize heterogeneous spatial fitting pattern of red blood cell plasma and simulate the transmission path of COVID-19 through Markov chain Monte Carlo fitting experiment, verifying the effectiveness of the model; Results:the necessary conditions for Turing instability on homogeneous and heterogeneous networks are found. On the heterogeneous lattice network, we observe the special patterns of equal density population. Sensitivity analysis shows that the higher the infection rate, the more infected people. On random networks, the higher the dimension, the better the effect of suppressing the spread of infectious diseases. Through comparison experiment, it is found that gradient descent algorithm has the best performance in parameter identification experiments. Red blood cell plasma fitting experiment reveals the spatial density distribution of infection rate; Conclusions:this study provides theoretical support for the prevention and control of infectious diseases, and the complex network model can simulate the transmission process of infectious diseases more accurately. Sensitivity analysis and parameter identification experiments reveal the key influencing factors of propagation and the role of network structure. The effectiveness of the model is supported by actual data, which is helpful for the government health departments to formulate scientific prevention and control strategies.

An Efficient Algorithm for the 2-Central Path Problem

In this paper we consider the following [Formula: see text]-Central Path Problem (2CPP): Given a set of [Formula: see text] polygonal curves [Formula: see text] in the plane, find two curves [Formula: see text] and [Formula: see text], called [Formula: see text]-central paths, that best represent all curves in [Formula: see text]. Despite its theoretical interest and a wide range of practical applications, 2CPP has not been well studied. In this paper, we first establish criteria that [Formula: see text] and [Formula: see text] ought to meet in order for them to best represent [Formula: see text]. In particular, we require that there exists parametrizations [Formula: see text] and [Formula: see text] ([Formula: see text]) of [Formula: see text] and [Formula: see text] respectively such that the maximum distance from [Formula: see text] to curves in [Formula: see text] is minimized. Then an efficient algorithm is presented to solve 2CPP under certain realistic assumptions. Our algorithm constructs [Formula: see text] and [Formula: see text] in [Formula: see text] time, where [Formula: see text] is the total complexity of [Formula: see text] (i.e., the total number of vertices and edges), [Formula: see text] is the number of curves in [Formula: see text], and [Formula: see text] is the inverse Ackermann function. Our algorithm uses parametric search technique and is considerably faster than arrangement-related algorithms (i.e. [Formula: see text]) when [Formula: see text] as in most real applications.

Approximating the shortest path problem with scenarios

This paper discusses the shortest path problem in a general directed graph with n nodes and K cost scenarios (objectives). In order to choose a solution, the min-max criterion is applied. The min-max version of the problem is hard to approximate within Ω(log1−ϵ⁡K) for any ϵ>0 unless NP⊆DTIME(npolylogn) even for arc series-parallel graphs and within Ω(log⁡n/log⁡log⁡n) unless NP⊆ZPTIME(nlog⁡log⁡n) for acyclic graphs. The best approximation algorithm for the min-max shortest path problem in general graphs, known to date, has an approximation ratio of K. In this paper, an O˜(n) flow LP-based approximation algorithm for min-max shortest path in general graphs is constructed. It is also shown that the approximation ratio obtained is close to an integrality gap of the corresponding flow LP relaxation.

The Logic and Application of Greedy Algorithms

Abstract. Being easy to implement and offering faster solutions, the greedy algorithms have widely been used in solving combinatorial optimization problems in computer science and many practical applications, such as resource allocation and data compression. This paper aims at analyzing the definitions, theory, and application of greedy algorithms in computer science as well as their logic and efficacy in numerous situations. In this analysis, concepts such as the greedy choice property and optimal substructure are examined as essential to understanding how greedy algorithms operate. The provided analysis mainly assumes prior knowledge of concepts and problems like the Fractional Knapsack problem and the Shortest Path problem solution as well as some practical problems, for example, resource allocation and the exact coin change problem. Analytical data and real applications are used to analyze the performance of greedy algorithms vis-a-vis other categories, such as the dynamic programming paradigm. The results reveal that greedy algorithms have the potential for great efficiency while also being restricted by certain parameters. They are ideal in the following aspects pertaining to computational aspects, that is, speed, ease of implementation, and applicability to large datasets. But they do not necessarily promise strong optimality in certain situations. The conclusion notes that greedy algorithms deserve further applications when the specified conditions are met and states that the effectiveness of these conditions needs to be studied.

Path planning strategies for logistics robots: Integrating enhanced A‐star algorithm and DWA

AbstractPath planning is the key part in the process of transportation conducted by logistics robots, and there often exist some problems with it. The path designed is not always smooth enough and its search efficiency is low, for example. As a common global path planning algorithm, A‐star is based on the traditional algorithm, which is unable to solve the problem of uneven path in the movement of logistics robots. Through improving the heuristic function of the traditional A‐star algorithm, weighing the heuristic function dynamically, removing the redundant points of the traditional star algorithm path with Floyd algorithm, and setting a safe distance to prevent the logistics robot from collision at the same time, the path is finally curved to be more appropriate to the movement path of the logistics robot. The MATLAB simulation of A‐star algorithm before and after the improvement shows that the turning points of the advanced A‐star algorithm reduced 61.5% on average compared to the traditional algorithm. The path length decreased 2.4% and the traversing points reduced 58.5%. At the same time, the DWA algorithm introduces dynamic weight coefficients, which can dynamically adjust the weight coefficients when encountering obstacles, so as to safely reach the target point.

Optimizing Bus Bridging Services with Mode Choice in Response to Urban Rail Transit Emergencies

During urban rail transit (URT) emergencies, stranded passengers may choose to seek alternative modes of transportation instead of waiting in the URT system for the bus bridging service to commence. To tackle this challenge, we present an optimization-based approach focused on identifying promising bus bridging lines and devising efficient services. Specifically, we introduce a candidate line generation (CLG) model designed to identify potential bus bridging lines. This model is akin to solving a k-all pair elementary shortest path problem with resource constraints (k-APESPPRC). We develop an exact algorithm based on the label setting algorithm and Lawler's algorithm to solve this model effectively. Subsequently, our approach allocates limited bus resources to determine line selection, frequency determination, bus deployment, and passenger assignment on the integrated network (i.e., partial URT network and bus network) with the consideration of mode choice. Given the inherent complexity of this problem, we introduce an optimization-based tabu search method (opt-tabu) designed to efficiently solve real-size instances. To demonstrate the effectiveness of our approach, we present a real case study conducted in Hong Kong, showcasing its efficiency and practicality. In summary, this study makes a valuable contribution to the transportation industry by providing a practical and efficient approach to managing URT emergencies, emphasizing the significance of considering mode choice in the context of bus bridging services.

Improved GA-LNS Algorithm for Solving Vehicle Path Problems Considering Carbon Emissions

Logistics, as a significant field for achieving energy-saving and carbon reduction goals, is recognized as a crucial direction for realizing the global “double carbon” objective, while vehicle path optimization is an effective method for promoting energy efficiency and reducing carbon emissions. In this paper, an improved genetic algorithm is proposed for optimizing logistics and distribution paths concerning the carbon emissions of fuel vehicles throughout the logistics and distribution process, and a low-carbon logistics and distribution path model is constructed based on time windows, vehicle loading, and carbon emissions. The INNC method is adopted to initialize the population, and an enhanced genetic algorithm (GA-LNS) is designed to solve the model in conjunction with a large-scale neighborhood vector search algorithm. The results indicate that the initialization of the population using the INNC method produces a higher-quality initial solution. Compared to traditional genetic algorithms and particle swarm optimization, the GA-LNS algorithm exhibits superior robustness, effectively addressing the limitations of traditional genetic algorithms that rely on initial solutions and are prone to local optima. By comparing the computational results of the low-carbon logistics distribution path model constructed in this study with those of traditional optimization objective models, it is demonstrated that this model effectively balances the trade-offs between objectives and benefits, achieving the lowest total logistics distribution cost while promoting sustainable low-carbon logistics. The research findings provide a theoretical foundation for optimizing logistics vehicle paths and formulating energy-saving and carbon reduction implementation plans in China.

A branch-and-price approach for the nurse rostering problem with multiple units

In this paper, we study the nurse rostering problem that considers multiple units and many soft time-related constraints. An efficient branch and price solution approach that relies on a fast algorithm to solve the pricing subproblem of the column generation process is presented. For the nurse rostering problem, its pricing subproblem can be formulated as a shortest path problem with resource constraints, which has been the backbone of several solutions for several classical problems like vehicle routing problems. However, approaches that perform well on these problems cannot be used since most constraints in the nurse rostering problem are soft. Based on ideas borrowed from global constraints in constraint programming to model rostering problems, an efficient dynamic programming algorithm with novel label definitions and dominating rules specific to soft time-related constraints is proposed. In addition, several acceleration strategies are employed to improve the branch and price algorithm. Computational results on two sets of instances ranging from 2 to 4 units over a horizon of 2 or 4 weeks demonstrate the effectiveness of the proposed algorithms. The accelerated dynamic programming algorithm is able to solve pricing subproblems to optimality with the fewest extended labels. When contrasted with Cplex, the branch and price approach yields solutions that are either equivalent or superior across all instances.

Improved Floyd-Warshall Algorithm for Solving Travelling Salesman Problem

The shortest path problem is a fundamental challenge in graph theory, focused on identifying the most efficient routes between nodes in a network. It stands as one of the extensively researched combinatorial optimization problems. In this paper, we explained the fundamental concepts of shortest path algorithms, with a particular emphasis on Floyd Warshall algorithm. We apply the algorithm and showed how this algorithm can be effectively employed to determine the shortest path in various scenarios. Furthermore, this paper addresses real-life applications, particularly focusing on the traveling salesman problem. Individuals often have the option to travel along different routes to reach their destination. However, selecting suboptimal routes can result in time-consuming journeys. To tackle this issue, we apply the Floyd Warshall algorithm to solve the traveling salesman problem (TSP). Additionally, we demonstrate the enhancement of the Floyd Warshall algorithm's efficiency for TSP using the rectangular algorithm. This paper concludes with a comparative analysis between the original and improved Floyd Warshall algorithms, emphasizing the computational reduction achieved through the proposed enhancements. Jagannath University Journal of Science, Volume 11, Number 1, June 2024, pp. 45−52

Polynomial Time Algorithm for Shortest Paths in Interval Temporal Graphs

We develop a polynomial time algorithm for the single-source all destinations shortest paths problem for interval temporal graphs (ITGs). While a polynomial time algorithm for this problem is known for contact sequence temporal graphs (CSGs), no such prior algorithm is known for ITGs. We benchmark our ITG algorithm against that for CSGs using datasets that can be solved using either algorithm. Using synthetic datasets, experimentally, we show that our algorithm for ITGs obtains a speedup of up to 32.5 relative to the state-of-the-art algorithm for CSGs.

Recoverable Robust Shortest Path Problem Under Interval Budgeted Uncertainty Representations

ABSTRACTThis article deals with the recoverable robust shortest path problem under interval uncertainty representations. In this problem, a first‐stage path is computed, which can be modified to some extent after observing changes in the cost structure. The uncertain second‐stage arc costs are modeled by intervals, and the robust min–max criterion is used to compute an optimal solution. The problem is known to be strongly NP‐hard and also hard to approximate in general digraphs. However, until now its complexity for acyclic digraphs was unknown. In this article, it is shown that the problem in acyclic digraphs can be solved in polynomial time for the traditional interval uncertainty and all natural neighborhoods known from the literature. More efficient algorithms for layered and arc series‐parallel digraphs are constructed. Hardness results for general digraphs are also strengthened. Finally, some exact and approximate methods of solving the problem under interval budgeted uncertainty are proposed.

Research and Application of Euler Cutting Path Based Optimisation Algorithm with Greedy-RRT Algorithm

With the development of social economy, mould processing enterprises have an increasingly strong demand for reducing costs and improving economic efficiency. The optimisation of steel plate cutting path is one of the key links to improve production efficiency. In this paper, the optimal cutting path problem of steel plate under different cutting tasks is investigated, and the optimal cutting path under complex geometries is found through various optimisation algorithms. For cutting task N3, the cutting path is divided into outer contour cutting, inner hole cutting and inner hole part cutting. According to the problem, all rectangular parts inside the ellipse need to be cut before the ellipse. Through the Eulerian cutting path optimisation algorithm, we solve the air-travel problem between the inner holes and the outer contour as well as the air-travel problem between the inner holes of the ellipse and the parts inside the ellipse. The total length of the finally determined optimal air-travel path is 97 units. By combining the greedy algorithm and the RRT algorithm, we determine the number and location of the bridges and design the optimal cutting path starting from the lower right corner of the steel plate. The final clearance of the bridges is 4 units, the total length of the combined optimal path clearance is 35.56 units, and the number of bridges is 8, which are located between adjacent rectangles.

Study of Optimal Cutting Paths for Steel Plates Based on Enumeration and Nonlinear Programming

With the development of society and economy, mould processing enterprises have an increasingly strong need to reduce costs and increase economic efficiency. Improving the efficiency of the cutting process is one of the key links to achieve this goal, and the planning of the cutting path occupies a major position in it. Under the condition that the actual cutting distance is fixed, the shortest air distance becomes the goal pursued by enterprises. In this paper, the optimal cutting path problem for steel plates is studied, and the optimal paths under different cutting tasks are found by enumeration method and nonlinear planning model.

Algorithms for the thief orienteering problem on directed acyclic graphs

We consider the scenario of routing an agent called a thief through a weighted graph G=(V,E) from a start vertex s to an end vertex t. A set I of items each with weight wi and profit pi is distributed among V∖{s,t}. The thief, who has a knapsack of capacity W, must follow a simple path from s to t within a given time T while packing in the knapsack a set of items taken from the vertices along the path of total weight at most W and maximum profit. The travel time across an edge depends on the edge length and current knapsack load.The thief orienteering problem (ThOP) is a generalization of the orienteering problem, the longest path problem, and the 0-1 knapsack problem. We prove that there exists no approximation algorithm for ThOP with constant approximation ratio unless P=NP, and we present a polynomial-time approximation scheme (PTAS) for a relaxed version of ThOP when G is directed and acyclic that produces solutions that use time at most T(1+ϵ) for any constant ϵ>0. We also present a fully polynomial-time approximation scheme (FPTAS) for ThOP on arbitrary undirected graphs where the travel time depends only on the lengths of the edges and T is the length of a shortest path from s to t plus a constant K. Finally, we present a FPTAS for a restricted version of the problem where the input graph is a clique.