Path Problem Research Articles

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.

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.

Overview of Path Planning Algorithms

Background: Path-planning algorithms are widely used in robotics, vehicles, UAVs, carrier-based aircraft towing vehicles, etc. Using these algorithms, an optimal path with safe obstacle avoidance and high efficiency can be planned. In recent years, path-planning algorithms have received more and more attention from scholars at home and abroad. Objective: In order to promote the application and development of path-planning algorithms, an in-depth analysis of the current development status of path-planning algorithms was presented. The most widely used and representative algorithms in several representative results were extracted, and the characteristics and advantages and disadvantages of each algorithm were analyzed and elaborated in detail for the readers' reference. Methods: The existing path-planning algorithms were classified, and a brief overview of each traditional algorithm was given, followed by an in-depth study of the improved algorithms to summarize the advantages and disadvantages of each type of algorithm. Finally, based on these research results, the future development trend of path-planning algorithms was projected. Results: Through the research and analysis of the path-planning algorithm, it was found that the path- planning algorithm before the improvement had the problems of an unsmooth path, low computational efficiency, a slow response time, the inability to safely avoid obstacles, etc. After the improvement and optimization of the path-planning algorithm, the performance was greatly improved. Conclusion: After research and analysis, it was found that multi-algorithm fusion had great potential for development in path-planning compared to the application and optimization of a single algorithm. In addition, further research is needed in the areas of algorithm adaptability, fusion, intelligent algorithms, and extending the range of algorithmic applications.

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.

Ship model-based route optimisation for decision support in deep sea shipping

Abstract We present a new approach and route optimization methodology to support analysis and planning of vessel and fleet performance in deep sea shipping for green, energy efficient, and safe navigation. The developed methodology combines the ship technical characteristics based on a ship model developed for a particular vessel type and energy-saving technology options and an optimization algorithm taking into account weather conditions. Optimization involves two stages: graph construction and Dynamic Programming labelling algorithm implemented to solve the shortest path problem with variable speed. The new approach is implemented as part of a decision-support tool EcoRouter enabling the user to conduct analysis of safe and Pareto optimal solutions. Several applications to support real fleet planning and ship performance analysis have been identified including project engineering for future energy-saving ship technologies, for example, wind-assisted propulsion.

Solving the Robust Shortest Path Problem with Multimodal Transportation

This paper explores the challenges of finding robust shortest paths in multimodal transportation networks. With the increasing complexity and uncertainties in modern transportation systems, developing efficient and reliable routing strategies that can adapt to various disruptions and modal changes is essential. By incorporating practical constraints in parameter uncertainty, this paper establishes a robust shortest path mixed-integer programming model based on a multimodal transportation network under transportation time uncertainty. To solve robust shortest path problems with multimodal transportation, we propose a modified Dijkstra algorithm that integrates parameter uncertainty with multimodal transportation. The effectiveness of the proposed multimodal transportation shortest path algorithm is verified using empirical experiments on test sets of different scales and a comparison of the runtime using a commercial solver. The experimental results on the multimodal transportation networks demonstrate the effectiveness of our approach in providing robust and efficient routing solutions. The results demonstrate that the proposed method can generate optimal solutions to the robust shortest path problem in multimodal transportation under time uncertainty and has practical significance.

Shortest Path Problem under Pythagorean Fuzzy Network Using Dijkstra’s Algorithm

In this article investigates the Shortest Path Problem (SPP) in uncertain settings using Pythagorean fuzzy numbers (PFNs). A heuristic methodology using modified Dijkstra's algorithm is developed to exploit error, uncertainty, and partial truth for a low-cost solution. The method calculates minimum distance between starting and destination nodes and evaluates its effectiveness. Pythagorean fuzzy graphs can handle ambiguous situations.

Reconfiguration of vertex-disjoint shortest paths on graphs

We introduce and study reconfiguration problems for (internally) vertex-disjoint shortest paths:Given two tuples of internally vertex-disjoint shortest paths for fixed terminal pairs in an unweighted graph, we are asked to determine whether one tuple can be transformed into the other by exchanging a single vertex of one shortest path in the tuple at a time, so that all intermediate results remain tuples of internally vertex-disjoint shortest paths.We also study the shortest variant of the problem, that is, we wish to minimize the number of vertex-exchange steps required for such a transformation, if exists. These problems generalize the well-studied Shortest Path Reconfiguration problem. In this paper, we analyze the complexity of these problems from the viewpoint of graph classes, and give some interesting contrast.

A nonlinear model predictive control method for ship path following in waves

ABSTRACT With the development of intelligent ships, the problem of ship path following has attracted much attention in recent years. Ship motion is inevitably affected by an external environment and thus the design of the ship control system in currents or waves, etc. has always been a challenging work. In the present work, a Nonlinear Model Predictive Control (NMPC) method is proposed for ship path following in waves. The NMPC controller can obtain the desired rudder angle of nonlinear ship system by solving an open-loop optimisation problem. The NMPC controller integrated with a Line-of-Sight (LOS) guidance is proposed and applied for a container ship which is controlled to follow two desired paths in both calm water and waves. The simulation results demonstrate the more effectiveness and greater anti-interference of the proposed NMPC method, compared with that the results by using a traditional Proportional-Derivative (PD) control method.

Node-to-Node and Node-to-Set Disjoint Paths Problems in Bicubes

Node-to-Node and Node-to-Set Disjoint Paths Problems in Bicubes

The Multi-Objective Shortest Path Problem with Multimodal Transportation for Emergency Logistics

The optimization of emergency logistical transportation is crucial for the timely dispatch of aid and support to affected areas. By incorporating practical constraints into emergency logistics, this study establishes a multi-objective shortest path mixed-integer programming model based on a multimodal transportation network. To solve multi-objective shortest path problems with multimodal transportation, we design an ideal point method and propose a procedure for constructing the complete Pareto frontier based on the k-shortest path multi-objective algorithm. We use modified Dijkstra and Floyd multimodal transportation shortest path algorithms to build a k-shortest path multi-objective algorithm. The effectiveness of the proposed multimodal transportation shortest path algorithm is verified using empirical experiments carried out on test sets of different scales and a comparison of the runtime using a commercial solver. The results show that the modified Dijkstra algorithm has a runtime that is 100 times faster on average than the modified Floyd algorithm, which highlights its greater applicability in large-scale multimodal transportation networks, demonstrating that the proposed method both has practical significance and can generate satisfactory solutions to the multi-objective shortest path problem with multimodal transportation in the context of emergency logistics.

LPulse: An efficient algorithm for service function chain placement and routing with delay guarantee

Modern network services increasingly depend on the effective orchestration of the Service Function Chain (SFC) with stringent end-to-end delay guarantees. To achieve this, the Delay-Constrained Service Function Chain Placement and Routing (DC-SFCPR) problem must be addressed. This problem involves the optimal selection of nodes for placing network functions and routes that adhere to a specific sequence of service functions, to minimize network bandwidth and CPU costs while strictly adhering to stringent end-to-end delay constraints. The DC-SFCPR problem is NP-hard and existing algorithms either fail to guarantee strict delay constraints or are computationally expensive, making them unsuitable for expanding network topologies. We propose the LPulse algorithm, designed to efficiently solve the DC-SFCPR problem. This algorithm utilizes a layered graph to embed the requirements of service functions, transforming the DC-SFCPR problem into a Delay-Constrained Shortest Path (DCSP) problem. The LPulse algorithm then applies Pulse, a depth-first search framework enhanced with efficient pruning strategies, and incorporates two novel acceleration strategies to solve the DCSP problem. We prove that LPulse ensures the optimality of solutions. Evaluations conducted across various topologies, with node scales ranging from 22 to 10,000, show that LPulse surpasses existing algorithms in both solution quality and speed. For instance, the number of cases meeting strict delay constraints with LPulse is 1.9× that of those solved by deep reinforcement learning algorithms; furthermore, its solving efficiency is 4.9× that of the highest-performing existing optimal algorithm, the LagrangianKsp algorithm.

Literature Review on Fresh Products Cold Chain Logistics and Distribution Issues

In this paper, the literature on the concepts of fresh product cold chain logistics, the container operation problems related to cold chain transport, product order picking, distribution and the integration of the two problems are sorted out to provide theoretical references for the further study of the transport and distribution problems of fresh product cold chain logistics. Through combing the literature at home and abroad, the current fresh product cold chain logistics transport and distribution mainly exists in the container intermodal transport research object is single, mostly focusing on the railway container centre station; order distribution problems related research is less, vehicle path problem solving algorithms and related mathematical models are less; order picking and distribution of the joint research is less, and most of them stay in the theoretical stage, the method of landing is more difficult and other problems.

A practical path planning method for optimal repair paths between multiple small-size defects

Purpose This study aims to solve the problem of repair path planning between multiple small-size defects in the field of additive manufacturing (AM) repair by using Python-based ant colony algorithm (ACO). The optimal parameter combination scheme is obtained by discussing the influencing factors of parameters in the ACO. Design/methodology/approach The effects of the information heuristic factor α, the expected heuristic factor ß and the pheromone volatile factor ρ on the simulation results were investigated by designing a three-factor and three-level orthogonal experiment. The fast convergence of ACO in finding the optimal solution of multiple small-size defect repair path problem is proved by comparing the simulation results with those of genetic algorithm (GA) on the same data set. Findings The ACO can effectively solve the repair path planning problem between multiple small-size defects by optimizing the parameters. In the case of 50 defect locations, the simulation results of the ACO with optimized parameters are 159.8 iterations and 3,688 average path lengths, while the GA has 4,027.2 average path lengths under the same data set and the same number of iterations, and by comparison, it is proved that the ACO can find the optimal solution quickly in the small-size defects repair path planning problem, which greatly improves the efficiency of defect repair. Originality/value The parameter-optimized ACO can be quickly applied to the planning problem of repair paths between multiple small-size defects in the field of AM repair, which can better improve the defect repair efficiency and reduce the waste of resources.

Research on motion planning system for wall-climbing mobile manipulator for large steel structures welding operation

Purpose The purpose of this study is to address the welding demands within large steel structures by presenting a global spatial motion planning algorithm for a mobile manipulator. This algorithm is based on an independently developed wall-climbing robot, which comprises a four-wheeled climbing mobile platform and a six-degree-of-freedom robotic manipulator, ensuring high mobility and operational flexibility. Design/methodology/approach A convex hull feasible domain constraint is developed for motion planning in the mobile manipulator. For extensive spatial movements, connected sequences of convex polyhedra are established between the composite robot’s initial and target states. The composite robot’s path and obstacle avoidance optimization problem are solved by constraining the control points on B-spline curves. A dynamic spatial constraint rapidlye-xploring random trees-connect (RRTC) motion planning algorithm is proposed for the manipulator, which quickly generates reference paths using spherical spatial constraints at the manipulator’s end, eliminating the need for complex nonconvex constraint modeling. Findings Experimental results show that the proposed motion planning algorithm achieves optimal paths that meet task constraints, significantly reducing computation times in task conditions and shortening operation times in non-task conditions. Originality/value The algorithm proposed in this paper holds certain application value for the realization of automated welding operations within large steel structures using mobile manipulator.