Path Optimization Problem Research Articles

Optimisation of Urban Logistics Distribution Routing with Time Window

Reasonable optimization of the path can not only reduce unnecessary logistics cost expenditure; efficient circulation speed can also enhance the economic development of the city. In the process of the transformation of the model, it will be directly affected by the change of the importance of logistics enterprises to logistics distribution work. Based on the background of urban logistics, the optimization process of multi-logistics distribution path with time window is comprehensively studied. The relevant theoretical knowledge involved in the distribution link is reviewed, and through the analysis of the existing problems of urban logistics and the vehicle path optimization problem, the heuristic algorithm is used to establish the path optimization model of urban logistics center with time window, which reduces the vehicle transportation cost, thus reducing the total cost of logistics, and at the same time, improves the efficiency of the internal circulation of urban logistics and accelerates the economic development.

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.

Optimization Analysis of Smart Energy Systems in the Fresh Supply Chain Based on Differential Games

The energy issue has gradually become a major focus of strategic competition among major nations in the contemporary world. Achieving a balance between energy, cost, and ecology is crucial, particularly in specific contexts. As one of the critical factors influencing global climate, carbon emissions have consistently been a green indicator of concern for countries worldwide. This paper addresses optimizing energy costs in the cold chain transportation of the fresh supply chain to obtain a model with low carbon emissions and transportation costs. Initially, the paper explores the equilibrium between energy and cost optimization using the theoretical framework of differential games in game theory. Building upon this, an intelligent energy system is proposed, and a basic model for constructing a smart grid is provided based on commonly used electric power. Using this as the foundational concept, a game model is constructed, considering the conflicting objectives of cost minimization, time efficiency, and energy conservation in addressing the primary issue of energy savings in the fresh supply chain, specifically the transportation path optimization problem. Compared to traditional models, the model presented in this paper reduces the scheduling of two refrigerated trucks. By optimizing this model, the transportation path's length is shortened by 5.50%, the carbon emission is decreased by 8.9%, and the model's overall cost is reduced by 4.94%. This study presents a game model that may efficiently optimize the fresh product transportation chain, reducing carbon emissions and expenses. The model has certain practical applications and serves as a guide.

Research on multi-path optimization problem based on particle swarm optimization algorithm

The problem of finding the optimal path within a certain range exists in various scenarios in our lives, such as the traveling salesman problem, robot automatic path selection problem, vehicle and pedestrian navigation, game path navigation, communication routing, logistics and transportation planning problems, etc. , through the optimization of path problems, we can help people improve resource utilization, improve work efficiency, reduce production costs, or complete the goal of a specific scenario, etc. Therefore, solving the path optimization problem is a very important task in our reality. In order to improve the game experience of the players in the game, this paper studies how to use the particle swarm optimization method to solve the optimal route of NPC.

Physical Delivery Network Optimization Based on Ant Colony Optimization Neural Network Algorithm

The development of modern logistics chains is not just simple cargo transportation, it has become a cross-integrated industry that integrates many emerging technologies such as IoT technology, intelligent transportation, cloud computing and mobile Internet. Based on the ant colony algorithm (ACA), this paper optimizes the physical delivery network of the optimized neural network algorithm, establishes a mathematical model for the constraints and optimization objectives in the optimization of the physical delivery path, and proposes some improvements to the ACA to improve the convergence of the algorithm. speed and global search ability, so as to use the improved algorithm to solve the physical delivery path optimization problem. Experiments show that the optimal distance of physical delivery path planning calculated by traditional ACA is 207.8544km, while the optimal distance of improved ACA path planning is 197.9879km. The performance of the improved ACA is improved by analyzing the results of solving typical examples.

Desensitized Optimal Control

Desensitized optimal control (DOC) enables the formulation of optimal control problems that incorporate the optimal reference solution’s sensitivities to state perturbations into the optimization process. Mathematically, this is achieved through the introduction of Lagrange multiplierlike quantities that act as additional state variables and capture the desired sensitivity information. By penalizing user-specified sensitivities, the reference solution becomes easier to control under feedback. Thus, the DOC method can be viewed as a method to improve nonlinear robustness. By converting fixed parameters appearing in the problem formulation to state variables with trivial dynamics, the DOC approach can be used to improve robustness to parameter uncertainties. The paper also analyzes the relationship between sensitivities and the covariance matrix and compares the benefits and limitations of covariance shaping versus DOC. A simple Zermelo-type boat path optimization problem with uncertainties in the water current is analyzed to demonstrate the DOC approach.

Large Scale Customer Points in Genetic Algorithms

Aiming at the path optimization problem of pharmaceutical green logistics distribution, a green logistics path optimization model is designed considering constraints such as time window limitation and vehicle capacity, with the optimization objective of minimizing the sum of vehicle transportation cost, overtime cost and green cost, and the constructed model is solved by using genetic algorithm. The constructed model and designed algorithm are verified by actual distribution data. The example experiments show that the genetic algorithm has better solution quality, higher efficiency and more stable results in solving the vehicle path problem at large-scale customer locations. The research results not only expand the vehicle path problem, but also provide decision-making reference for the distribution optimization of related express logistics enterprises.

Trajectory optimization with hybrid probabilistic roadmap approach to achieve time efficient navigation of unmanned vehicles in unstructured environment

PurposeThis paper aims to focus on solving the path optimization problem by modifying the probabilistic roadmap (PRM) technique as it suffers from the selection of the optimal number of nodes and deploy in free space for reliable trajectory planning.Design/methodology/approachTraditional PRM is modified by developing a decision-making strategy for the selection of optimal nodes w.r.t. the complexity of the environment and deploying the optimal number of nodes outside the closed segment. Subsequently, the generated trajectory is made smoother by implementing the modified Bezier curve technique, which selects an optimal number of control points near the sharp turns for the reliable convergence of the trajectory that reduces the sum of the robot’s turning angles.FindingsThe proposed technique is compared with state-of-the-art techniques that show the reduction of computational load by 12.46%, the number of sharp turns by 100%, the number of collisions by 100% and increase the velocity parameter by 19.91%.Originality/valueThe proposed adaptive technique provides a better solution for autonomous navigation of unmanned ground vehicles, transportation, warehouse applications, etc.

A Multi-strategy Enhanced Arithmetic Optimization Algorithm and Its Application in Path Planning of Mobile Robots

A multi-strategy enhanced arithmetic optimization algorithm called MSEAOA is proposed to address the issues of low population diversity, imbalanced exploration and exploitation capabilities, and low accuracy of optimal solution in the Arithmetic Optimization Algorithm. Firstly, using the good point set strategy for population initialization to improve population diversity and thus accelerate convergence speed. Secondly, we integrate the exploration and exploition capabilities of differential self-learning strategy, best example learning strategy, and second-order differential perturbation strategy balancing algorithm. Finally, the introduction of somersault foraging strategy improves the accuracy of the optimal solution. We select 14 classical benchmark test functions and the CEC2019 function test set to test the optimization ability of MSEAOA, and apply MSEAOA to the path planning problem of mobile robots. MSEAOA is compared with other meta-heuristic optimization algorithms, and the experimental results are statistically analyzed by the Wilcoxon rank-sum test. The simulation experimental results show that MSEAOA performs the best among 14 benchmark functions, but for 10 CEC2019 functions, MSEAOA has the best optimization performance among 5 of them (50%). In the path optimization problem of mobile robots, the path obtained by MSEAOA is also the best among all algorithms, its path shortening rate exceeds 8.8% in 83% of environments. The results indicate that MSEAOA is a reliable algorithm suitable for function optimization and practical optimization problems.

Measuring the similarity between shapes of buildings using graph edit distance

ABSTRACT Building data play a crucial role in geographic information science, and building shape similarity can be used for spatial inquiry, cartographic generalization, map updating, data quality assessment, and other spatial data mining applications. However, conventional shape representation and measurement methods use geometric and statistical measures and may not effectively capture the subtle differences among building shapes. Geospatial artificial intelligence methods often overlook nuanced differences in building contours, posing a challenge when precise fine-grained measurements are required. Furthermore, they have low interpretability. This study proposes a graph edit distance-based method for measuring the similarity between building shapes. It uses geometrics characteristics to construct a graph, matches and associates similar regional features between two building contours, and defines edit costs based on geometric and positional differences that align with the Gestalt principle of visual similarity. It converts the optimal edit path problem to the maximum weighted cluster solution problem and utilizes a heuristic approach to achieve the exact optimal solution within a moderately suitable timeframe. The experimental results demonstrated that the proposed method identifies detailed differences between building contours, providing accurate similarity measurement with high interpretability.

A Snowmelt Optimization Algorithm Applied to Green Low Carbon Logistics Pathways Optimization Problems

INTRODUCTION: Efficient and accurate optimization of green and low-carbon logistics paths, as one of the key technologies of green and low-carbon logistics, can not only promote the high-quality development of the economy, but also reduce the negative impacts of logistics on the environment and increase the cost of logistics delivery.
 OBJECTIVES: To address the problems of slow convergence and easy to fall into local optimization in the current performance prediction research on talent team building.
 METHODS: This paper proposes a snowmelt heuristic optimization algorithm to solve the green low-carbon logistics path optimization problem. Firstly, the objective function of green low-carbon logistics path optimization is designed by analyzing the optimization cost and conditional constraints of the green low-carbon logistics path optimization problem; then, a method based on intelligent optimization algorithm is proposed by designing the position-order array coding and fitness function, combined with the snow-melting optimization algorithm; finally, the validity and superiority of the proposed method are verified by simulation experiments.
 RESULTS: The results show that the proposed method not only improves the convergence speed but also increases the optimization fitness value.
 Conclusion: The problem of slow convergence and easy to fall into local optimum in the solution of green low-carbon logistics path optimization problem is solved.

Research on Path Optimization of Vehicle-Drone Joint Distribution considering Customer Priority

To meet the personalized distribution needs of customers, comprehensively consider customer value, the urgency of customer needs, and the impact of priority distribution to the customer on the enterprise, and based on regional restrictions, put forward vehicle-drone joint distribution path optimization problem considering customer priority. First, the goal is to minimize the sum of total distribution cost and customer priority cost integrating soft time windows and constructing a path optimization model of the vehicle-drone joint distribution. Second, a two-stage hybrid algorithm is proposed for the problem model. In the first stage, the deep neural network and the grid search improved support vector machine algorithm (DNN-GSM-SVM) are used to screen and classify customer priority features, and in the second stage, adaptive large-scale neighborhood search improved genetic algorithms (ALNS-GA) are used to solve the problem of vehicle-drone joint distribution path planning problem. Finally, combined with the numerical example, the optimization scheme of the vehicle-drone joint distribution path considering priority is analyzed. Compared with the three algorithms and error analysis, the effectiveness of the model and the two-stage algorithm was verified. Compared with the results of the scheme that does not consider priority, the results show that priority can significantly improve customer satisfaction. The efficiency of the vehicle-drone joint distribution was verified by comparing the three scenarios.

A precise solution to the shortest path optimization problem in graphs using Z-numbers

<p>Communication networks are exposed to internal or external risks that can affect all or part of the system. The most important components that form the infrastructure of these systems are routers, which act as nodes. In the field of graph theory, there are sophisticated techniques that can be used to optimize the path of a packet as it travels through various routers from its origin to its destination. A notable example of such an algorithm is Dijkstra's algorithm, which is designed to efficiently determine the shortest path. The algorithm works under the assumption that the system operates under ideal conditions. Real-time systems can perform better if risk factors and optimal conditions are taken into account. The relationship between the nodes can be expressed by various metrics such as distance, delay, and bandwidth. The aforementioned metrics facilitate the calculation of the optimal path, with the ultimate objective of achieving low-latency networks characterized by rapid response times. Round-trip time (RTT) can be employed as a metric for measuring enhancements in a range of latency types, including those associated with processing, transmission, queuing, and propagation. The use of Z-numbers was employed in this study to incorporate risk into the optimal path metric. RTT was the preferred metric and reliability was represented by fuzzy linguistic qualifiers. A comparison of several scenarios was shown using a numerical example of a communication network. It is expected that this study will have a significant impact on the evolution from models that consider only ideal conditions to real-time systems that include risks using Z-numbers.</p>

Path Planning for Unified Scheduling of Multi-Robot Based on BSO Algorithm

The technology for path planning of independent mobile robots is mature, but multi-robot path planning for unified scheduling and allocation is much more complex than single-robot path planning. This requires consideration of collision problems between robots, general optimal path problems, etc. This paper proposes the use of the BSO algorithm for unified scheduling and allocation of multiple robots to improve the efficiency of task execution. The BSO algorithm is a new type of intelligent optimization algorithm that uses clustering ideas to search for local optimal solutions and obtains global optimal solutions by comparing local optimal solutions. It also uses mutation ideas to increase the diversity of the algorithm and avoid becoming trapped in local optimal solutions. Using the GA/SA algorithm and the proposed BSO algorithm for computer simulation comparison, we obtained the optimal path planning for the three robots under unified scheduling. The total distance of the optimal path obtained by the BSO algorithm was 27.36% and 25.31% shorter than those of the GA and SA algorithms, respectively. To further test the performance of the BSO algorithm, we conducted additional experiments on the unified scheduling of multiple robots. The experimental results show that the proposed BSO algorithm can significantly improve the efficiency. The multi-robot under unified scheduling performs point-to-point path planning without collisions, and they can traverse all task target points in the shortest path without repetition. This algorithm is suitable for multi-robot tasks in large-scale environments.

SOZIL: Self-Optimal Zero-Shot Imitation Learning

Zero-shot imitation learning has demonstrated its superiority to learn complex robotic tasks with less human participation. Recent studies show convincing performance under the condition that the robot follows the demonstration strictly by the learned inverse model. However, these methods are difficult to achieve satisfactory performance in imitation when the demonstration is suboptimal, and the learning of the learned inverse models is vulnerable to label ambiguity issues. In this paper, we propose Self-Optimal Zero-shot Imitation Learning (SOZIL) to tackle these problems. The contribution of SOZIL is twofold. First, Goal Consistency Loss (GCL) is designed to learn the multi-step goal-conditioned policy from exploration data. By directly using the goal state as supervision, GCL solves the label ambiguity problem caused by trajectory and action diversity. Second, Estimation-based Keyframe Extraction (EKE) is developed to optimize demonstrations. We formulate the keyframe extraction process as a path optimization problem under suboptimal control. By predicting the performance of the learned policy in executing transitions of any two states, EKE creates a directed graph containing all candidate paths and extracts keyframes by solving the graph’s shortest path problem. Furthermore, the proposed method is evaluated with various simulated and real-world robotic manipulating experiments such as cable harness assembly, rope manipulation, and block moving. Experimental results show that SOZIL achieves a superior success rate and manipulation efficiency than baselines.

APPLICATION OF LANCHESTER'S MATHEMATICAL LAWS IN MILITARY STRATEGY

Mathematics, as the science of numbers, structures, and models, plays an important role in many aspects of military operations and strategies. From calculating the probability of success or failure of military operations to determining the best ways to deploy troops and resources, mathematics provides military strategists with powerful tools to make informed and effective decisions. One of the most important aspects of using mathematics in the military is developing strategies for combat operations. From determining the location of troops and the size of forces to the conditions of operations, mathematical methods and models help to optimize decisions. To determine the probability of success of military operations, mathematics uses probability theory and statistics. This allows us to estimate the probability of achieving the goal, taking into account various factors such as military equipment, enemy location, and other external conditions. The analysis of previous military conflicts and data allows us to statistically estimate probability distributions and predict military events. Mathematics also plays an important role in solving logistics and resource allocation problems. Determining the optimal route for the movement of troops and resources can be formulated as a path optimization problem. Mathematical methods are also used in the field of intelligence and the development of new technologies. Cryptography, which protects important information from unauthorized access, is based on complex mathematical algorithms. Mathematical models can also be used to simulate military operations, study the impact of new weapons systems, or analyze missile trajectories. It is worth adding that mathematical laws help to analyze and predict the outcomes of military conflicts, in particular, to determine the impact of the size and effectiveness of the enemy forces on the probability of success. In this article, the main focus is on the laws of Lanchester's mathematical models. The article presents the derivation of Lanchester's linear law and an example of its application. The mathematical principles of the quadratic Lanchester's law are considered on an example. It is indicated and highlighted how these mathematical laws can be applied in the context of the Russian-Ukrainian conflict.

Optimization of Personnel Work Paths During Decommissioning of Nuclear Facilities

During the decommissioning process of nuclear facilities, workers are exposed to radiation and face the risk of exceeding safe dose limits. Ensuring the safety of personnel requires not only enhancing radiation protection measures but also optimizing work paths to minimize exposure time and avoid high-radiation areas. This paper proposes a nested optimization algorithm that combines an ant colony optimization (ACO) with an improved A* algorithm for the decommissioning of a nonradiation source. The algorithm aims to minimize the total radiation dose and transforms the original path optimization problem into an equivalent traveling salesperson problem. The improved A* algorithm is employed in the inner layer to calculate the path with the lowest radiation dose for any given sales order. The ACO operates in the outer layer to determine a set of optimal working paths that traverse all target points. The provided solution example demonstrates that the proposed path optimization algorithm effectively integrates the radiation field and obstacles. It successfully identifies a sequence for dismantling with the lowest dose and corresponding optimal work path while ensuring the completion of the dismantling task. These findings are expected to offer valuable insights for optimizing personnel work paths during the subsequent decommissioning process of nuclear facilities.

Lightweight 3D hand pose estimation by cascading CNNs with reinforcement learning

This paper proposes a novel strategy for lightweight 3D hand pose estimation. The strategy decomposes the estimation process into feature extraction and feature exploitation, where feature extraction performs dimension reduction on the original input and outputs feature vectors. Feature exploitation is further analyzed and considered as a path optimization problem, and reinforcement learning (RL) is proved to be capable of tackling the problem accurately. A framework cascading convolutional neural networks (CNNs) and RL is next introduced to validate the effectiveness of the proposed strategy, where two different backbones are used to extract features, and RL is extended into continuous space to enhance accuracy. Ablation studies and experiments are carried out on NYU and ICVL datasets using the proposed strategy with continuous RL. The results show that the accuracy of continuous RL exceeds discrete RL, and the rapidity and accuracy leads the backbones. Comparative studies show the strategy achieves leading rapidity and accuracy in single-view depth-based methods.

Multivisit Drone-Vehicle Routing Problem with Simultaneous Pickup and Delivery considering No-Fly Zones

The employment of drones for the distribution of goods represents a significant avenue for addressing logistical challenges at the end of the supply chain. The truck-drone cooperative delivery model overcomes drone limitations such as limited capacity and endurance and has emerged as a crucial mode of drone participation in logistics delivery. This delivery model effectively reduces delivery costs and shortens delivery times. Herein, we examine a variant of the truck-drone routing problem, which encompasses the strategic deployment and routing of multiple fleets of trucks, each equipped with an auxiliary drone. The objective is to fulfill all the pickup and delivery demands of a designated customer base while minimizing the overall route cost. Within this problem domain, drones are authorized to serve multiple customers within their capacity and endurance limits, providing both pickup and delivery services during each trip. However, the utilization of drones for servicing all customers is impeded by the existence of no-fly zones that have been implemented in numerous cities worldwide. These prescribed no-fly zones cause significant challenges when attempting to optimize the routing of truck-drone operations. Thus, this study constructs a mixed integer linear programming (MILP) model for the path optimization problem of joint service of trucks and drones considering no-fly zones and simultaneous pickup and delivery. Given the intricacy of the MILP model, we propose a two-stage heuristic algorithm based on a simulated annealing approach, combined with strategies for rectifying infeasible solutions and expediting algorithmic processes. During the phase of computational experimentation, we explore the advantages derived from enabling drones to serve multiple customers and assess the effectiveness of the proposed model and two-stage heuristic algorithm. Finally, sensitivity analysis is conducted on two key parameters.

NFLCS: An Service Function Chain Path Optimization Strategy Based on Network-Functional Layout Clustering

Under the background of 5 G and 6 G super bandwidth and ultra-low delay, Software Defined Networking and Network Function Virtualization (SDN&NFV) makes the communication technology develop rapidly. Service Function Chain (SFC) selection is a crucial aspect of SDN&NFV, which faces many challenges of poor algorithm performance, high latency, and low profit. Moreover, most of the existing studies are stuck in optimizing for a single metric, which leads to a poor generalization of the proposed path optimization method. In this paper, we propose an SFC path optimization strategy based on the clustering of network functional layouts to address the urgent problem. First, we design a topological network identification algorithm, model the SFC path optimization problem as an attention problem and use a multi-headed attention mechanism to optimize different kinds of SFC layouts in a targeted manner. Among them, the multi-headed attention mechanism achieves the effective capture of multiple features in the SFC path selection problem compared with the traditional strategy. The experimental results demonstrate the effectiveness of Network-Functional Layout Clustering Strategy (NFLCS) in optimizing SFC paths and show the ability to optimize the service function chain paths well in future complex network situations.