Salesman Problem Research Articles

OPTIMIZING CARTON PRODUCT DELIVERY BY SOLVING TRAVELLING SALESMAN PROBLEM AT PACKAGING COMPANIES

Optimization of delivery routes is one form of increasing business productivity to achieve the company's main goal of distributing each product to customers. The Traveling Salesman Problem (TSP) is a combinatorial optimization problem where a salesman goes on a distribution journey that starts from the depot, then visits all customers exactly once, and ends with returning to the depot. This study aims to optimize the distribution route of carton products for packaging companies using the TSP model. The research methodology includes observation, interviews, and document studies to understand the distribution process of carton products at packaging companies. To complete the TSP model, Branch and Bound (BB) and Nearest Neighbor (NN) methods are applied to find the best solution for determining the distribution route of carton products. The way the BB method works is by utilizing branch cuts and boundaries to reduce search space and speed up the resolution process. In the NN method, the nearest point is chosen to get the shortest route distance. Research findings show that the use of the BB method results in a mileage difference from the initial route of 125 km (53% more efficient) and a fuel cost difference of 121,231 IDR (45% cheaper). Meanwhile, the NN method results in a mileage difference from the initial route of 115 km (48.94%) and a fuel cost difference of 109,901 IDR (41.27%). So, the method that produces the best solution is the BB method. The limitations of this study lie in the scale of the model used and the assumptions underlying the analysis. Future research can broaden the scope of the model and consider other factors that may affect the distribution of carton products. The results of this study contribute to improving the efficiency of carton product distribution.

Combining spatial clustering and tour planning for efficient full area exploration

AbstractAutonomous exploration in unknown environments has become a critical capability of mobile robots. Many methods often suffer from problems such as exploration goal selection based solely on information gain and inefficient tour optimization. Recent reinforcement learning-based methods do not consider full area coverage and the performance of transferring learned policy to new environments cannot be guaranteed. To address these issues, a dual-stage exploration method has been proposed, which combines spatial clustering of possible exploration goals and Traveling Salesman Problem (TSP) based tour planning on both local and global scales, aiming for efficient full-area exploration in highly convoluted environments. Our method involves two stages: exploration and relocation. During the exploration stage, we introduce to generate local navigation goal candidates straight from clusters of all possible local exploration goals. The local navigation goal is determined through tour planning, utilizing the TSP framework. Moreover, during the relocation stage, we suggest clustering all possible global exploration goals and applying TSP-based tour planning to efficiently direct the robot toward previously detected but yet-to-be-explored areas. The proposed method is validated in various challenging simulated and real-world environments. Experimental results demonstrate its effectiveness and efficiency. Videos and code are available at https://github.com/JiatongBao/exploration.

Cumulative Capacitated Colored Traveling Salesman Problem.

A colored traveling salesman problem (CTSP) is a generalization of the well-known multiple traveling salesman problem, which introduces colors to distinguish the accessibility of its cities to salesmen. This work proposes a city/customer-centric model called cumulative capacitated CTSP (C2-CTSP) to tackle some practical problems with fast response requirements. Its hypergraph and mathematical programming formulations are developed for the first time. A general variable neighborhood search (GVNS) metaheuristic is designed to solve it. Specifically, greedy backtracking is proposed to initialize a solution taking into account the cumulative cost and two constraints including colors and capacities. Next, 2-swap, reinsertion, and double-bridge operations are randomly selected and carried out to execute the perturbation. Moreover, neighborhood-list-2-opt, relocation move, and generalized partition crossover are organized as variable neighborhood descent to constitute the local search for better solutions. Extensive experiments are conducted to compare the proposed GVNS with four genetic algorithms, two hybrid ant colony systems, two variable neighborhood search methods, and a perturb-based local search in 20 regular and random cases. The statistical results demonstrate that GVNS is superior to all competitors tuned by irace package in terms of both search ability and convergence rate. In addition, the study of six GVNS variants lacking different operators validates the significant role of each corresponding operator in GVNS's outstanding performance.

Distribution of Soap X in East Java Region with Bhumal Method and Traveling Salesman Problem

The product distribution process is an effort by producers to deliver their products to consumers with a registered and programmed system. Product distribution to consumers must be handled carefully and carefully. Because this can be one of the obstacles for companies in winning competition with other companies if the distribution speed is not high. The speed or slowness of product distribution to consumers, one of which depends on the proximity between the dealer's warehouse and the market (consumers). The purpose of this data presentation and analysis is to better understand how to make data, analyse, and make conclusions that can determine a decision on a logistics process in general and bar soap products with transportation cost optimisation using the bhumal method and Traveling Salesman Problem.

Enhanced Dynamic Programming Approaches for Efficient Solutions to the Traveling Salesman Problem

This study aims to enhance dynamic programming techniques for efficiently solving the Traveling Salesman Problem, a fundamental combinatorial optimization challenge. Given its NP-hard classification, traditional exact algorithms become computationally infeasible as the problem size increases. The research revisits foundational dynamic programming principles, notably the Held-Karp algorithm, and identifies existing limitations. The study begins with a comprehensive literature review, followed by an analysis of the dynamic programming challenges specific to TSP. Novel algorithms are then developed, implemented, and rigorously tested against benchmark instances. Performance evaluation is conducted using metrics such as execution time, memory usage, and solution optimality across different problem sizes. Results demonstrate significant improvements in efficiency and scalability, with enhanced algorithms achieving optimal solutions in reduced time and computational resource usage. However, the exponential growth in complexity remains a challenge for larger instances. The study concludes with recommendations for future research, focusing on further algorithmic refinements and exploring hybrid approaches to address large-scale TSPs.

Advanced UAV Material Transportation and Precision Delivery Utilizing the Whale-Swarm Hybrid Algorithm (WSHA) and APCR-YOLOv8 Model

This paper proposes an effective material delivery algorithm to address the challenges associated with Unmanned Aerial Vehicle (UAV) material transportation and delivery, which include complex route planning, low detection precision, and hardware limitations. This novel approach integrates the Whale-Swarm Hybrid Algorithm (WSHA) with the APCR-YOLOv8 model to enhance efficiency and accuracy. For path planning, the placement paths are transformed into a Generalized Traveling Salesman Problem (GTSP) to be able to compute solutions. The Whale Optimization Algorithm (WOA) is improved for balanced global and local searches, combined with an Artificial Bee Colony (ABC) Algorithm and adaptive weight adjustment to quicken convergence and reduce path costs. For precise placement, the YOLOv8 model is first enhanced by adding the SimAM attention mechanism to the C2f module in the detection head, focusing on target features. Secondly, GhoHGNetv2 using GhostConv is the backbone of YOLOv8 to ensure accuracy while reducing model Params and FLOPs. Finally, a Lightweight Shared Convolutional Detection Head (LSCDHead) further reduces Params and FLOPs through shared convolution. Experimental results show that WSHA reduces path costs by 9.69% and narrows the gap between the best and worst paths by about 34.39%, compared to the Improved Whale Optimization Algorithm (IWOA). APCR-YOLOv8 reduces Params and FLOPs by 44.33% and 34.57%, respectively, with mAP@0.5 increasing from 88.5 to 92.4 and FPS reaching 151.3. This approach can satisfy the requirements for real-time responsiveness while effectively preventing missed, false, and duplicate detections during the inspection of emergency airdrop stations. In conclusion, combining bionic optimization algorithms and image processing significantly enhances the efficiency and precision of material placement in emergency management.

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.

An Integrated Route and Path Planning Strategy for Skid–Steer Mobile Robots in Assisted Harvesting Tasks with Terrain Traversability Constraints

This article presents a combined route and path planning strategy to guide Skid–Steer Mobile Robots (SSMRs) in scheduled harvest tasks within expansive crop rows with complex terrain conditions. The proposed strategy integrates: (i) a global planning algorithm based on the Traveling Salesman Problem under the Capacitated Vehicle Routing approach and Optimization Routing (OR-tools from Google) to prioritize harvesting positions by minimum path length, unexplored harvest points, and vehicle payload capacity; and (ii) a local planning strategy using Informed Rapidly-exploring Random Tree (IRRT*) to coordinate scheduled harvesting points while avoiding low-traction terrain obstacles. The global approach generates an ordered queue of harvesting locations, maximizing the crop yield in a workspace map. In the second stage, the IRRT* planner avoids potential obstacles, including farm layout and slippery terrain. The path planning scheme incorporates a traversability model and a motion model of SSMRs to meet kinematic constraints. Experimental results in a generic fruit orchard demonstrate the effectiveness of the proposed strategy. In particular, the IRRT* algorithm outperformed RRT and RRT* with 96.1% and 97.6% smoother paths, respectively. The IRRT* also showed improved navigation efficiency, avoiding obstacles and slippage zones, making it suitable for precision agriculture.

Flying Sidekick Traveling Salesman Problem in Truck–Drone Team Logistics with Energy Issues

Last-mile delivery has become increasingly important in recent years because of changes in customer needs. In this study, single-truck–multi-drone team logistics is considered. A mixed integer mathematical model is developed for the flying sidekick traveling salesman problem, a single-truck–multi-drone problem by considering technical and energy issues. Two different objective functions are used in the model. The first objective function is to minimize the sum of arrival times. Minimizing the sum of arrival times for customers also minimizes the distance traveled by the vehicles and, accordingly, the cost. The second objective function is to minimize total tardiness. A dataset is generated to test the proposed model. Trade-offs between the results for the two objective functions are analyzed. The technical requirements of the drone, energy limits, and fleet size are considered in the proposed mathematical model. The effects of the flight ranges of the drones are investigated with respect to the energy constraint. It has been observed that changes in the number of customers and drones affect the results of the objective functions. The total arrival time and tardiness decreased with increasing number of drones. Thus, the number of deliveries by truck decreases for customers. In addition, the advantages of this hybrid approach have been proven by comparing situations where only land vehicles are used with truck–drone team logistics.

A new heuristic for the continuous fixed-radius disc cover problem

The continuous fixed-radius disc cover (CFDC) problem is a location model to cover the given demand points by finding the minimum number of fixed-radius discs in the plane. It is an NP-hard problem, and only a few approximate algorithms have been proposed over the past three decades. In the article, a new heuristic called dynamic reduction (DR) is introduced. The heuristic works by initiating an upper bound on the number of discs, and then reducing the number by removing redundant discs during updates to the disc centres. Experimental results, using different radius settings on some datasets of a travelling salesman problem library (TSP-Lib), show that the proposed heuristic greatly outperforms the recent approximation algorithm in accuracy. Notably, an enhancement of the heuristic is also provided.

On a Traveling Salesman Problem for Points in the Unit Cube

Let X be an n-element point set in the k-dimensional unit cube [0,1]k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[0,1]^k$$\\end{document} where k≥2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k \\ge 2$$\\end{document}. According to an old result of Bollobás and Meir (Oper Res Lett 11:19–21, 1992) , there exists a cycle (tour) x1,x2,…,xn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x_1, x_2, \\ldots , x_n$$\\end{document} through the n points, such that ∑i=1n|xi-xi+1|k1/k≤ck\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left( \\sum _{i=1}^n |x_i - x_{i+1}|^k \\right) ^{1/k} \\le c_k$$\\end{document}, where |x-y|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|x-y|$$\\end{document} is the Euclidean distance between x and y, and ck\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_k$$\\end{document} is an absolute constant that depends only on k, where xn+1≡x1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x_{n+1} \\equiv x_1$$\\end{document}. From the other direction, for every k≥2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k \\ge 2$$\\end{document} and n≥2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n \\ge 2$$\\end{document}, there exist n points in [0,1]k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[0,1]^k$$\\end{document}, such that their shortest tour satisfies ∑i=1n|xi-xi+1|k1/k=21/k·k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left( \\sum _{i=1}^n |x_i - x_{i+1}|^k \\right) ^{1/k} = 2^{1/k} \\cdot \\sqrt{k}$$\\end{document}. For the plane, the best constant is c2=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_2=2$$\\end{document} and this is the only exact value known. Bollobás and Meir showed that one can take ck=9231/k·k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_k = 9 \\left( \\frac{2}{3} \\right) ^{1/k} \\cdot \\sqrt{k}$$\\end{document} for every k≥3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k \\ge 3$$\\end{document} and conjectured that the best constant is ck=21/k·k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_k = 2^{1/k} \\cdot \\sqrt{k}$$\\end{document}, for every k≥2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k \\ge 2$$\\end{document}. Here we significantly improve the upper bound and show that one can take ck=35231/k·k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_k = 3 \\sqrt{5} \\left( \\frac{2}{3} \\right) ^{1/k} \\cdot \\sqrt{k}$$\\end{document} or ck=2.91k(1+ok(1))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_k = 2.91 \\sqrt{k} \\ (1+o_k(1))$$\\end{document}. Our bounds are constructive. We also show that c3≥27/6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_3 \\ge 2^{7/6}$$\\end{document}, which disproves the conjecture for k=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=3$$\\end{document}. Connections to matching problems, power assignment problems, related problems, including algorithms, are discussed in this context. A slightly revised version of the Bollobás–Meir conjecture is proposed.

Hungarian Method and Branch and Bound Method for Solving Travelling Salesman Problem in Interval Number in Rice Distribution

Hungarian Method and Branch and Bound Method for Solving Travelling Salesman Problem in Interval Number in Rice Distribution

Symmetric optical multipass matrix systems and the general rapid design methodology

We proposed an original type of multipass cell named symmetric optical multipass matrix system (SMMS), in which the same matrix patterns of various sizes can be formed on both sides. According to its special symmetric configurations, the SMMS design problem is modeled as a variant of the classical traveling salesman problem, which can be rapidly solved by evolutionary optimization algorithms. Two sets of 3-mirror SMMSs are designed, analyzed and built, which show superior characteristics of high stability, desirable beam quality and adjustable optical path lengths. Additionally, they can support simultaneous detection of multiple species with multi-laser channels. The proposed method is further extended to design a 4-mirror SMMS, which verifies the universality and robustness of the design methodology. The experimental observations are in consistent with the theoretical calculations. The newly proposed SMMSs have a broad application prospect in trace gas measurement.

Picker routing in scattered storage warehouses: an evaluation of solution methods based on TSP transformations

AbstractTo optimize their order fulfillment processes, many e-commerce warehouses employ a storage assignment strategy known as scattered or mixed-shelves storage. Under this approach, unit loads of homogeneous products are divided, and individual pieces are stored in various shelves throughout the warehouse. This arrangement ensures that products that appear together on unpredictable pick lists are stored in close proximity somewhere in the huge warehouses, reducing the travel distance for pickers. Despite these advancements, efficiently guiding pickers through the warehouse remains a significant planning challenge. Since the same products can be found in multiple storage positions, the traditional picker routing problem becomes more complex, as an additional selection task arises regarding which shelf to retrieve each requested product from. While previous research has developed several tailor-made solution algorithms, we demonstrate that known transformation schemes used for different variants of the well-known Traveling Salesman Problem (TSP) can be utilized to convert the single picker routing problem with scattered storage (SPRP-SS) into a classical TSP. This approach enables us to leverage the extensive array of state-of-the-art TSP solvers. The purpose of this paper is to explore the performance of these solvers when applied to solving the SPRP-SS. Through our computational study, we found that existing TSP solvers exhibit good performance, allowing near-optimal solutions to be obtained in less than a second for real-world scale SPRP-SS instances. Moreover, the efficiency of these TSP solvers remains unaffected by the number of cross aisles in the warehouse. Consequently, we exploit this flexibility to investigate the impact of cross aisles on picking performance in scattered storage warehouses.

Bio-Inspired Optimization Algorithm Associated with Reinforcement Learning for Multi-Objective Operating Planning in Radioactive Environment.

This paper aims to solve the multi-objective operating planning problem in the radioactive environment. First, a more complicated radiation dose model is constructed, considering difficulty levels at each operating point. Based on this model, the multi-objective operating planning problem is converted to a variant traveling salesman problem (VTSP). Second, with respect to this issue, a novel combinatorial algorithm framework, namely hyper-parameter adaptive genetic algorithm (HPAGA), integrating bio-inspired optimization with reinforcement learning, is proposed, which allows for adaptive adjustment of the hyperparameters of GA so as to obtain optimal solutions efficiently. Third, comparative studies demonstrate the superior performance of the proposed HPAGA against classical evolutionary algorithms for various TSP instances. Additionally, a case study in the simulated radioactive environment implies the potential application of HPAGA in the future.

A novel fractional-order memristive Hopfield neural network for traveling salesman problem and its FPGA implementation

This paper proposes a novel fractional-order memristive Hopfield neural network (HNN) to address traveling salesman problem (TSP). Fractional-order memristive HNN can efficiently converge to a globally optimal solution, while conventional HNN tends to become stuck at a local minimum in solving TSP. Incorporating fractional-order calculus and memristors gives the system long-term memory properties and complex chaotic characteristics, resulting in faster convergence speeds and shorter average distances in solving TSP. Moreover, a novel chaotic optimization algorithm based on fractional-order memristive HNN is designed for the calculation process to deal with mutual constraint between convergence accuracy and convergence speed, which circumvents random search and diminishes the rate of invalid solutions. Numerical simulations demonstrate the effectiveness and merits of the proposed algorithm. Furthermore, Field Programmable Gate Array (FPGA) technology is utilized to implement the proposed neural network.

Intelligent optimization of inspection route based on multi-population integer coding particle swarm optimization algorithm

Aiming at the problems of premature convergence and slow convergence speed in the optimization process of single population particle swarm optimization algorithm, in order to improve the global convergence performance of particle swarm optimization algorithm, a hierarchical three-population integer coded particle swarm optimization algorithm based on grade evaluation with parallel structure is proposed and used to solve the traveling salesman problem (TSP). The algorithm imitates the form of biological aggregation in nature. In the initialization stage, three independent populations are generated according to different particle fitness, including an elite population composed of small-scale individuals with high fitness and two large-scale civilian populations composed of remaining individuals. The three populations apply the immigration strategy based on grade evaluation to exchange particles after a certain number of evolutionary generations. By applying the grade evaluation strategy, the natural law of the biological cluster is integrated into the particle swarm optimization algorithm, which effectively improves the optimization efficiency of the particle swarm optimization algorithm. The above algorithm is applied to the inspection route optimization of one of the traveling salesman problems. The results show that the improved algorithm is superior to the single population particle swarm optimization algorithm in terms of convergence speed, global optimization ability and stability.

Two-Tier Efficient QoE Optimization for Partitioning and Resource Allocation in UAV-Assisted MEC.

Unmanned aerial vehicles (UAVs) have increasingly become integral to multi-access edge computing (MEC) due to their flexibility and cost-effectiveness, especially in the B5G and 6G eras. This paper aims to enhance the quality of experience (QoE) in large-scale UAV-MEC networks by minimizing the shrinkage ratio through optimal decision-making in computation mode selection for each user device (UD), UAV flight trajectory, bandwidth allocation, and computing resource allocation at edge servers. However, the interdependencies among UAV trajectory, binary task offloading mode, and computing/network resource allocation across numerous IoT nodes pose significant challenges. To address these challenges, we formulate the shrinkage ratio minimization problem as a mixed-integer nonlinear programming (MINLP) problem and propose a two-tier optimization strategy. To reduce the scale of the optimization problem, we first design a low-complexity UAV partition coverage algorithm based on the Welzl method and determine the UAV flight trajectory by solving a traveling salesman problem (TSP). Subsequently, we develop a coordinate descent (CD)-based method and an alternating direction method of multipliers (ADMM)-based method for network bandwidth and computing resource allocation in the MEC system. Extensive simulations demonstrate that the CD-based method is simple to implement and highly efficient in large-scale UAV-MEC networks, reducing the time complexity by three orders of magnitude compared to convex optimization methods. Meanwhile, the ADMM-based joint optimization method achieves approximately an 8% reduction in shrinkage ratio optimization compared to baseline methods.

Improvement to application of PSO algorithm on TSP problems

In the field of swarm intelligence algorithms, particle swarm optimization algorithms have the ability of fast search and are widely used in lots of application scenarios because they are easy to implement. Therefore, different improvements have been made for their various properties. In this paper, aiming to accelerate its convergence speed, we further improve the existing hybrid particle swarm algorithm by using the idea of self adaptive and simulated annealing, examining its performance by solving Travelling salesman problem. It demonstrate that the relevant improvements can optimize the algorithm performance and have better convergence speed when iteration value was set 30, 50, or 70 by making comparions between the experiment results of both algorithm. The code used in this article is available on github. The experimental results show that the optimization proposed in this paper can optimize the algorithm to a certain extent at 30, 50, and 70 iterations, mainly because the improved algorithm can keep the convergence speed stable in more iterations.

A two-stage budget-feasible mechanism for mobile crowdsensing based on maximum user revenue routing

Through user participation, mobile crowdsensing (MCS) services overcome the problem of the excessive costs of relying solely on the active deployment of sensors and of achieving large-scale and low-cost applications of the Internet of Things, which is a research hotspot. However, current research on MCS issues adopts the perspective of service providers and does not consider user strategies, so the corresponding models cannot accurately reflect the complete status of the system. Therefore, this paper decomposes the MCS problem into a two-stage game process. By doing so, the strategies of both users and service providers can be considered, thus maximizing the interest for both parties. In the first stage, users determine the optimal route based on information released by the service provider. In the second stage, the service provider determines the winning users and the corresponding payment plan based on the route and bid information submitted by all users. Specifically, we express the user’s optimal route decision-making problem as a traveling salesman problem with time windows and node number constraints. Accordingly, we design the F-MAX-RR algorithm based on an evolutionary algorithm. We show that this algorithm can achieve an approximation ratio of (1−1/e), with the expected number of iterations being 8eL2(L+1)M. In the second stage, to maximize the total utility of the system, we transform the problem into an integer programming model with a budget constraint, which satisfies submodular characteristics. We design the S-MAX-TUM mechanism based on monotonic allocation and critical price theory to solve the problem of winning user decision-making and pricing. We demonstrate the economic characteristics of the mechanism, including truthfulness, individual rationality, and budget feasibility. The experimental results indicate the effective performance of the designed mechanisms.