Salesman Problem Research Articles

A Fuzzy Control Strategy for Multi-Goal Autonomous Robot Navigation

This paper addresses the complex problem of multi-goal robot navigation, framed as an NP-hard traveling salesman problem (TSP), in environments with both static and dynamic obstacles. The proposed approach integrates a novel path planning algorithm based on the Bump-Surface concept to optimize the shortest collision-free path among static obstacles, while a Genetic Algorithm (GA) is employed to determine the optimal sequence of goal points. To manage static or dynamic obstacles, two fuzzy controllers are developed: one for real-time path tracking and another for dynamic obstacle avoidance. This dual-controller system enables the robot to adaptively adjust its trajectory while ensuring collision-free navigation in unpredictable environments. The integration of fuzzy logic with TSP-based path planning and real-time dynamic obstacle handling represents a significant advancement in autonomous robot navigation. Simulations conducted in CoppeliaSim validate the effectiveness of the proposed method, demonstrating robust navigation and obstacle avoidance in realistic environments. This work provides a comprehensive framework for solving multi-goal navigation tasks by incorporating TSP optimization with dynamic, real-time path adjustments.

The Future of Last-Mile Delivery: Lifecycle Environmental and Economic Impacts of Drone-Truck Parallel Systems

With rapid advancements in unmanned aerial vehicle (UAV) technology, its integration into logistics operations has emerged as a promising solution for improving efficiency and sustainability. Among the emerging solutions, a collaborative delivery model involving drones and trucks addresses last-mile delivery challenges by leveraging the complementary strengths of both modes of transport. However, evaluating the environmental and economic impacts of this transportation mode requires a systematic framework to capture its unique characteristics and minimize environmental impacts and costs. This paper investigates the Parallel Drone Scheduling Traveling Salesman Problem (PDSTSP) to evaluate the environmental and economic sustainability of a collaborative drone-truck delivery system. Specifically, a mathematical model for this delivery system is developed to optimize joint delivery operations. Environmental impacts are assessed using a comprehensive Life Cycle Assessment (LCA), including emissions and operational noise, while a Life Cycle Cost Analysis (LCCA) quantifies economic performance across five cost dimensions. Sensitivity analysis explores factors such as delivery density, traffic congestion, and wind conditions. Results show that, compared to the electric vehicle fleet, the proposed model achieves an approximate 20% reduction in carbon emissions, while delivering a 20–30% cost reduction relative to the fuel truck fleet. Drones’ efficiency in short-distance deliveries alleviates trucks’ load, cutting environmental and operational costs. This study offers practical insights and recommendations for implementing drone-truck parallel delivery systems, particularly in high-demand density areas.

Multi-AUV sediment plume estimation using Bayesian optimization

Sediment plumes created by dredging or mining activities have an impact on the ecosystem in a much larger area than the mining or dredging area itself. It is therefore important and sometimes mandatory to monitor the developing plume to quantify the impact on the ecosystem including its spatial-temporal evolution. To this end, a Bayesian Optimization (BO)-based approach is proposed for plume monitoring using autonomous underwater vehicles (AUVs), which are used as a sensor network. Their paths are updated based on the BO, and additionally, a split-path method and the traveling salesman problem are utilized to account for the distances the AUVs have to travel and to increase the efficiency. To address the time variance of the plume, a sliding-window approach is used in the BO and the dynamics of the plume are modeled by a drift and decay rate of the suspended particulate matter (SPM) concentration measurements. Simulation results with SPM data from a simulation of a dredge experiment in the Pacific Ocean show that the method is able to monitor the plume over space and time with good overall estimation error.

An Intelligent 5G Unmanned Aerial Vehicle Path Optimization Algorithm for Offshore Wind Farm Inspection

In recent years, clean energy has gained increasing attention, with offshore wind power playing a crucial role in global energy production. However, the high operating and maintenance costs of offshore wind farms remain a significant challenge. The advent of 5G technology provides a solution for efficiently monitoring and controlling wind power equipment. The use of 5G unmanned aerial vehicles (UAVs) for blade inspections is a promising development. A key challenge is efficiently planning UAV flight paths for fast and effective inspections in complex offshore environments. To address this problem, we conduct an in-depth study of the 5G UAV path optimization method. In this paper, the UAV inspection path problem is modeled as an obstacle avoidance traveling salesman problem (TSP), taking into full account UAV flight constraints and complex sea environment factors, particularly the impact of sea wind on UAV flight speed. We propose a novel Sea Wind-Aware Improved A*-Guided Genetic Algorithm (SWA-IAGA), which integrates an improved A* algorithm to guide the genetic algorithm for efficient path planning, with the assistance of relevant graphical knowledge. This algorithm overcomes the limitations of traditional single-path planning methods, enabling more accurate and efficient path planning.

Improved dynamic programming method for solving multi-objective and multi-stage decision-making problems

Multi-objective and multi-stage decision-making problems require balancing multiple objectives at each stage and making optimal decision in multi-dimensional control variables, where the commonly used intelligent optimization algorithms suffer from low solving efficiency. To this end, this paper proposes an efficient algorithm named non-dominated sorting dynamic programming (NSDP), which incorporates non-dominated sorting into the traditional dynamic programming method. To improve the solving efficiency and solution diversity, two fast non-dominated sorting methods and a dynamic-crowding-distance based elitism strategy are integrated into the NSDP algorithm. The proposed algorithm has been verified on 12 benchmark test functions and a multi-objective travelling salesman problem. The results demonstrate that the NSDP algorithm achieves better outcome in multiple performance metrics and higher solving efficiency, compared with non-dominated sorting genetic algorithm II and multi-objective particle swarm optimization.

A novel heuristic for the generalized traveling salesman problems with imprecise cost matrices

A novel heuristic for the generalized traveling salesman problems with imprecise cost matrices

Fast spot order optimization to increase dose rates in scanned particle therapy FLASH treatments.

The advent of ultra-high dose rate irradiation, known as FLASH radiation therapy, has shown promising potential in reducing toxicity while maintaining tumor control. However, the clinical translation of these benefits necessitates efficient treatment planning strategies. This study introduces a novel approach to optimize proton therapy for FLASH effects using traveling salesperson problem (TSP) heuristics. We applied these heuristics to optimize the arrangement of proton spots in treatment plans for 26 prostate cancer patients, comparing the performance against conventional sorting methods and global optimization techniques. Our results demonstrate that TSP-based heuristics significantly enhance FLASH coverage to the same extent as the global optimization technique, but with computation times reduced from hours to a few seconds. This approach offers a practical and scalable solution for enhancing the effectiveness of FLASH therapy, paving the way for more effective and personalized cancer treatments. Future work will focus on further optimizing run times and validating these methods in clinical settings.

Counter‐Example to Diaby’s et al. Linear Programming Solution to the Traveling Salesman Problem

Counter‐Example to Diaby’s et al. Linear Programming Solution to the Traveling Salesman Problem

Analysis of the Computational Performance in Traveling Salesman Problem: An Application of the Grey Prediction Hybrid Black Hole Algorithm

Grey prediction evolution algorithm (GPEA) is a nature-inspired intelligent approach applied to global optimization and engineering problems in 2020. The performance of the GPEA is evaluated on benchmark functions, global optimization, and tested on six engineering-constrained design problems. The comparison shows the effectiveness and superiority of the GPEA. Although the pure GPEA is better than other algorithms in global optimization, and engineering problems, it shows poor performance in combinatorial optimization. In this work, GPEA hybridizes with the black hole algorithm and tabu search for the event horizon condition. Besides, the GPHBH is implemented with heuristics, such as 2-opt, 3-opt, and k-opt swap, and tries to improve with constructive heuristics, such as NN (nearest neighbor), and k-NN. All the algorithms have been tested under appropriate parameters in this work. The traveling salesman problem has been used as a benchmark problem so eight benchmark OR-Library datasets are experimented with. The experimental solutions are presented as best, average solutions, std. deviation and CPU time for all datasets. As a result, GPHBH and its derived forms give alternative and acceptable solutions to combinatorial optimization in admissible CPU time.

On the Method of Solving the Fuzzy Multicriteria Traveling Salesman Problem

The paper studies a fuzzy multi-criteria traveling salesman problem with criteria in the form of distance and travel time along the route. The problem statement is formalized, the concept of a compromise is defined. Two-criteria problems with an additional condition on the order of visiting nodes of the transport network are considered. A new algorithm for solving the resulting problem is proposed. Numerous experiments and a comparison of the obtained solutions with optimal ones for standard single-criteria statements are conducted

Bibliometric Analysis Of Travelling Salesman Problem With Drones (TSP-D)

The growing need for efficient package delivery systems in Last Mile Delivery (LMD) has attracted significant attention, bringing the Travelling Salesman Problem with Drones (TSP-D) to the forefront of scholarly research. The research under consideration generated a surge in scientific output across various domains, including economics, industry, and logistics, owing to the potential benefits it presents. The primary objective of this study is to compile, organize, and analyze the literature on TSP-D in the context of LMD. A comprehensive bibliometric analysis scrutinized the progress made in this field during the period spanning 2017 to 2024. The study encompassed an extensive analysis of a corpus of 2,397 scholarly publications, yielding numerous intriguing conclusions derived from a meticulously constructed framework. This review addresses inquiries about the most prevalent research categories on resolving TSP-D, focusing on exact and metaheuristic approaches.

ABOUT OF THE ANNEALING METHOD USING FOR THE TRAVELING SALESMAN PROBLEM SOLUTION WITH THE FUZZY TIME PERCEPTION

Context. The article considers a technique for the use of fuzzy numbers and the annealing method for solving the traveling salesman problem, which is formulated as the problem of finding a route to visit a given number of cities without repetitions with a minimum duration of movement. The task of formalizing the algorithm for solving the traveling salesman problem by the annealing method using fuzzy numbers for subjective time perception is posed. The use of fuzzy numbers to increase the accuracy to represent real-world circumstances is proposed. Objective. The goal of the work is to develop an algorithm for solving the traveling salesman problem based on the implementation of the annealing method with fuzzy numbers representing the subjective time perception for traveling between the cities with the minimum perceived duration of movement along the route. Method. This paper proposes a method for solving the traveling salesman problem by the annealing method with fuzzy numbers for subjective time perception. A scheme for formalizing the procedure for solving the traveling salesman problem with the minimal perceived duration of movement along the route is described. A variant of the original traveling salesman problem is proposed, which consists in using fuzzy numbers to represent the uncertainty and subjective time perception in traveling between cities as opposed to regular crisp numbers to show regular distance and/or time of traveling. The results of the proposed algorithm for calculating solutions to the traveling salesman problem with minimization of the perceived duration of movement are presented, the obtained solutions are compared with the solutions found by other heuristic methods. Results. The method for solving the traveling salesman problem using the annealing method with fuzzy numbers for subjective time perception is developed. A variant of the original traveling salesman problem is proposed, which consists in using fuzzy numbers to represent the uncertainty and subjective time perception in traveling between cities as opposed to regular crisp numbers to show regular distance and/or time of traveling. The application of fuzzy numbers makes it possible to perform calculation over possibly uncertain or subjective data, making results more accurate in the case of realistic deviations from the expected mean values in distance coverage. The results of the proposed algorithm for calculating solutions to the traveling salesman problem with minimization of the perceived duration of movement are presented, the obtained solutions are compared with the solutions found by other heuristic methods. Conclusions. The paper considers a method for formalizing the algorithm for solving the traveling salesman problem using fuzzy numbers for subjective time perception. The use of fuzzy numbers to increase the accuracy to represent real-world circumstances is proposed. The scheme for formalizing the procedure for solving the traveling salesman problem with the minimal perceived duration of movement along the route is described. A variant of the original traveling salesman problem is proposed, which consists in using fuzzy numbers to represent the uncertainty and subjective time perception in traveling between cities as opposed to regular crisp numbers to show regular distance and/or time of traveling.

Solving method of traveling salesman problem based on performer graph self-attention mechanism

Solving method of traveling salesman problem based on performer graph self-attention mechanism

Universal and Automated Approaches for Optimising the Processing Order of Geometries in a CAM Tool for Redundant Galvanometer Scanner-Based Systems

The combination of highly dynamic systems with a limited work envelope with a less dynamic system with a larger working envelope promises to combine the advantages of both systems while eliminating the disadvantages. For these systems, separation algorithms determine the trajectories based on the target geometries. However, arbitrary processing orders of these result in inefficient trajectories because successive geometries may be geometrically far apart. This causes the dynamic system to operate below its potential. Current planning tools do not optimise the processing order for such redundant systems. The aim is to design and implement a planning tool for the application of laser marking. The tool considers the processing order of the 2D geometries from a geometric point of view. The resulting sequenced path data can then be used by trajectory generation algorithms to make full use of the potential of redundant systems. The approach analyses literature on Travelling Salesman Problems (TSP), which is then transferred to the given application. A heuristic and a genetic algorithm are developed and integrated into a planning tool. The results show the heuristic algorithm being faster while still producing solutions whose total path length is similar to that of the genetic algorithm. Even though the solutions don’t meet any optimality standards, the presented automated approaches are superior to manual approaches and are to be seen as a starting point for further research.

Solving the traveling salesman problem by statistical testing using complex Markov chains

A method was proposed for solving the traveling salesman problem (TSP) using N -complex Markov chains (N -MC), the state sequence of which simulates a path through N points, each visited only once. Transition probabilities from each point to one of the next l points were set, where l < N. The complexity of implementing all stages of the method, depending on the values of N and l, was analyzed. Estimates of the complexity of the N -MC generator were obtained based on the composition of a finite deterministic automaton and a probabilistic memoryless automaton. The complexity of the N -MC generator is characterized by the volume of input sets, internal states, and outputs, as well as the amount of memory required to implement the transition and output functions of the automata. The delay time of the N -MC generator operation was also estimated. The probability of generating valid paths, i. e., those resolving TSP, and the memory requirements for storing valid paths were calculated.

Results of Computational Experiment for Solving the Minimum Traveling Salesman Problem by the Cycle Merging Algorithm

The traveling salesman problem is an important combinatorial optimization problem, which consists in finding the shortest path that passes through each city exactly once and ends at the starting point. Despite its simple formulation, this problem turns out to be computationally complex, and its exact solution requires significant computational resources. In this regard, the search for efficient algorithms to solve the traveling salesman problem remains an urgent task in the context of modern technological challenges. In this paper we present the results of a computational experiment that gives an insight into the quality of the cycle merging algorithm for the minimum traveling salesman problem. The quality of the cycle merging algorithm is investigated on seven sets of instances of the traveling salesman problem. The results obtained are compared with the results of computational experiments for some known heuristics. The analysis allows us to say that the cycle merging algorithm shows relatively good results for all tested sets and can be used for a wide range of instances of the traveling salesman problem as a relatively fast heuristic of good enough quality.

Crossover Operator Inspired by the Selection Operator for an Evolutionary Task Sequencing Algorithm

This paper proposes a novel crossover operator for evolutionary algorithms in task sequencing and verifies its efficacy. Unlike the conventional blind and entirely stochastic selection of sequence fragments exchanged with the second individual, the proposed operator employs a method where the probability of fragment selection is influenced by the total cost of internal connections within the exchanged fragments. At the same time, the new operator retains its stochastic nature and is not a deterministic operator, which reduces the risk of the evolutionary algorithm getting stuck in a local minimum. The idea of the proposed crossover operator was based on the main mechanism of the evolutionary algorithm that determines the success of this type of algorithm selection. To assess its effectiveness, the new operator was compared against previously employed crossover operators using a traveling salesman problem (TSP) instance in a multidimensional space in order to map the problem of symmetric sequencing tasks described with multiparameters (e.g., a symmetric variant of production tasks sequencing).

A Global Coverage Path Planning Method for Multi-UAV Maritime Surveillance in Complex Obstacle Environments

The study of unmanned aerial vehicle (UAV) coverage path planning is of great significance for ensuring maritime situational awareness and monitoring. In response to the problem of maritime multi-region coverage surveillance in complex obstacle environments, this paper proposes a global path planning method capable of simultaneously addressing the multiple traveling salesman problem, coverage path planning problem, and obstacle avoidance problem. Firstly, a multiple traveling salesmen problem–coverage path planning (MTSP-CPP) model with the objective of minimizing the maximum task completion time is constructed. Secondly, a method for calculating obstacle-avoidance path costs based on the Voronoi diagram is proposed, laying the foundation for obtaining the optimal access order. Thirdly, an improved discrete grey wolf optimizer (IDGWO) algorithm integrated with variable neighborhood search (VNS) operations is proposed to perform task assignment for multiple UAVs and achieve workload balancing. Finally, based on dynamic programming, the coverage path points of the area are solved precisely to generate the globally coverage path. Through simulation experiments with scenarios of varying scales, the effectiveness and superiority of the proposed method are validated. The experimental results demonstrate that this method can effectively solve MTSP-CPP in complex obstacle environments.

Dynamic open time‐dependent traveling salesman problem with speed optimization

AbstractIncreased awareness of people of the problems caused by CO2 emissions brings companies to consider environmental issues in their distribution systems. The rapid advance in technology allows logistics companies to tackle with dynamic nature of distribution networks (e.g., a change in the vehicle speed due to unexpected events). The planned routes at the beginning of the time horizon could be subject to modification at any point in time to account for the recent traffic information. This study addresses a dynamic open time‐dependent traveling salesman problem. The problem also involves speed optimization that aims to find optimal vehicle speed in a dynamic setting by respecting real‐time traffic conditions. We develop a mixed integer linear programming (MILP) formulation for the addressed problem to determine routing and vehicle speed decisions. Furthermore, a MILP‐based myopic‐clustering decomposition heuristic algorithm has been introduced to solve large‐sized instances within reasonable solution times. The use of the heuristic algorithm provides decision‐makers with a responsiveness capacity by enabling fast incorporation of dynamically observed data during operations. The numerical analyses demonstrate the potential benefits of employing the proposed tools.

HamLib: A library of Hamiltonians for benchmarking quantum algorithms and hardware

In order to characterize and benchmark computational hardware, software, and algorithms, it is essential to have many problem instances on-hand. This is no less true for quantum computation, where a large collection of real-world problem instances would allow for benchmarking studies that in turn help to improve both algorithms and hardware designs. To this end, here we present a large dataset of qubit-based quantum Hamiltonians. The dataset, called HamLib (for Hamiltonian Library), is freely available online and contains problem sizes ranging from 2 to 1000 qubits. HamLib includes problem instances of the Heisenberg model, Fermi-Hubbard model, Bose-Hubbard model, molecular electronic structure, molecular vibrational structure, MaxCut, Max-k-SAT, Max-k-Cut, QMaxCut, and the traveling salesperson problem. The goals of this effort are (a) to save researchers time by eliminating the need to prepare problem instances and map them to qubit representations, (b) to allow for more thorough tests of new algorithms and hardware, and (c) to allow for reproducibility and standardization across research studies.