Salesman Problem Research Articles

Optimizing the Vehicle Routes of End Devices Installation for Internet Speed Test Platform Using the Hybrid OVRP-TSP Model

The National Broadcasting and Telecommunications Commission (NBTC) Thailand has implemented a policy to evaluate the quality of Fixed Broadband (FBB) internet in response to numerous customer complaints across the country. One of the proposed solutions for assessing FBB internet quality involves installing end devices to test internet speeds with various internet service providers in the experimental area. However, due to the presence of many providers within the area, planning the vehicle routes for this mission is challenging, particularly given resource limitations. This paper proposes an approach to optimize the vehicle routes for the installation of internet speed test devices. The objective is to minimize the total transportation time, thereby reducing overall costs and carbon emissions. A hybrid OVRP-TSP (Open Vehicle Routing Problem - Traveling Salesman Problem) approach is introduced to address this challenge and is compared with the Clake-Wright Savings Heuristic, the Nearest Neighbor Heuristic, and existing methods. Furthermore, the hybrid OVRP-TSP is tested on 30 provider locations in the eastern region of Thailand. The results demonstrate that the hybrid OVRP-TSP provides the best solution across all measures (Total Time, Total Cost, and Total Emissions), while the other methods also yield efficient solutions compared to existing approaches.

Measuring the effectiveness and efficiency of simulation optimization metaheuristic algorithms

Metaheuristic algorithms have proven capable as general-purpose algorithms for solving simulation optimization problems. Researchers and practitioners often compare different metaheuristic algorithms by examining one or more measures that are derived through empirical analysis. This paper presents a single measure that can be used to empirically compare different metaheuristic algorithms for optimization problems. This measure incorporates both the effectiveness and efficiency of the metaheuristic algorithm, which is especially important in simulation optimization applications because the number of simulation runs available to the analyst (i.e., the run budget) can vary significantly with each simulation study. Therefore, the trade-off between the effectiveness and efficiency of a metaheuristic algorithm must be examined. This single measure is especially useful for multi-objective optimization problems; however, determining this measure is non-trivial for two or more objective functions. Additional details for calculating this measure for multi-objective optimization problems are provided as well as a procedure for comparing two or more metaheuristic algorithms. Finally, computational results are presented and analyzed to compare the performance of metaheuristic algorithms using knapsack problems, pure binary integer programs, traveling salesman problems, and the average results obtained across a diverse set of optimization problems that include simulation and multi-objective optimization problems.

Fast agglomerative clustering using approximate traveling salesman solutions

Agglomerative clustering, and Ward’s method, in particular, provide good clustering accuracy for most applications. However, its adoption has been limited by its quadratic time complexity, which makes it slow for large datasets. It also consumes O(N2) memory for non-vectorial data. In this work, we propose a fast variant of Ward’s method that reduces the number of distance calculations and only needs O(N) memory. It works by constraining the merges to neighboring nodes on a novel fully connected graph that consists of multiple approximate traveling salesman problem (TSP) solutions. This avoids the problems caused by disconnected graph components that can occur with a k-nearest neighbors graph. The method is general and works for all types of data for which a distance function can be defined. For a dataset of size 1.28 million, the proposed method achieves a speedup factor of 25:1 compared with the best exact implementation of Ward’s method and obtains identical results. The algorithm allows a flexible compromise between clustering quality and running time. For a moderate degradation in quality (NMI 0.90 to 0.80), the speedup factor improves further to 625:1. The proposed TSP-graph can also be used in other applications that require a connected neighborhood graph.

Ant Colony Optimization (ACO) for Traveling Salesman Problem: A Review

The traveling salesman problem (TSP) is a fundamental combinatorial optimization problem with applications in resource management, logistics, and communications. In order to address TSP and its differences, this paper discusses developments in Ant Colony Optimization (ACO), a biologically inspired algorithm. Inspired by the foraging activity of ants, ACO's decentralized and recursive methodology has proven successful in solving difficult routing problems. ACO's scalability, convergence speed, and solution quality have been greatly enhanced over time through innovations including hybridization with algorithms such as Firefly, genetic algorithms, parallel computing frameworks, and adaptation mechanisms. These developments have given the ACO the flexibility and efficiency to handle dynamic situations, such as real-time vehicle guidance and underwater navigation. Despite its progress, issues remain such as scalability in resource-limited contexts, processing overhead, and reliance on parameter modification. This work summarizes current developments in ACO, noting how revolutionary the TSP solution is, pointing out its drawbacks, and suggesting areas for further study. Leveraging emerging technologies like machine learning and quantum computing, ACO has huge potential to progressively address challenging real-world problems. This review provides a comprehensive framework for developing uses of ACOs and reaffirms their status as a key component of improvement research.

Optimal scheduling for many-to-many on-orbit service manoeuvers considering variances in target accessibility

Abstract In this article, we delve into the optimal scheduling challenge for many-to-many on-orbit services, taking into account variations in target accessibility. The scenario assumes that each servicing satellite is equipped with singular or multiple service capabilities, tasked with providing on-orbit services to multiple targets, each characterised by distinct service requirements. The mission’s primary objective is to determine the optimal service sequence, orbital transfer duration and on-orbit service time for each servicing satellite, with the ultimate goal of minimising the overall cost. We frame the optimal scheduling dilemma as a time-related colored travelling salesman problem (TRCTSP) and propose an enhanced firefly algorithm (EFA) to address it. Finally, experimental results across various scenarios validate the effectiveness and superiority of the proposed algorithm. The principal contribution of this work lies in the modeling and resolution of the many-to-many on-orbit service challenge, considering accessibility variations — a domain that has, until now, remained unexplored.

An innovative method to escape local minima using quantum system degeneracy in Simulated Annealing

Simulated Annealing (SA) is often used to provide satisfactory solutions to solving combinatorial problems. However, the SA is limited by its tendency to get stuck in local minima, which often prevents the global optimal solution from being reached for large or very complex problems. To overcome this obstacle, we present a new method inspired by the properties of degenerate quantum systems, named Degenerate Quantum Simulated Annealing (SA-DQS). This innovative approach exploits the coexistence of several quantum states of the same energy; this multiplicity of states is advantageous because it allows to finding of several solutions with identical energies, thus increasing the chances of discovering and building a promising solution among them, and of getting out of the traps of local minima more efficiently. The traveling salesman problem (TSP) is used as an application benchmark to validate the effectiveness of SA-DQS. Compared to standard simulated annealing (SA-S), SA-DQS showed superior performance on multiple instances of TSP. On average, the solutions provided by SA-DQS are equal to or closer to the optimum known in TSPLIB, in addition, it also offers a shorter computation time compared to that of other heuristic methods.

Automatic Extraction and Compensation of P-Bit Device Variations in Large Array Utilizing Boltzmann Machine Training

A Probabilistic Bit (P-Bit) device serves as the core hardware for implementing Ising computation. However, the severe intrinsic variations of stochastic P-Bit devices hinder the large-scale expansion of the P-Bit array, significantly limiting the practical usage of Ising computation. In this work, a behavioral model which attributes P-Bit variations to two parameters, α and ΔV, is proposed. Then the weight compensation method is introduced, which can mitigate α and ΔV of P-Bit device variations by rederiving the weight matrix, enabling them to compute as ideal identical P-Bits without the need for weights retraining. Accurately extracting the α and ΔV simultaneously from a large P-Bit array which is prerequisite for the weight compensation method is a crucial and challenging task. To solve this obstacle, we present the novel automatic variation extraction algorithm which can extract device variations of each P-Bit in a large array based on Boltzmann machine learning. In order for the accurate extraction of variations from an extendable P-Bit array, an Ising Hamiltonian based on a 3D ferromagnetic model is constructed, achieving precise and scalable array variation extraction. The proposed Automatic Extraction and Compensation algorithm is utilized to solve both 16-city traveling salesman problem (TSP) and 21-bit integer factorization on a large P-Bit array with variation, demonstrating its accuracy, transferability, and scalability.

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.

"Application of Genetic Algorithms to Solve the Clustered Generalized Traveling Salesman Problem"

"This paper explores the application of genetic algorithms (GAs) to solve the Traveling Salesman Problem (TSP) and its variants, specifically the Clustered Generalized Traveling Salesman Problem (CGTSP). In CGTSP, nodes (or cities) are grouped into clusters, and the primary objective is to determine the most efficient route that includes precisely one node from each cluster while minimizing the overall travel distance This particular variation plays a crucial role in practical scenarios, such as logistics, vehicle routing, and network design. In these applications, destinations are naturally grouped, and visiting one representative from each group is often essential or mandatory. CGTSP effectively tackles the complexity and real-world constraints more adeptly than the traditional TSP by integrating the element of clustering. This feature makes it a versatile and applicable model for a wide range of industrial and scientific problems. The study aims to assess the effectiveness of Genetic Algorithms (GAs) in solving these complex optimization problems. The paper provides an overview of the TSP and CGTSP, shows how to rewrite a CGTSP in the form of a TSP and vice versa, discusses the fundamentals of GAs, and presents the application of GAs to the problem variants. In addition, we investigate a new method to generate the initial population in the genetic algorithm and evaluate the proposed algorithm’s performance through experimental results. The findings highlight the potential of GAs as powerful tools for solving challenging optimization problems."

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

Aspiration Level Based Multi-Objective Quasi Oppositional Jaya Algorithm to Solve Constrained Multi-Objective Solid Traveling Salesman Problem

The Traveling Salesman Problem with heterogeneous conveyances consists of multiple fuzzy objectives widely applied in computer science to find the most efficient route. In some situations, solutions obtained by classical methods of this problem don’t satisfy the acuity of the decision maker. To overcome this, a systematic algorithm is used to solve the Constrained Multi-Objective Solid Traveling Salesman Problem (CMOSTSP) in a crisp and fuzzy environment. Aspiration level-based Multi-Objective Quasi Oppositional Jaya Algorithm has an advantage over other evolutionary algorithms; it doesn’t require algorithm-specific parameters. To evaluate the efficacy of fuzzy CMOSTSP, possibility and necessity measures are used by the decision-maker (DM). AL-based MOQO Jaya solves numerical illustrations with 10, 20, and 50 cities and is further compared with CPLEX and Hybrid GA. The AL-based MOQO Jaya provides compromise solutions, while CPLEX and HGA give a single solution. The run time of AL-based MOQO Jaya is 8.7106 sec, which is relatively less compared to CPLEX, which takes 6.5477 min, and HGA, which takes 9.6043 sec for 50 cities. This article also discussed performance measures and sensitivity analysis with different shape parameters and aspiration levels. The article concludes that the developed approach solved Fuzzy CMOSTSP and provided alternative solutions to DM.

ДИВЕРСИФІКАЦІЯ ПОШУКУ В АЛГОРИТМАХ ОМК ТА ЇЇ ЗАСТОСУВАННЯ

This paper presents a novel approach to the development of diversified ant colony optimization (ACO) algorithms, which are among the most widely used methods in combinatorial optimization. The proposed diversification in ACO algorithms is based on considering multiple options for extending the current solution fragment by incorporating several vertices of the problem graph into the route instead of just one, as is typically done. The ability of ants to foresee multiple search steps ahead increases the likelihood of avoiding suboptimal solutions and finding more accurate ones. This approach is applied to create metaheuristic algorithms for solving various combinatorial optimization problems. The results of computational experiments on a series of applied combinatorial optimization problems across different classes demonstrate the successful modification of the known ACO algorithms. Keywords: combinatorial optimization, Ant Colony Optimization, routing, traveling salesman problem, UAV, optimization of flight routes, computational experiment.

Application of Discrete Event Simulation to Enhance the Efficiency of the Ant Colony Optimization Algorithm

The application of the Ant Colony Optimization (ACO) algorithm to solve the the Traveling Salesman Problem (TSP) has been extensively studied by scientists worldwide. However, implementing the algorithm faces challenges due to the randomness in the departure and movement times of ants, as well as the limitations of computer hardware. These factors reduce the algorithm's convergence ability and overall effectiveness. This paper proposes an approach to implement the algorithm by utilizing discrete event simulation (DES). Artificial ants are modeled to depart and move completely randomly, closely mimicking the behavior of natural ants. This approach accelerates the algorithm's convergence, minimizes the likelihood of falling into local optima, and enhances overall performance. The simulation results clearly demonstrate the advantages of this method.

How Do Dynamic Events Change the Fitness Landscape of Traveling Salesman Problems?

How Do Dynamic Events Change the Fitness Landscape of Traveling Salesman Problems?

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

This article presents a method of constructing counter‐examples and a complete counter‐example to the linear programming model alleged to be the solution to the traveling salesman problem. The counter‐example is checked against the model proposed by Diaby et al. However, it applies to all similar formulations of the TSP problem.Although the model in question was published in 2006, and there were several discussions regarding its correctness, the counter‐example was never presented.The presented counter‐example is a regular graph, and the aim was not to have an example with the least possible size; therefore, the focus was on clarity. The counter‐example has, therefore, 366 nodes in two main clusters, each node (in the main part) having exactly four connections to other nodes in the cluster.

Formulations and Branch-and-cut algorithms for the Period Travelling Salesman Problem

Formulations and Branch-and-cut algorithms for the Period Travelling Salesman Problem