Salesman Problem Research Articles

Discrete orca predation algorithm for the traveling salesman problem

Discrete orca predation algorithm for the traveling salesman problem

Plug-In Hybrid Electric Vehicle Traveling-Salesman Problem with Drone

Plug-In Hybrid Electric Vehicle Traveling-Salesman Problem with Drone

Local elimination in the traveling salesman problem

Hougardy and Schroeder (WG 2014) proposed a combinatorial technique for pruning the search space in the traveling salesman problem, establishing that, for a given instance, certain edges cannot be present in any optimal tour. We describe an implementation of their technique, employing an exact TSP solver to locate k-opt moves in the elimination process. In our computational study, we combine LP reduced-cost elimination together with the new combinatorial algorithm. We report results on a set of geometric instances, with the number of points n ranging from 3038 up to 115,475. The test set includes all TSPLIB instances having at least 3000 points, together with 250 randomly generated instances, each with 10,000 points, and three currently unsolved instances having 100,000 or more points. In all but two of the test instances, the complete-graph edge sets were reduced to under 3n edges. For the three large unsolved instances, repeated runs of the elimination process reduced the graphs to under 2.5n edges.

On delivery policies for a truck-and-drone tandem in disaster relief

This paper introduces the traveling salesman problem with a truck and a drone under incomplete information (TSP-DI). TSP-DI is motivated by the deliveries of emergency supplies under unknown road conditions in the immediate aftermath of a disastrous event. The urgency may force the immediate dispatch of relief vehicles, such that road damages blocking the truck’s planned route are detected ’on-the-fly’. The relief transport must schedule deliveries anticipating possible unplanned truck detours, enforce (planned) drone detours for early checking of key road segments, and consider the dynamic nature of road condition information. In this paper, we perform a competitive analysis of a widely used delivery policy for TSP-DI in practice – the online re-optimization policy (Reopt) – and compare it to several alternative delivery strategies. Competitive analysis examines the worst-case performance of the strategies and is particularly important in the context of disaster relief, where worst-case outcomes must be avoided. Our analysis shows that Reopt is dominated by alternative delivery policies in terms of the competitive ratio even at a medium level of damage on the road. It also underscores the importance of surveillance detours performed by the drone, even if the surveillance delays the start of the deliveries.

Control parameter optimisation using the evidence framework for the ant colony optimisation algorithm

The ant colony optimization (ACO) algorithm is a metaheuristic initially designed to solve the travelling salesman problem (TSP). The design of experiments, finding the suitable ACO algorithm configuration, and calibrating the adaptive control parameters are exhaustive and time-consuming exercises, especially for TSPs where the number of cities can exceed 1000. This paper presents an evidence framework driven control parameter optimisation (EFCPO) algorithm for an ACO algorithm solving TSPs. EFCPO performs auto-tuning of the adaptive control parameters and makes recommendations about the ACO algorithms that are best suited for the TSPs in question using the log evidence. In addition, with this ability, the algorithm can take a solution provided by an ACO algorithm and improve the results. The EFCPO accomplishes this over a number of cycles through auto-tuning of the control parameters and re-running the ACO until the process is completed. The capabilities of EFCPO are compared to another configuration tool, irace, using benchmark ACO algorithms to test the efficiency of the framework. The benchmark algorithms make use of a local search strategy to solve TSPs. The results show that ACO algorithms are able to find new and improved solution tours within reasonable times. The improvements are also significant. In addition, ACO algorithms that are best suited for the TSP in question are preferred, making the EFCPO an effective tool for real-time configuration of ACO algorithms for solving TSPs .

Making a Complete Mess and Getting Away With It: Traveling Salesperson Problems With Circle Placement Variants

Making a Complete Mess and Getting Away With It: Traveling Salesperson Problems With Circle Placement Variants

Minimizing charging task time of WRSN assisted with multiple MUVs and laser-charged UAVs

This paper investigates the framework of wireless rechargeable sensor network (WRSN) assisted by multiple mobile unmanned vehicles (MUVs) and laser-charged unmanned aerial vehicles (UAVs). On the basis of framework, we cooperatively investigate the trajectory optimization of multi-UAVs and multi-MUVs for charging WRSN (TOUM) problem, whose goal aims at designing the optimal travel plan of UAVs and MUVs cooperatively to charge WRSN such that the remaining energy of each sensor in WRSN is greater than or equal to the threshold and the time consumption of UAV that takes the most time of all UAVs is minimized. The TOUM problem is proved NP-hard. To solve the TOUM problem, we first investigate the multiple UAVs-based TSP (MUTSP) problem to balance the charging tasks assigned to every UAV. Then, based on the MUTSP problem, we propose the TOUM algorithm (TOUMA) to design the detailed travel plan of UAVs and MUVs. We also present an algorithm named TOUM-DQN to make intelligent decisions about the travel plan of UAVs and MUVs by extracting valuable information from the network. The effectiveness of proposed algorithms are verified through extensive simulation experiments. The results demonstrate that the TOUMA algorithm outperforms the solar charging method, the base station charging method, and the TOUM-DQN algorithm in terms of time efficiency. Simultaneously, the experimental results show that the execution time of TOUM-DQN algorithm is significantly lower than TOUMA algorithm.

Due date-oriented picker routing, an efficient exact solution algorithm, and its application to pick-from-store omnichannel retailing

The advent of e-commerce and omnichannel retailing has sparked renewed interest in picker routing in warehouses. This paper presents two significant methodological advances in this well-established field. First, it is a well-known fact that the parallel-aisle layout of warehouses, as opposed to general graphs, allows for polynomial-time solutions of the Traveling Salesman Problem. We show that the parallel-aisle structure can also be exploited when pickers are tasked with visiting storage positions associated with specific due dates. We establish that picker routing in warehouses, subject to soft due date constraints, is a binary NP-hard problem. We also present an exact branch-and-bound algorithm with pseudo-polynomial time complexity. This algorithm effectively solves instances with up to 60 picking positions and five cross aisles within a few seconds while guaranteeing optimality. Second, for even larger pick lists, we demonstrate the successful integration of our algorithm into a real-time framework. This approach allows us to avoid extended solution times that would otherwise delay the picker’s departure, without compromising the quality of the solution. To illustrate the practical relevance of these two methodological innovations, we apply our routing algorithm to the context of pick-from-store omnichannel retailing. By assigning due dates to critical products, we significantly reduce stockout occurrences for online customers. These stockouts occur when the stock level, initially deemed sufficient to confirm an online order, is depleted by walk-in customers before the picker reaches the relevant shelf.

Design and experiment of citrus picking system based on dual robot collaboration

AbstractFor citrus trees cultivated by dwarf dense planting, the fruits are randomly distributed in space, which poses difficulties for mechanized picking. To improve picking efficiency, a citrus picking system based on dual robot collaboration is designed and a global scanning picking scheme that scans the entire fruit tree to achieve orderly fruit picking is proposed in this research. The dual‐robot calibration with the iterative method and closed‐form method is completed in the research. The picking problem is attributed to the single traveling salesman problem, and the trajectory planning and the picking task are completed with genetic algorithm in the research. The picking experiments are designed in the research. As a result, in the picking experiments, the average time for planning the picking sequence of citrus was 0.1184 s, the longest time is 0.1560 s. In each group of citrus picking experiments, the total picking time averaged 158.9 s, the longest group took 170 s, the picking success rate is 82%. The picking results show that the built dual‐machine system can effectively complete the picking task and meet the real‐time requirement of picking. The proposed dual‐robot picking system can provide a reference for the establishment of other picking robot system.

Reducing The Order Of The Travelling SalesmanProblems By Minimin Optimization Theory AndToStudyBy DAS Technique

The purpose of this article is to propose a new approach for finding the guaranteed solution set of minimizedassignment problems and maximized assignment problems. Firstly the existence of the minimin and maximaxoptimization problems are studied with the help of newly defined weakly φ-convex function in φ-convex set. Next the assignment problems and traveling problems are converted to a complete bipartite graph in a unifiedapproach. The concept dominated assignment simulation (DAS) technique based on the theory of miniminandmaximax optimization problems. Later a pair of traveling salesman problems are studied using the DAS technique and complete bipartite graphas an application of minimin optimization problem. Finally, a pair of comparison studies are discussed to showequality of solutions and the number of steps in between Hungarian method and DAS technique

Двоетапний метод розв’язання задачі комівояжера на основі генетичного алгоритму

One of the main tasks in logistics is to find the most efficient route in the traveling salesman problem on a given transportation network, allowing for the servicing of the maximum number of customers while considering certain criteria. In the typical traveling salesman problem, the objective function is most often the route length or duration. However, such a formulation does not account for the subjectivity in evaluating the travel durations at different stages, which may be influenced by various objective and subjective factors. The problem of the traveling salesman with fuzzily defined travel durations between network nodes is considered. The approach to solving the problem is based on a genetic algorithm with enhanced mutation procedures and population diversity generation. Trapezoidal fuzzy numbers are used to formalize fuzzy values, presented in the generalized case based on the application of Gaussian distribution and corresponding characteristics. A two-stage scheme for solving the optimization problem of the traveling salesman on a given transportation network is proposed, combining the genetic algorithm and Ward's clustering method. In the first stage, a clustering procedure is conducted using Ward's method. In the second stage, based on the obtained set of clusters and the identified optimal inter-cluster distances, route duration optimization is performed within the clusters. To test the efficiency of the developed method, two types of models were generated: one with a limited number of available paths and one with a fully connected topology. Computational experiments were conducted to apply the developed method to solving the traveling salesman problem with travel durations between cities represented as fuzzy numbers. A comparison of numerical calculation results was performed. The obtained results demonstrated the effectiveness of preliminary clustering when using the genetic algorithm to find the best local optima under the same input parameters.

Multi-Objective Combinatorial Optimization Algorithm Based on Asynchronous Advantage Actor–Critic and Graph Transformer Networks

Multi-objective combinatorial optimization problems (MOCOPs) are designed to identify solution sets that optimally balance multiple competing objectives. Addressing the challenges inherent in applying deep reinforcement learning (DRL) to solve MOCOPs, such as model non-convergence, lengthy training periods, and insufficient diversity of solutions, this study introduces a novel multi-objective combinatorial optimization algorithm based on DRL. The proposed algorithm employs a uniform weight decomposition method to simplify complex multi-objective scenarios into single-objective problems and uses asynchronous advantage actor–critic (A3C) instead of conventional REINFORCE methods for model training. This approach effectively reduces variance and prevents the entrapment in local optima. Furthermore, the algorithm incorporates an architecture based on graph transformer networks (GTNs), which extends to edge feature representations, thus accurately capturing the topological features of graph structures and the latent inter-node relationships. By integrating a weight vector layer at the encoding stage, the algorithm can flexibly manage issues involving arbitrary weights. Experimental evaluations on the bi-objective traveling salesman problem demonstrate that this algorithm significantly outperforms recent similar efforts in terms of training efficiency and solution diversity.

Ant Colony Optimization and Beam-Ant Colony Optimization on Traveling Salesman Problem with Traffic Congestion

The Traveling Salesman Problem (TSP) is a well-known combinatorial optimization problem that has various implications in a variety of industries. Even the purest formulation of TSP has applications on from logistics routes to microchip manufacturing, unexpectedly, it can be used on DNA sequencing with slight modification as a sub-problem. In this paper, two versions of TSP were studied, a classical TSP and the TSP containing traffic congestion data. Two state-of-the-art solution methods were used, Ant Colony Optimization (ACO) and Beam-ACO. These algorithms were hybridized with 2-Opt local search and their performances compared on the same benchmark instances. The experimental results show the efficiency of Beam-ACO compared to ACO.

Traveling Salesman Problem with Backend Information Processing

This paper introduces the Traveling Salesman Problem (TSP) with Backend Information Processing (bTSP), which integrates backend processing times into path planning to minimize the makespan. The study develops a mixed integer linear programming formulation and conducts a theoretical analysis to understand the relationship between the TSP and the bTSP. The results show that an optimal solution for the bTSP can be efficiently derived by leveraging the connection to the standard TSP.

Fuzzy Traveling Salesman Problem of Fuzzy Hexagonal Numbers using Ranking Method and Dijkstra's Algorithms

Fuzzy Traveling Salesman Problem of Fuzzy Hexagonal Numbers using Ranking Method and Dijkstra's Algorithms

An Efficient Tour Construction Heuristic for Generating the Candidate Set of the Traveling Salesman Problem with Large Sizes

In this paper, we address the challenge of creating candidate sets for large-scale Traveling Salesman Problem (TSP) instances, where choosing a subset of edges is crucial for efficiency. Traditional methods for improving tours, such as local searches and heuristics, depend greatly on the quality of these candidate sets but often struggle in large-scale situations due to insufficient edge coverage or high time complexity. We present a new heuristic based on fuzzy clustering, designed to produce high-quality candidate sets with nearly linear time complexity. Thoroughly tested on benchmark instances, including VLSI and Euclidean types with up to 316,000 nodes, our method consistently outperforms traditional and current leading techniques for large TSPs. Our heuristic’s tours encompass nearly all edges of optimal or best-known solutions, and its candidate sets are significantly smaller than those produced with the POPMUSIC heuristic. This results in faster execution of subsequent improvement methods, such as Helsgaun’s Lin–Kernighan heuristic and evolutionary algorithms. This substantial enhancement in computation time and solution quality establishes our method as a promising approach for effectively solving large-scale TSP instances.

Modification of the hopfield neural network model for solving the task of optimal task allocation in a group of mobile robots

In the context of group interaction among mobile robots, there arises the challenge of task distribution within the group, considering the robots' characteristics and the working environment. This study aims to modify the Hopfield neural network and develop methodologies for its application in solving the task allocation problem for an arbitrary number of tasks within a group of mobile robots. To achieve this, the Hopfield neural network is represented as a graph. An algorithm is presented, demonstrating the transition from the initial problem to the Traveling Salesman Problem (TSP). The application of the Hopfield model to the task distribution problem in a group of robots is described, along with the development of an optimization function calculation algorithm. An assessment is conducted to evaluate the impact of neural network parameters on the quality and speed of solving the optimization problem. By comparing it with other heuristic methods (genetic and ant colony algorithms), the domains of application for the modified algorithm are determined.

A Decision Tree Application for the Development of a Novel Approach to the Traveling Salesman Issue

The Traveling Salesman Problem (TSP) is a combinatorial problem related to computer science and operations research. There are many methods proposed in the literature to solve TSP with profit and losses. In this classical problem, the objective is to visit a finite number of locations exactly once, one by one, while minimizing the total distance traveled by the connecting links (arcs) needed to reach these sites (nodes). This study presents a new procedure that applies TSP and makes use of the decision tree notion. Anywhere in the TSP network, where n is the total number of places (nodes) in the network, this system ends after n-1 iterations. The method's step-by-step computational criteria make it efficient and readily applicable. To demonstrate the process's validity and efficiency, numerical examples are provided.

Sustainable paddy farming in rural Japan: Leveraging farmer integration and agricultural UAVs for synergistic solutions

For sustainable rice farming, IoT-based smart agricultural technologies are attracting worldwide attention. In particular, agricultural UAVs, which are expected to be utilized in various seasonal processes of rice farming, are a facility that is expected to spread in the future. In Japan, however, the smooth spread of UAVs has not progressed because of uncertainty about the effectiveness of their introduction. In this study, we clarify the effect of the introduction and its limitations by simulating the synergy effect between customary management improvement methods by farmers' integration and the efficiency improvement of agricultural work using UAVs, using a mountainous area in Japan as an example. The visualization of the expected increase in labor productivity provides a strong basis for future policies to promote smart agricultural technologies. The simulation model was built on the theoretical basis of the optimal route search based on the traveling salesman problem, in which the farmer's behavior of visiting farmland is considered a traveling salesman problem, and the effect of introducing UAVs was predicted using annual working hours as an evaluation index. The results showed that the introduction of UAVs could achieve a greater reduction in labor hours than the case where farmer integration alone was used to improve labor productivity without the introduction of UAVs. In other words, the combination of farmer integration and UAVs is expected to synergize. However, even when assuming reasonable UAVs performance, labor productivity improved by about 20%, and even when using high-performance UAVs assuming drastic technological innovation, labor productivity improved by only about 30%. Furthermore, as the number of farmlands to be managed increased, the effect of UAVs was expected to reach a ceiling. In other words, the results suggest an appropriate size of farmland to manage by introducing UAVs. This result is expected to be convincing material to promote the introduction of UAVs to farmers in the future and to make a practical contribution to their management plans.

Path planning of manure-robot cleaners using grid-based reinforcement learning

The use of a robot cleaner for manure removal improves housing conditions for dairy cows in the face of labor shortages. However, current robot cleaners follow programmed fixed routes without considering the dynamic behaviors of cows. This cleaning approach is less efficient and leads to more cow-robot encounters or collisions, thus affecting animal welfare. To address these issues, this paper (1) developed heatmap models for cow locations and defecation behaviors; (2) proposed a dynamic path planning approach for the manure robot cleaner using Grid-based Reinforcement Learning; (3) incorporated cow location information and defecation behavior into the path planning process; (4) compared the performance of the proposed approach with two different cleaning methods: the current fixed programmed cleaning in practice and the ideal path produced by simulated annealing for traveling salesman problem. The simulations mimic the situation in a barn at Dairy Campus of Wageningen Livestock Research located in Leeuwarden (the Netherlands). Obviously, the best performance was achieved when the route was executed without cows present, resulting in no cow-robot collision. However, with cows present, the proposed dynamic path planning strategy achieved a 67.6% reduction in cow-robot encounters while maintaining 85.4% of the cleaning performance compared to the current programmed fixed routes. Compared to the ideal path produced by simulated annealing for traveling salesman problem, the proposed dynamic path planning approach achieved 5% better cleaning performance, at the cost of 25% more cow-robot encounters due to its longer working path. We conclude the proposed grid-based Reinforcement Learning solution for manure robots in barns cleaned most efficient with the least interference with cow traffic.