Multi-traveling Salesman Problem Research Articles

A Heuristic Routing Algorithm for Heterogeneous UAVs in Time-Constrained MEC Systems

The rapid proliferation of Internet of Things (IoT) ground devices (GDs) has created an unprecedented demand for computing resources and real-time data-processing capabilities. Integrating unmanned aerial vehicles (UAVs) into Mobile Edge Computing (MEC) emerges as a promising solution to bring computation and storage closer to the data sources. However, UAV heterogeneity and the time window constraints for task execution pose a significant challenge. This paper addresses the multiple heterogeneity UAV routing problem in MEC environments, modeling it as a multi-traveling salesman problem (MTSP) with soft time constraints. We propose a two-stage heuristic algorithm, heterogeneous multiple UAV routing (HMUR). The approach first identifies task areas (TAs) and optimal hovering positions for the UAVs and defines an effective fitness measurement to handle UAV heterogeneity. A novel scoring function further refines the path determination, prioritizing real-time task compliance to enhance Quality of Service (QoS). The simulation results demonstrate that our proposed HMUR method surpasses the existing baseline algorithms on multiple metrics, validating its effectiveness in optimizing resource scheduling in MEC environments.

Relative distances approach for multi-traveling salesmen problem

In this paper, we present a novel approach to addressing the Multi-Traveling Salesman Problem (MTSP), a complex optimization challenge involving the simultaneous fulfillment of multiple tasks such as cargo delivery and warehouse placement by multiple autonomous agents. In general there are two primary objectives to be achieved: minimizing the total path cost and minimizing the maximum cost incurred by agents, also known as makespan. While our primary focus centers on cost minimization, prioritizing this aspect alone often amplifies makespan. Our approach strikes a balance by ensuring that makespan remains within a reasonable threshold. Given the problem’s combinatorial nature, attaining cost-optimal solutions proves infeasible under current constraints. Hence, our emphasis shifts towards swift solution discovery to align with practical applicability. Consequently, we posit that the third pivotal objective is to curtail complexity and expedite solution acquisition, thereby enhancing the problem’s real-world viability. The Multi-Traveling Salesman Problem (MTSP) is typically approached in two distinct phases. In the initial phase, tasks are allocated to salesmen using various methods (such as K-Means or DBSCAN). The second phase involves determining the optimal routes for each salesman, a problem identical to the classic Traveling Salesman Problem (TSP). Our novel heuristic approach integrates these phases into a single method through our relative distance model. This model facilitates the easy addition and removal of tasks within the problem space and enables real-time scheduling.

Multi-Traveler Salesman Problem for Unmanned Vehicles: Optimization through Improved Hopfield Neural Network

In response to the COVID-19 pandemic, communities utilize unmanned vehicles to minimize person-to-person contact and lower the risk of infection. This paper addresses the critical considerations of these unmanned vehicles’ maximum load capacity and service time, formulating them as constraints within a multi-traveling salesman problem (MTSP). We propose a comprehensive optimization approach that combines a genetic simulated annealing algorithm with clustering techniques and an improved Hopfield neural network (IHNN). First, the MTSP is decomposed into multiple independent TSPs using the fuzzy C-means clustering algorithm based on a genetic simulated annealing algorithm (SA-GA-FCM). Subsequently, the HNN is employed to introduce the data transformation technique and dynamic step factor to prepare more suitable inputs for the HNN training process to avoid the energy function from falling into local solutions, and the simulated annealing algorithm is introduced to solve multiple TSP separately. Finally, the effectiveness of the proposed algorithm is verified by small-scale and large-scale instances, and the results clearly demonstrate that each unmanned vehicle can meet the specified constraints and successfully complete all delivery tasks. Furthermore, to gauge the performance of our algorithm, we conducted ten simulation comparisons with other combinatorial optimization and heuristic algorithms. These comparisons indicate that IHNN outperforms the algorithms mentioned above regarding solution quality and efficiency and exhibits robustness against falling into local solutions. As presented in this paper, the solution to the unmanned vehicle traveling salesman problem facilitates contactless material distribution, reducing time and resource wastage while enhancing the efficiency of unmanned vehicle operations, which has profound implications for promoting low-carbon sustainable development, optimizing logistics efficiency, and mitigating the risk of pandemic spread.

A model-based decision framework for the multi-depot multi-travelling salesman problem with split and delivery demand considering different key performance indicators

A model-based decision framework for the multi-depot multi-travelling salesman problem with split and delivery demand considering different key performance indicators

A Hybrid Large Neighborhood Search Algorithm for Solving the Multi Depot UAV Swarm Routing Problem

This paper focuses on a modified Multi-Depot Unmanned Aerial Vehicle Routing Problem (MMDUAVRP). Comparing to classic multi-depot vehicle routing problem, our studied problem has no constraints to restrict the depot where the Unmanned Aerial Vehicle (UAV) departs and returns. This work aims to minimize the number of UAVs and total distance traveled by all UAVs. This problem is mathematically formulated in this paper and a heuristic-assignment based hybrid large neighborhood search(HLNS) is proposed to solve it. Extensive computational experiments are conducted to verify the performance of HLNS. The HLNS algorithm was first tested on Multi Traveling Salesman Problem which is a simplified version of the MMDUAVRP, and high quality solutions have been obtained. Experimental results by compared with CPLEX and other well-known algorithms suggest that our proposed algorithm provides better solutions within a comparatively shorter period of time. In addition, we also conduct sensitivity analysis on the location of depots and task points that may affect the total cost of solution.

Parallel Swarm Intelligent Motion Planning with Energy‐Balanced for Multirobot in Obstacle Environment

Multirobot motion planning is always one of the critical techniques in edge intelligent systems, which involve a variety of algorithms, such as map modeling, path search, and trajectory optimization and smoothing. To overcome the slow running speed and imbalance of energy consumption, a swarm intelligence solution based on parallel computing is proposed to plan motion paths for multirobot with many task nodes in a complex scene that have multiple irregularly‐shaped obstacles, which objective is to find a smooth trajectory under the constraints of the shortest total distance and the energy‐balanced consumption for all robots to travel between nodes. In a practical scenario, the imbalance of task allocation will inevitably lead to some robots stopping on the way. Thus, we firstly model a gridded scene as a weighted MTSP (multitraveling salesman problem) in which the weights are the energies of obstacle constraints and path length. Then, a hybridization of particle swarm and ant colony optimization (GPSO‐AC) based on a platform of Compute Unified Device Architecture (CUDA) is presented to find the optimal path for the weighted MTSPs. Next, we improve the A∗ algorithm to generate a weighted obstacle avoidance path on the gridded map, but there are still many sharp turns on it. Therefore, an improved smooth grid path algorithm is proposed by integrating the dynamic constraints in this paper to optimize the trajectory smoothly, to be more in line with the law of robot motion, which can more realistically simulate the multirobot in a real scene. Finally, experimental comparisons with other methods on the designed platform of GPUs demonstrate the applicability of the proposed algorithm in different scenarios, and our method strikes a good balance between energy consumption and optimality, with significantly faster and better performance than other considered approaches, and the effects of the adjustment coefficient q on the performance of the algorithm are also discussed in the experiments.

A Model-Based Decision Framework for the Multi-Depot Multi-Traveling Salesman Problem with Split and Delivery Demand considering different Key Performance Indicators

A Model-Based Decision Framework for the Multi-Depot Multi-Traveling Salesman Problem with Split and Delivery Demand considering different Key Performance Indicators

A simulated annealing approach to solve a multi traveling salesman problem in a FMCG company

FMCG Companies are fast spreading across the globe and there is a huge need for efficient delivery of goods to the consumers. In the normal context the regular vehicle routing problem was defined for various cities but within a city there is a need for multiple vehicular movements with different warehouse hubs to facilitate the delivery of goods. Often such problems are defined as hub and spoke mechanism. The hub may be defined as the central resource station from which the various goods will originate and spoke represents the various destination to reach out the customers. In this paper we have used simulated annealing approach to design a Multi traveling sales man problem.

Design and Analysis of Multi-Objective Optimization Problem Using Evolutionary Algorithms.

Abstract In this paper a major amount of work has been listed regarding multi-objective optimization problem using evolutionary algorithms. From time immemorial optimization have been required in every industry for improvement of the business or other scientific results. Evolutionary algorithms is a direct search algorithm and has been applied for various mathematical models to attain optimal results because of its adaptability with the system. The aim of the study is to find a multi-objective transportation problem by using evolutionary algorithm in bipartite graph. In multi-travelling salesman problem the objective to derive the optimal sequencing schedule of a salesman which is formed as a multiple objective problem.

A Hierarchical Cooperative Mission Planning Mechanism for Multiple Unmanned Aerial Vehicles

In this paper, the cooperative multi-task online mission planning for multiple Unmanned Aerial Vehicles (UAVs) is studied. Firstly, the dynamics of unmanned aerial vehicles and the mission planning problem are studied. Secondly, a hierarchical mechanism is proposed to deal with the complex multi-UAV multi-task mission planning problem. In the first stage, the flight paths of UAVs are generated by the Dubins curve and B-spline mixed method, which are defined as “CBC)” curves, where “C” stands for circular arc and “B” stands for B-spline segment. In the second stage, the task assignment problem is solved as multi-base multi-traveling salesman problem, in which the “CBC” flight paths are used to estimate the trajectory costs. In the third stage, the flight trajectories of UAVs are generated by using Gaussian pseudospectral method (GPM). Thirdly, to improve the computational efficiency, the continuous and differential initial trajectories are generated based on the “CBC” flight paths. Finally, numerical simulations are presented to demonstrate the proposed approach, the designed initial solution search algorithm is compared with existing methods. These results indicate that the proposed hierarchical mission planning method can produce satisfactory mission planning results efficiently.

A hyper-heuristic based artificial bee colony algorithm for k-Interconnected multi-depot multi-traveling salesman problem

This paper addresses a newly introduced variant of traveling salesman problem, viz. k-Interconnected Multi-Depot Multi-Traveling Salesman Problem (k-IMDMTSP). This problem has the potential to address a variety of problems as it is a general problem that can change its characteristics according to the combination of parameter values. In fact, k-IMDMTSP can become an altogether different problem depending on the choice of its parameter values. According to the No Free Lunch Theorem [43], it is not possible to have a general algorithm that can outperform all algorithms across all problems emanating from k-IMDMTSP due to various parameter values. However, an appropriate combination of different algorithms can successfully deal with all such problems emanating from k-IMDMTSP. Here, we have made an attempt in this direction with the help of hyper-heuristics. A hyper-heuristic based artificial bee colony algorithm is proposed for k-IMDMTSP. A new solution encoding scheme is proposed for representing a k-IMDMTSP solution within the proposed approach, and its associated search space is analyzed theoretically. It has been proved that our encoding scheme yields a search space that is considerably smaller in comparison to encoding schemes used previously. Experimental results on standard benchmark instances show that the proposed approach outperforms other state-of-the-art approaches available in literature in terms of both solution quality and running time.

An Application of Genetic Algorithm in Determining Salesmen’s Routes: A Case Study

This paper presents a case study of determining vehicles’ routes. The case is taken from a pharmaceutical products distribution problem faced by a distribution company located in the city of Padang, Indonesia. The objective of this paper is to reduce the total distribution time required by the salesmen of the company. Since the company uses more than one salesman, then the problem is modeled as a multi travelling salesman problem (m-TSP). The problem is solved by employing genetic algorithm (GA) and a Matlab® based computer program is developed to run the algorithm. It is found that, by employing two salesmen only, the routes produced by GA results in a 30% savings in total distribution time compared to the current routes used by the company (currently the company employs three salesmen). This paper determines distances based on the latitude and longitude of the locations visited by the salesmen. Therefore, the distances calculated in this paper are approximations. It is suggested that actual distances are used for future research.

Multi-objective optimized connectivity restoring of disjoint segments using mobile data collectors in wireless sensor network

Wireless sensor networks (WSNs) have been used extensively in a range of applications, which realizes data acquisition, processing, transmission, and analysis in an interesting area. Harsh surroundings and their inherent vulnerability often mean that these networks suffer from simultaneous node failure possibly causing the network to become partitioned into multiple disjointed segments. This in turn can prevent the gathering of data from the sensors and subsequent transmission to the sink, causing the whole network to fail. In this paper, a strategy is presented for restoring multi-objective optimization connectivity of these segments using mobile data collectors (MDCs), by considering the segments as collections of sensor nodes and not as some representative node. Different from existing uses of MDCs for restoration, the delay in data collection and task balance is considered, and the network connectivity and data acquisition path optimization problem are transformed into an improved multi-travelling salesman problem (iMTSP). An improved multi-objective optimization genetic algorithm for solving the optimal collection data collector position and moving paths is proposed, which introduces virtual segments and hierarchical chromosome structure, improved population diversity, and custom coding and decoding. The simulation results show that the proposed method can effectively solve the iMTSP of the Pareto optimal solution and can provide a new strategy for connectivity-restoring technology in WSNs. Compared with NSGA-II, the diversity of the proposed gene algorithm represents a clear improvement.

A Framework for the Design and Analysis of an Evolutionary Algorithm for Multi Travelling Salesman Problem

This paper mainly deals with the design of an evolutionary algorithm for a Multi Travelling Salesman problem. The solution for this problem in multi application fields becomes a highly NP hard type problems which is in need of an efficient solution. The aim of the study is to find an optimal schedule of a salesman which is formed as a multiple objective problem. The mathematical model for the Multi Objective in Multi Travelling salesman problem is stated with the corresponding notations. To get an optimal schedule an evolutionary based approach is proposed to meet the criteria.The proposed algorithm is modelled and stimulated as a program and tested with a suitable example. The output results are given as a grant chart, with the optimal sequence schedule of each salesman.

A population-based algorithm for the multi travelling salesman problem

A population-based algorithm for the multi travelling salesman problem

Probabilistic multi‐hypothesis tracker for multiple platform path planning

This study considers the problem of automatically coordinating multiple platforms to explore an unknown environment. The goal is a planning algorithm that provides a path for each platform in such a way that the collection of platforms cooperatively sense the environment in a globally efficient manner. The environment is described by a spatially non-homogeneous priority function. The method samples this function to produce a discrete collection of locales that the platforms use as waypoints. The key feature of the method is to treat the assignment of locales to platforms as a target tracking problem and to use the probabilistic multi-hypothesis tracker (PMHT) as a method of performing multi-platform batch data association. This paper introduces the PMHT path planner (PMHT-pp) and compares this algorithm as a method of performing multiple platform batch data association with the Genetic Algorithm to solve the modified multi-travelling salesman problem.

A linear MmTSP formulation of robust location-routing problem: a dairy products supply chain case study

The location-routing problem (LRP), which integrates location and routing decisions, has been an attraction to both researchers and practitioners. LRP as an important business problem has its own inherent uncertainty; especially, considering phenomena such as traffic congestion and weather conditions and their impact on transportation costs, routing in LRP is subject to uncertainty. In this paper, we propose a multi-depot multi-travelling salesman problem (MmTSP) formulation of robust LRP (RLRP) considering uncertainty in transportation costs. In addition, an appropriate technique is utilised to linearise the RLRP model. In order to justify the applicability of the proposed model, a dairy products supply chain case study is provided. Furthermore, comprehensive numerical examples are presented to characterise the performance of the proposed model.

A novel method for solving the multiple traveling salesmen problem with multiple depots

Multi-traveling salesman problem (MTSP) is an extension of traveling salesman problem, which is a famous NP hard problem, and can be used to solve many real world problems, such as railway transportation, routing and pipeline laying. In this paper, we analyze the general properties of MTSP, and find that the multiple depots and closed paths in the graph is a big issue for MTSP. Thus, a novel method is presented to solve it. We transform a complicated graph into a simplified one firstly, then an effective algorithm is proposed to solve the MTSP based on the simplified results. In addition, we also propose a method to optimize the general results by using 2-OPT. Simulation results show that our method can find the global solution for MTSP efficiently.

A reactive tabu search algorithm for the multi-depot container truck transportation problem

A container truck transportation problem that involves multiple depots with time windows at both origins and destinations, including the reposition of empty containers, is formulated as a multi-traveling salesman problem with time windows (m-TSPTW) with multiple depots. Since the problem is NP-hard, a cluster method and a reactive tabu search (RTS) algorithm are developed to solve the problem. The two methods are compared with the mixed integer program which can be used to find optimum solutions for small size problems. The computational results show that the developed methods, particularly the RTS algorithm, can be efficiently used to solve the problem.

Exact and inexact solution procedures for the order picking in an automated carousal conveyor

In many modern logistic systems, automated carousal conveyors are frequently used for storing/retrieving small to medium items to fulfil the customer's demand. The system is used to process a sequence of orders from customers in a dynamic fashion. Each order includes one or several items to be picked from the carousal storage or bin. The sequence between orders and the sequences among items within each order are to be determined, to minimise the total order processing or associated picking cost. This multi-order picking problem is formulated as 0–1 integer programming model, which resembles the well-known Multi-travelling salesman problem. Some important properties of this unique order processing system are described. New theoretical properties are established to characterise the optimal retrieval sequence in an order with multiple items to be picked. Based on these properties, efficient and effective heuristics are developed to solve this multi-order picking problem. The computational detail of these approaches is illustrated by an example. Numerical experiments with problem sizes up to 500 items for a batch of 50 orders are performed, where different order densities and order rates are considered.