K-DSA for the multiple traveling salesman problem

Aimed at a multiple traveling salesman problem(MTSP)with multiple depots and closed paths,this paper proposes a k-means clustering donkey and a smuggler algorithm(KDSA).The algorithm first uses the k-means clustering method to divide all cities into several categories based on the center of various samples;the large-scale MTSP is divided into multiple separate traveling salesman problems(TSPs),and the TSP is solved through the DSA.The proposed algorithm adopts a solution strategy of clustering first and then carrying out,which can not only greatly reduce the search space of the algorithm but also make the search space more fully explored so that the optimal solution of the problem can be more quickly obtained.The experimental results from solving several test cases in the TSPLIB database show that compared with other related intelligent algorithms,the K-DSA has good solving performance and computational efficiency in MTSPs of different scales,especially with large-scale MTSP and when the convergence speed is faster;thus,the advantages of this algorithm are more obvious compared to other algorithms.

求解TSP的离散野马优化算法

针对求解TSP问题,提出一种新的元启发式算法离散野马优化算法(DWHO),应用最小位置匹配值法(MPMV)对求解结果进行离散化解码;为提高算法搜索能力,结合野马放牧、交配、领导者交流与选拔行为,引入变邻域搜索策略,增强了算法的局部搜索能力、加快算法收敛速度。选取TSPLIB标准库33个算例进行实验,并与交换序列人工蜂群算法(ABCSS)、离散蜘蛛猴优化算法(DSMO)两种算法进行比较。实验结果表明,DWHO求得的最优解与ABCSS、DSMO两种算法的最优解相比,最优解改进率最大值分别达到4.52%和3.41%。同时,将离散野马优化算法求解TSP收敛速度与以上两种算法进行比较,其收敛速度具有一定的优势。结果表明离散野马优化算法求解能力和精度具有优势。

基于信息熵的改进蚁群算法求解TSP问题

针对蚁群算法求解精度低、易陷入局部最优的缺点,提出一种基于信息熵的自适应改进蚁群算法。通过算法自身特性定义结合熵值对种群参数进行自适应优化;采用分组合作的信息素更新策略,通过较活跃性个体引导整个种群,扩大搜索范围;通过对较优路径的奖励,平衡收敛速度和搜索范围之间的关系;在种群信息熵过低时,加入局部搜索策略,进一步提高算法精度。实验结果表明,相较于蚁群算法,改进算法具有较好的求解精度以及跳出局部最优的能力。

A Hybrid Genetic Algorithm for the Traveling Salesman Problem with Pickup and Delivery

In this paper, a hybrid genetic algorithm （GA） is proposed for the traveling salesman problem （TSP） with pickup and delivery （TSPPD）. In our algorithm, a novel pheromone-based crossover operator is advanced that utilizes both local and global information to construct offspring. In addition, a local search procedure is integrated into the GA to accelerate convergence. The proposed GA has been tested on benchmark instances, and the computational results show that it gives better convergence than existing heuristics.

Collision-free Scheduling of Multi-bridge Machining Systems： A Colored Traveling Salesman Problem-based Approach

Multi-bridge machining systems(MBMS) have gained wide applications in industry due to their high production capacity and efficiency. They contain multiple bridge machines working in parallel within their partially overlapping workspaces.Their scheduling problems can be abstracted into a serial-colored travelling salesman problem in which each salesman has some exclusive cities and some cities shared with its neighbor(s). To solve it, we develop a greedy algorithm that selects a neighboring city satisfying proximity. The algorithm allows a salesman to select randomly its shared cities and runs accordingly many times. It can thus be used to solve job scheduling problems for MBMS. Subsequently, a collision-free scheduling method is proposed to address both job scheduling and collision resolution issues of MBMS. It is an extension of the greedy algorithm by introducing time window constraints and a collision resolution mechanism. Thus, the augmented greedy algorithm can try its best to select stepwise a job for an individual machine such that no time overlaps exist between it and the job sequence of the neighboring machine dealt in the corresponding overlapping workspace; and remove such a time overlap only when it is inevitable. Finally, we conduct a case study of a large triplebridge waterjet cutting system by applying the proposed method.

Traveling Salesman Problem Using an Enhanced Hybrid Swarm Optimization Algorithm

The traveling salesman problem( TSP) is a well-known combinatorial optimization problem as well as an NP-complete problem. A dynamic multi-swarm particle swarm optimization and ant colony optimization( DMPSO-ACO) was presented for TSP.The DMPSO-ACO combined the exploration capabilities of the dynamic multi-swarm particle swarm optimizer( DMPSO) and the stochastic exploitation of the ant colony optimization( ACO) for solving the traveling salesman problem. In the proposed hybrid algorithm,firstly,the dynamic swarms,rapidity of the PSO was used to obtain a series of sub-optimal solutions through certain iterative times for adjusting the initial allocation of pheromone in ACO. Secondly,the positive feedback and high accuracy of the ACO were employed to solving whole problem. Finally,to verify the effectiveness and efficiency of the proposed hybrid algorithm,various scale benchmark problems were tested to demonstrate the potential of the proposed DMPSO-ACO algorithm. The results show that DMPSO-ACO is better in the search precision,convergence property and has strong ability to escape from the local sub-optima when compared with several other peer algorithms.

Parallel discrete lion swarm optimization algorithm for solving traveling salesman problem

As a typical representative of the NP-complete problem, the traveling salesman problem(TSP) is widely utilized in computer networks, logistics distribution, and other fields. In this paper, a discrete lion swarm optimization(DLSO) algorithm is proposed to solve the TSP. Firstly, we introduce discrete coding and order crossover operators in DLSO. Secondly, we use the complete 2-opt(C2-opt) algorithm to enhance the local search ability.Then in order to enhance the efficiency of the algorithm, a parallel discrete lion swarm optimization(PDLSO) algorithm is proposed.The PDLSO has multiple populations, and each sub-population independently runs the DLSO algorithm in parallel. We use the ring topology to transfer information between sub-populations. Experiments on some benchmarks TSP problems show that the DLSO algorithm has a better accuracy than other algorithms, and the PDLSO algorithm can effectively shorten the running time.

Ant-cycle based on Metropolis rules for the traveling salesman problem

In this paper, recent developments of some heuristic algorithms were discussed. The focus was laid on the improvements of ant-cycle (AC) algorithm based on the analysis of the performances of simulated annealing (SA) and AC for the traveling salesman problem (TSP). The Metropolis rules in SA were applied to AC and turned out an improved AC. The computational results obtained from the case study indicated that the improved AC algorithm has advantages over the sheer SA or unmixed AC.

Learning-Based Metaheuristic Approach for Home Healthcare Optimization Problem

This research focuses on the home health care optimization problem that involves staff routing and scheduling problems.The considered problem is an extension of multiple travelling salesman problem.It consists of finding the shortest path for a set of caregivers visiting a set of patients at their homes in order to perform various tasks during a given horizon.Thus,a mixed-integer linear programming model is proposed to minimize the overall service time performed by all caregivers while respecting the workload balancing constraint.Nevertheless,when the time horizon become large,practical-sized instances become very difficult to solve in a reasonable computational time.Therefore,a new Learning Genetic Algorithm for mTSP(LGA-mTSP)is proposed to solve the problem.LGA-mTSP is composed of a new genetic algorithm for mTSP,combined with a learning approach,called learning curves.Learning refers to that caregivers’productivity increases as they gain more experience.Learning curves approach is considered as a way to save time and costs.Simulation results show the efficiency of the proposed approach and the impact of learning curve strategy to reduce service times.

路径交叉测绘任务规划问题

不同于传统多旅行商问题,小型飞机测绘任务规划问题的每个测绘目标需要测绘多个测绘载荷,同时多次测绘间要有时间间隔,称之为路径交叉的多旅行商路径规划问题。针对点目标测绘任务场景,将最少飞机数量的求解目标转化为求解最短航行路径。在采用遗传算法求解最短路径的基础上,结合探测载荷约束、探测任务时长约束等条件,进一步规划出最优的调度方案。针对点目标和区域目标测绘任务规划问题,考虑各机场测绘任务工作量的均衡,定义测绘工作量指标为每个机场完成的测绘目标点和目标道路的数目,求解调度策略和飞机数量。在此基础上求解均衡性,使3个机场探测的目标点和目标道路数量相当。结果表明,所提方案兼顾了测绘代价与任务分配的均衡性。

结合竞争交互策略和淘汰重组机制的异构多蚁群算法

针对传统的蚁群算法在解决旅行商问题时(traveling salesman problem,TSP)存在着收敛速度慢、容易陷入局部最优等问题,提出了一种结合竞争交互策略和淘汰重组机制的异构多蚁群算法。建立一个异构多种群系统,算法采用竞争交互策略,根据不同时期各种群的汉明距离来自适应的调节交互周期;并利用竞争系数来差异化匹配交互对象,经过匹配后的交互对象之间通过最优解和信息素矩阵进行交互,通过该机制实现了算法收敛速度和多样性的平衡。算法采用了淘汰重组机制,会定期对寻优能力差的种群进行淘汰与重组,以加快算法的求解精度。采用多组不同规模的TSP算例进行仿真实验,结果表明,该算法在提高求解精度和收敛速度方面表现更优。

求解TSP问题的多级归约算法

TSP(traveling salesman problem)问题是最经典的NP-hard组合优化问题之一.长期以来,人们一直在寻求快速、高效的近似算法,以便在合理的计算时间内解决大规模问题.由于对较大规模的问题,目前的近似算法尚不能在较短的时间内给出高质量的解,因此提出了多重归约算法.该算法的基本原理是通过对TSP问题的局部最优解与全局最优解之间关系的分析,发现对局部最优解的简单的相交操作能以很高的概率得到全局最优解的部分解.利用这些部分解可以大大缩小原问题的搜索空间,同时也不会降低搜索的性能.这就是所谓的归约原理.再通过多次归约使问题的规模降到足够小,然后对这个较小规模的实例直接用已有的算法求解,最后通过相反的次序拼接部分解,最终得到一个合法的解.在TSPLIB(traveling salesman problem library)中,典型实例上的实验结果表明,此算法在求解质量和求解速度上与目前已知的算法相比有较大的改进.

求解TSP问题的一种改进的遗传算法

TSP问题是典型的NP完全问题,遗传算法是求解NP完全问题的一种理想方法。文章针对解决TSP问题,提出使用改进的遗传算法,即用浓度控制选择策略以保证群体的多样性,用贪婪交叉算子和启发式倒位变异算子来提高算法的收敛速度,较好地解决了群体的多样性和收敛速度的矛盾。算法的分析和测试表明,该文算法的改进是有效的。

改进的混沌粒子群算法在TSP中的应用

针对基本粒子群(PSO)算法不能较好地解决旅行商优化问题(TSP),分析了基本粒子群算法的优化机理,在新定义粒子群进化方程中进化算子的基础上利用混沌运动的随机性、遍历性等特点,提出一种结合混沌优化和粒子群算法的改进混沌粒子群算法。该算法对惯性权重进行自适应调整,引入混沌载波调整搜索策略避免陷入局部最优,形成一种同时满足全局和局部寻优搜索的混合离散粒子群算法,使其适合解决TSP此类组合优化问题。利用MATLAB对其进行了仿真。仿真结果说明此算法的搜索精度、收敛速度及优化效率均较优,证明了此算法在TSP中应用的有效性,且为求解TSP提供了一种参考方法。

一种求解TSP的混合遗传蚁群算法

结合遗传算法和蚁群算法,提出了一种求解TSP的基于启发式遗传信息的蚁群遗传算法。该算法由蚁群遗传算法和基于启发式遗传信息的蚁群算法两部分组成。蚁群遗传算法将蚁群算法和遗传算法结合起来,提高了遗传算法的种群的多样性;基于启发式遗传信息的蚁群算法是将启发式遗传信息加入到蚁群算法中,防止蚁群算法对信息素过分依赖,缩小最优解的搜索空间。HGI-ACGA算法是将启发式遗传信息加入到蚁群遗传算法中,可以提高蚁群算法的收敛速度和寻优能力。实验结果表明,HGI-ACGA算法在收敛速度和收敛精度上均优于ACGA和ACA算法。

蚁群算法中参数α、β、ρ设置的研究——以TSP问题为例

以TSP问题为例 ,对蚁群算法中参数α、β、ρ的作用作了理论上的研究 ,同时对最优的参数配置问题作了分析。在保证获得解的前提下 ,为了提高计算速度 ,对基本蚁群算法中的选择路线策略进行了调整。通过实例计算表明 ,这种调整是切实可行的 ,有较好的实用价值。

面向TSP求解的混合蚁群算法

针对蚁群算法的早熟和停滞等现象,将免疫算法机制引入蚁群算法,提出用于TSP求解的混合算法。该算法具有蚁群算法的自适应反馈机理、收敛速度快和免疫算法操作算子简单和维持种群多样性、防止种群退化等特性。从算法解的质量与效率方面与基本蚁群算法和免疫算法进行比较,结果表明融合免疫机制的蚁群算法性能显著提高,也为解决其他组合优化问题提供一个新的思路。

基于局部优化策略求解TSP的蚁群算法

为了克服基本蚁群算法收敛速度慢、易于停滞的缺陷,提出了一种基于局部优化策略的蚁群算法(LO-ACA)。该算法根据TSP的特点,采用了三种局部优化算子来交换搜索路径中城市的位置,以改进解的质量。以TSP为例进行的实验结果表明,该算法优于ACA和ACAGA。

旅行商问题(TSP)的几种求解方法

旅行商问题(TSP)是组合优化领域里的一个典型的、易于描述却难以处理的NP完全难题,其可能的路径数目与城市数目是呈指数型增长的,求解非常困难。而快速、有效地解决TSP有着重要的理论价值和极高的实际应用价值。该文首先介绍了什么是TSP,接着论述了六种目前针对TSP比较有效的解决方法(模拟退火算法、禁忌搜索算法、Hopfie ld神经网络优化算法、蚁群算法、遗传算法和混合优化策略)的基本思想,并且简单阐述了它们的求解过程,最后分别指出了各自的优缺点并对解决TSP的前景提出了展望。

求解TSP的新量子蚁群算法

鉴于蚁群算法(ACA)在求解TSP时表现出的优越性,以及量子进化算法(QEA)在求解组合优化问题时表现出的高效性,将ACA与QEA的算法思想进行融合,提出一种新的求解TSP的量子蚁群算法。该算法对各路径上的信息素进行量子比特编码,设计了一种新的信息素表示方式,即量子信息素;采用量子旋转门及最优路径对信息素进行更新,加快算法收敛速度;为了避免搜索陷入局部最优,设计了一种量子交叉策略,以改善种群信息结构。仿真实验结果表明了该算法具有较快的收敛速度和全局寻优能力,性能明显优于ACS。