求解TSP的混合遗传算法

介绍一种求解TSP的混合遗传算法,该算法结合了基于邻域的LK算法和采用Inver-Over算子的遗传算法,并在算法中增加一些控制策略,加快算法的收敛速度,又保证群体的多样性。实验表明该算法是有效的。     

多目标旅行商问题的模拟植物生长算法求解

针对多目标旅行商问题,提出了一种基于模拟植物生长的优化算法。该算法将Deb等人提出的非支配排序及构造偏序集等方法用于模拟植物生长的过程中,克服了模拟植物生长算法搜索空间过大及收敛性不够理想的缺点。基于该算法的核心思想,用MATLAB编程实现,对参考文献的算例进行仿真测试。与其他算法比较,获得了满意的结果。     

Discrete symbiotic organisms search algorithm for travelling salesman problem

A Discrete Symbiotic Organisms Search (DSOS) algorithm for finding a near optimal solution for the Travelling Salesman Problem (TSP) is proposed. The SOS is a metaheuristic search optimization algorithm, inspired by the symbiotic interaction strategies often adopted by organisms in the ecosystem for survival and propagation. This new optimization algorithm has been proven to be very effective and robust in solving numerical optimization and engineering design problems. In this paper, the SOS is improved and extended by using three mutation-based local search operators to reconstruct its population, improve its exploration and exploitation capability, and accelerate the convergence speed. To prove that the proposed solution approach of the DSOS is a promising technique for solving combinatorial problems like the TSPs, a set of benchmarks of symmetric TSP instances selected from the TSPLIB library are used to evaluate its performance against other heuristic algorithms. Numerical results obtained show that the proposed optimization method can achieve results close to the theoretical best known solutions within a reasonable time frame.     

Discrete cuckoo search algorithm for the travelling salesman problem

In this paper, we present an improved and discrete version of the Cuckoo Search (CS) algorithm to solve the famous traveling salesman problem (TSP), an NP-hard combinatorial optimisation problem. CS is a metaheuristic search algorithm which was recently developed by Xin-She Yang and Suash Deb in 2009, inspired by the breeding behaviour of cuckoos. This new algorithm has proved to be very effective in solving continuous optimisation problems. We now extend and improve CS by reconstructing its population and introducing a new category of cuckoos so that it can solve combinatorial problems as well as continuous problems. The performance of the proposed discrete cuckoo search (DCS) is tested against a set of benchmarks of symmetric TSP from the well-known TSPLIB library. The results of the tests show that DCS is superior to some other metaheuristics.     

A self-organised travelling salesman

Using the principles of self-organisation and Darwin's theory of evolution, an algorithm has been developed to solve the geometric travelling salesman problem (TSP). In this approach, we have virtual and real nodes (cities) which can have equal or different masses (weights). The virtual nodes and their neighours are attracted toward the fixed cities by a Newtonian force. The birth and death of the virtual nodes creates a world in which only the fittest survive. This approach has been successfully tested on many problems of different sizes, with a constant error of about 4.6% across the whole range. The computing time follows a power series (square law) versus the number of cities. Comparison of our results with those obtained by a simulated annealing method showed the solutions that obtained by this self-organisation method are of a better quality, especially for large size problems.     

A hybrid swarm intelligence algorithm for the travelling salesman problem

Abstract: We present a hybrid model named HRKPG that combines the random‐key search method and an individual enhancement scheme to thoroughly exploit the global search ability of particle swarm optimization. With a genetic algorithm, we can expand the area of exploration of individuals in the solution space. With the individual enhancement scheme, we can enhance the particle swarm optimization and the genetic algorithm for the travelling salesman problem. The objective of the travelling salesman problem is to find the shortest route that starts from a city, visits every city once, and finally comes back to the start city. With the random‐key search method, we can search the ability of the particle and chromosome. On the basis of the proposed hybrid scheme of HRKPG, we can improve solution quality quite a lot. Our experimental results show that the HRKPG model outperforms the particle swarm optimization and genetic algorithm in solution quality.     

The intermittent travelling salesman problem

In this paper, we introduce a new variant of the travelling salesman problem, namely the intermittent travelling salesman problem (ITSP), which is inspired by real‐world drilling/texturing applications. In this problem, each vertex can be visited more than once and there is a temperature constraint enforcing a time lapse between two consecutive visits. A branch‐and‐bound approach is proposed to solve small instances to optimality. We furthermore develop four variable neighbourhood search metaheuristics which produce high‐quality solutions for large instances. An instance library is built and made publicly available.     

求解旅行商问题的多尺度量子自由粒子优化算法

针对目前元启发式算法在求解组合优化问题中的旅行商问题(TSP)时求解缓慢的问题,受量子理论中波函数的启发提出一种多尺度自适应的量子自由粒子优化算法。首先,在可行域中随机初始化表示城市序列的粒子,作为初始的搜索中心;然后,以每个粒子为中心进行当前尺度下的均匀分布函数的采样,并交换采样位置上的城市编号产生新解;最后,根据新解相较上一次迭代中最优解的优劣进行搜索尺度的自适应调整,并在不同的尺度下进行迭代搜索直到满足算法结束条件。将该算法和混合粒子群优化(HPSO)算法、模拟退火(SA)算法、遗传算法(GA)和蚁群优化算法应用在TSP上进行性能测试,实验结果表明自由粒子模型算法适合求解组合优化问题,在TSP数据集上相比目前较优算法在求解速度上平均提升50%以上。     

A novel discrete bat algorithm for solving the travelling salesman problem

The travelling salesman problem (TSP) is one of the well-known NP-hard combinatorial optimization and extensively studied problems in discrete optimization. The bat algorithm is a new nature-inspired metaheuristic optimization algorithm introduced by Yang in 2010, especially based on echolocation behavior of microbats when searching their prey. Firstly, this algorithm is used to solve various continuous optimization problems. In this paper we extend a discrete bat-inspired algorithm to solve the famous TSP. Although many algorithms have been used to solve TSP, the main objective of this research is to investigate this discrete version to achieve significant improvements, not only compared to traditional algorithms but also to another metaheuristics. Moreover, this study is based on a benchmark dataset of symmetric TSP from TSPLIB library.     

Two truck travelling salesman simulation

There are many algorithms currently available to approximate solutions to the ‘travelling salesman’ problem of finding the shortest route connecting n points in a complete tour. Conley (1988 CONLEY , W. C. , ( 1988 ), Int. J. Systems Sei. , 19 , 2115 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) presents a multi–stage simulation on a rank ordered distance array to solve a one vehicle problem for n = 20. A modification of that approach is presented here to deal with sending out two delivery trucks (or one truck making two trips) to touch all n points and return. An example for n = 33 is developed. The multi–stage simulation approach is then compared with other techniques.     

A memetic ant colony optimization algorithm for the dynamic travelling salesman problem

Ant colony optimization (ACO) has been successfully applied for combinatorial optimization problems, e.g., the travelling salesman problem (TSP), under stationary environments. In this paper, we consider the dynamic TSP (DTSP), where cities are replaced by new ones during the execution of the algorithm. Under such environments, traditional ACO algorithms face a serious challenge: once they converge, they cannot adapt efficiently to environmental changes. To improve the performance of ACO on the DTSP, we investigate a hybridized ACO with local search (LS), called Memetic ACO (M-ACO) algorithm, which is based on the population-based ACO (P-ACO) framework and an adaptive inver-over operator, to solve the DTSP. Moreover, to address premature convergence, we introduce random immigrants to the population of M-ACO when identical ants are stored. The simulation experiments on a series of dynamic environments generated from a set of benchmark TSP instances show that LS is beneficial for ACO algorithms when applied on the DTSP, since it achieves better performance than other traditional ACO and P-ACO algorithms.     

A branch and bound algorithm for the travelling salesman and the transportation routing problems

In this paper, a branch and bound model with penalty tour building is developed for solving travelling salesman and transportation routing problems. The algorithm for determining the optimal solution of the problem is of the general form which can solve symmetric and asymmetric single and multiple travelling salesman problems (STS and MTS), and the transportation routing problems with capacity restrictions for the vehicles of same or of different capacities. The behavior of the developed algorithm is tested with randomly generated data. As an application, the routes for gas distribution is planned and carried out in several interior towns of a state, with the objective of making an efficient distribution in order to minimize the total cost of delivery with an optimal solution.     

A hybrid algorithm combining glowworm swarm optimization and complete 2-opt algorithm for spherical travelling salesman problems

The Travelling Salesman Problem (TSP) is one of the most well-known combinatorial optimization problems and has attracted a lot of interests from researchers. Many studies have proposed various methods for solving the two-dimensional TSP. In this study, we extend the two-dimensional TSP to the three-dimensional TSP, namely the spherical TSP in which all points (cities) and paths (solutions) are on the surface of a sphere. A hybrid algorithm based on the glowworm swarm optimization (GSO) and the complete 2-opt algorithm is proposed, in which the carriers of the luciferin are transformed from glowworms to edges between cities, and the probabilistic formula and the luciferin updating formula are modified. In addition, the complete 2-opt algorithm is performed to optimize the selected optimal routes every few iterations. Numerical experimental results show that the proposed algorithm has a better performance than the basic GSO in solving the spherical TSP. Meanwhile, the complete 2-opt algorithm can speed up the convergence rate.     

A low-latency computing framework for time-evolving graphs

The Journal of Supercomputing - The demand to deliver fast responses in processing time-evolving graphs is higher than ever before in a large number of big data applications. This problem promotes...     

The Euclidean travelling salesman problem is NP-complete

The Travelling Salesman Problem is shown to be NP-Complete even if its instances are restricted to be realizable by sets of points on the Euclidean plane.     

基于近邻策略的旅行商问题求解

根据TSP问题的特征信息并借鉴邻域搜索算法的有关思想,提出了一种基于近邻策略的TSP问题求解算法,该算法首先依据TSP问题的特殊性求出相应的近邻模式,再将近邻模式用于初始种群的生成,而后在进化过程中随机引入这类模式。该算法可以大大缩短遗传进程,提高进化效率。通过仿真实验,验证了该算法的有效性,并且随着城市数目的增加其优越性更为明显。     

带固定半径近邻搜索3-opt的离散烟花算法求解旅行商问题

传统烟花算法求解大规模离散问题存在收敛速度慢、求解精度不高等问题.针对旅行商问题的特点,提出一种带固定半径近邻搜索3-opt的离散烟花算法.该算法基于基本烟花算法进行离散化改进,采用整数编码的路径表示方法来表示旅行商问题的解,对爆炸算子、高斯变异算子进行离散化操作策略设计.为了使算法具有较好的局部搜索能力,提出固定半径近邻搜索3-opt策略来提高算法精度和收敛速度,同时采用不检测标志策略提高算法效率.实验结果表明:该算法能有效地求解旅行商问题,其离散烟花算子在全局收敛能力、收敛精度、求解时间和稳定性等方面均优于传统烟花算子;基准测试算例的最优解平均误差率仅为0.002％,优于对比算法.