Accelerating ant colony optimisation for the travelling salesman problem on the GPU

Recent graphics processing units (GPUs) can be used for general purpose parallel computation. Ant colony optimisation (ACO) approaches have been introduced as nature-inspired heuristics to find good solutions of the travelling salesman problem (TSP). In ACO approaches, a number of ants traverse the cities of the TSP to find better solutions of the TSP. The ants randomly select next visiting cities based on the probabilities determined by total amounts of their pheromone spread on routes. The main contribution of this paper is to present sophisticated and efficient implementation of one of the ACO approaches on the GPU. In our implementation, we have considered many programming issues of the GPU architecture including coalesced access of global memory and shared memory bank conflicts. In particular, we present a very efficient method for random selection of next cities by a number of ants. Our new method uses iterative random trial which can find next cities in few computational costs with high probability. This idea can be applied in not only GPU implementation but also CPU implementation. The experimental results on NVIDIA GeForce GTX 580 show that our implementation for 1002 cities runs in 8.71 s, while the CPU implementation runs in 190.05 s. Thus, our GPU implementation attains a speed-up factor of 22.11.     

Ant colony optimization with immigrants schemes for the dynamic travelling salesman problem with traffic factors

Traditional ant colony optimization (ACO) algorithms have difficulty in addressing dynamic optimization problems (DOPs). This is because once the algorithm converges to a solution and a dynamic change occurs, it is difficult for the population to adapt to a new environment since high levels of pheromone will be generated to a single trail and force the ants to follow it even after a dynamic change. A good solution to address this problem is to increase the diversity via transferring knowledge from previous environments to the pheromone trails using immigrants schemes. In this paper, an ACO framework for dynamic environments is proposed where different immigrants schemes, including random immigrants, elitism-based immigrants, and memory-based immigrants, are integrated into ACO algorithms for solving DOPs. From this framework, three ACO algorithms, where immigrant ants are generated using the aforementioned immigrants schemes and replace existing ants in the current population, are proposed and investigated. Moreover, two novel types of dynamic travelling salesman problems (DTSPs) with traffic factors, i.e., under random and cyclic dynamic environments, are proposed for the experimental study. The experimental results based on different DTSP test cases show that each proposed algorithm performs well on different environmental cases and that the proposed algorithms outperform several other peer ACO algorithms.     

求解旅行商问题的改进蚁群算法研究

针对蚁群算法收敛速度慢的问题,对蚁群算法信息素更新规则进行研究,提出一个基于迭代思想的信息素更新规则。对信息残留因子进行实验,确定在新的信息素更新规则下信息素挥发系数的最佳合理值。最后针对eil51问题和dantzig42问题两个例子的仿真实验对比基本蚁群算法。实验结果表明,改进的蚁群算法在收敛性和求得最优解方面都明显优于基本蚁群算法和其它人工智能算法。     

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。     

A memetic algorithm for the generalized traveling salesman problem

The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly one city from each group. The recent studies on this subject consider different variations of a memetic algorithm approach to the GTSP. The aim of this paper is to present a new memetic algorithm for GTSP with a powerful local search procedure. The experiments show that the proposed algorithm clearly outperforms all of the known heuristics with respect to both solution quality and running time. While the other memetic algorithms were designed only for the symmetric GTSP, our algorithm can solve both symmetric and asymmetric instances.     

A model induced max-min ant colony optimization for asymmetric traveling salesman problem

A large number of hybrid metaheuristics for asymmetric traveling salesman problem (ATSP) have been proposed in the past decades which produced better solutions by exploiting the complementary characteristics of different optimization strategies. However, most of the hybridizations are criticized due to lacking of sufficient analytical basis. In this paper, a model induced max-min ant colony optimization (MIMM-ACO) is proposed to bridge the gap between hybridizations and theoretical analysis. The proposed method exploits analytical knowledge from both the ATSP model and the dynamics of ACO guiding the behavior of ants which forms the theoretical basis for the hybridization. The contribution of this paper mainly includes three supporting propositions that lead to two improvements in comparison with classical max-min ACO optimization (MM-ACO): (1) Adjusted transition probabilities are developed by replacing the static biased weighting factors with the dynamic ones which are determined by the partial solution that ant has constructed. As a byproduct, nonoptimal arcs will be indentified and excluded from further consideration based on the dual information derived from solving the associated assignment problem (AP). (2) A terminal condition is determined analytically based on the state of pheromone matrix structure rather than intuitively as in most traditional hybrid metaheuristics. Apart from the theoretical analysis, we experimentally show that the proposed algorithm exhibits more powerful searching ability than classical MM-ACO and outperforms state of art hybrid metaheuristics.     

针对混合变量优化问题的协同进化蚁群优化算法

针对由连续变量和分类变量构成的混合变量优化问题(MVOP),采用协同进化策略来对混合变量决策空间进行搜索,提出了一种协同进化蚁群优化算法(CACOAMV).CACOAMV分别采用连续和离散蚁群优化(ACO)策略生成连续和分类变量子种群,通过合作者来对连续和分类变量子向量进行评价,分别对连续和分类变量子种群进行更新来实现...     

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 new ant colony optimization algorithm for the multidimensional Knapsack problem

The paper proposes a new ant colony optimization (ACO) approach, called binary ant system (BAS), to multidimensional Knapsack problem (MKP). Different from other ACO-based algorithms applied to MKP, BAS uses a pheromone laying method specially designed for the binary solution structure, and allows the generation of infeasible solutions in the solution construction procedure. A problem specific repair operator is incorporated to repair the infeasible solutions generated in every iteration. Pheromone update rule is designed in such a way that pheromone on the paths can be directly regarded as selecting probability. To avoid premature convergence, the pheromone re-initialization and different pheromone intensification strategy depending on the convergence status of the algorithm are incorporated. Experimental results show the advantages of BAS over other ACO-based approaches for the benchmark problems selected from OR library.     

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。     

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.     

A memetic algorithm for the travelling salesperson problem with hotel selection

In this paper, a metaheuristic solution procedure for the travelling salesperson problem with hotel selection (TSPHS) is presented. The metaheuristic consists of a memetic algorithm with an embedded tabu search, using a combination of well-known and problem-specific neighbourhoods. This solution procedure clearly outperforms the only other existing metaheuristic in the literature. For smaller instances, whose optimal solution is known, it is able to consistently find the optimal solution. For the other instances, it obtains several new best known solutions.     

基于改进蚁群算法的网格资源调度研究

为进一步掌握网格资源动态运行状态,以便合理调度网格资源,提高任务执行效率,提出了一种基于改进蚁群算法的网格资源调度策略。该算法引入了一个网格资源空闲所需时间向量F,通过向量F动态调整网格资源负载情况,达到快速实现遥感资源空间检索的目的。从仿真实验结果可以看出,改进蚁群算法比蚁群算法和其他算法更优,网格资源的利用效率更高。     

一种求解Job-Shop调度问题的新型蚁群算法

Job-Shop调度问题是一类具有很高理论研究和工程应用价值的问题。针对使用蚁群算法求解Job-Shop调度问题时较难设置合适参数的问题,提出一种动态设置参数的新型蚁群求解算法。分析了蚁群算法中参数对求解结果的影响,给出了算法求解Job-Shop调度问题的关键技术和实现过程。最后对五个基本测试问题进行了仿真实验,并与遗传算法、模拟退火算法、基本蚁群算法进行了比较。结果表明,该算法能得到较优的结果,具有一定的应用价值。     

改进蚁群优化方法求解立体表面TSP问题

给出立体表面TSP问题的数学模型,提出一种改进的蚁群优化算法,用于解决立体表面TSP问题。该算法能快速找到最优路径或近似最优路径,得到的解质量较高且计算时间短。实验方法表明,改进后的蚁群算法在TSP的求解中,收敛速度和全局寻优能力均得到较大的提高。     

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 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.     

时间依赖型车辆路径问题的一种改进蚁群算法

时间依赖型车辆路径规划问题(TDVRP),是研究路段行程时间随出发时刻变化的路网环境下的车辆路径优化.传统车辆路径问题(VRP)已被证明是NP-hard问题,因此,考虑交通状况时变特征的TDVRP问题求解更为困难.本文设计了一种TDVRP问题的改进蚁群算法,采用基于最小成本的最邻近法(NNC算法)生成蚁群算法的初始可行解,通过局部搜索操作提高可行解的质量,采用最大--最小蚂蚁系统信息素更新策略.测试结果表明,与最邻近算法和遗传算法相比,改进蚁群算法具有更高的效率,能够得到更优的结果;对于大规模TDVRP问题,改进蚁群算法也表现出良好的性能,即使客户节点数量达到1000,算法的优化时间依然在可接受的范围内.     

An ant colony optimization algorithm for the bi-objective shortest path problem

Multi-objective shortest path problem (MOSP) is an extension of a traditional single objective shortest path problem that seeks for the efficient paths satisfying several conflicting objectives between two nodes of a network. MOSP is one of the most important problems in network optimization with wide applications in telecommunication industries, transportation and project management. This research presents an algorithm based on multi-objective ant colony optimization (ACO) to solve the bi-objective shortest path problem. To analyze the efficiency of the algorithm and check for the quality of solutions, experimental analyses are conducted. Two sets of small and large sized problems that generated randomly are solved. Results on the set problems are compared with those of label correcting solutions that is the most known efficient algorithm for solving MOSP. To compare the Pareto optimal frontiers produced by the suggested ACO algorithm and the label correcting algorithm, some performance measures are employed that consider and compare the distance, uniformity distribution and extension of the Pareto frontiers. The results on the set of instance problems show that the suggested algorithm produces good quality non-dominated solutions and time saving in computation of large-scale bi-objective shortest path problems.