A Pheromone-Rate-Based Analysis on the Convergence Time of ACO Algorithm

Ant colony optimization (ACO) has widely been applied to solve combinatorial optimization problems in recent years. There are few studies, however, on its convergence time, which reflects how many iteration times ACO algorithms spend in converging to the optimal solution. Based on the absorbing Markov chain model, we analyze the ACO convergence time in this paper. First, we present a general result for the estimation of convergence time to reveal the relationship between convergence time and pheromone rate. This general result is then extended to a two-step analysis of the convergence time, which includes the following: 1) the iteration time that the pheromone rate spends on reaching the objective value and 2) the convergence time that is calculated with the objective pheromone rate in expectation. Furthermore, four brief ACO algorithms are investigated by using the proposed theoretical results as case studies. Finally, the conclusions of the case studies that the pheromone rate and its deviation determine the expected convergence time are numerically verified with the experiment results of four one-ant ACO algorithms and four ten-ant ACO algorithms.      

蚁群算法的收敛速度分析

蚁群算法(ACO)作为一类新型的机器学习技术,已经广泛用于组合优化问题的求解,同时也应用于工业工程的优化设计.相对于遗传算法(GA),蚁群算法的理论研究在国内外均起步较晚,特别是收敛速度的分析理论是该领域急待解决的第一大公开问题.文中的研究内容主要是针对这一公开问题而开展的.根据蚁群算法的特性,该研究基于吸收态Markov过程的数学模型,提出了蚁群算法的收敛速度分析理论.作者给出了估算蚁群算法期望收敛时间的几个理论方法,以分析蚁群算法的收敛速度,并结合著名的ACS算法作了具体的案例研究.基于该文提出的收敛速度分析理论,作者还提出ACO-难和ACO-易两类问题的界定方法;最后,利用ACS算法求解TSP问题的实验数据,验证了文中提出的分析结论,得出了初步的算法设计指导原则.     

一类自适应蚁群算法及其收敛性分析

为了克服蚁群算法易陷入局部最小点的缺点,同时提高算法的收敛速度,提出一类自适应蚁群算法.该算法利用自适应改变信息激素的挥发系数改善传统蚁群算法的全局搜索能力和收敛速度.通过马尔科夫过程对算法的全局收敛性进行分析,得出该类蚁群算法全局收敛性条件.并构造出该类算法的一种信息激素更新策略,证明了这种算法全局收敛性.利用提出的算法对典型的TSP问题进行仿真研究,结果表明比典型蚁群算法在收敛速度和解的性能上都有较大改善.     

A low-complexity hybrid algorithm based on particle swarm and ant colony optimization for large-MIMO detection

With rapid increase in demand for higher data rates, multiple-input multiple-output (MIMO) wireless communication systems are getting increased research attention because of their high capacity achieving capability. However, the practical implementation of MIMO systems rely on the computational complexity incurred in detection of the transmitted information symbols. The minimum bit error rate performance (BER) can be achieved by using maximum likelihood (ML) search based detection, but it is computationally impractical when number of transmit antennas increases. In this paper, we present a low-complexity hybrid algorithm (HA) to solve the symbol vector detection problem in large-MIMO systems. The proposed algorithm is inspired from the two well known bio-inspired optimization algorithms namely, particle swarm optimization (PSO) algorithm and ant colony optimization (ACO) algorithm. In the proposed algorithm, we devise a new probabilistic search approach which combines the distance based search of ants in ACO algorithm and the velocity based search of particles in PSO algorithm. The motivation behind using the hybrid of ACO and PSO is to avoid premature convergence to a local solution and to improve the convergence rate. Simulation results show that the proposed algorithm outperforms the popular minimum mean squared error (MMSE) algorithm and the existing ACO algorithms in terms of BER performance while achieve a near ML performance which makes the algorithm suitable for reliable detection in large-MIMO systems. Furthermore, a faster convergence to achieve a target BER is observed which results in reduction in computational efforts.     

多维背包问题的一个蚁群优化算法

蚁群优化(ACO)是一种通用的启发式方法,已被用来求解很多离散优化问题.近年来,已提出几个ACO算法求解多维背包问题(MKP).这些算法虽然能获得较好的解但也耗用太多的CPU时间.为了降低用ACO求解MKP的复杂性,文章基于一种已提出但未实现过的MKP的信息素表示定义了新的选择概率的规则和相应的基于背包项的一种序的启发式信息,从而提出了一种计算复杂性较低、求解性能较好的改进型蚁群算法.实验结果表明,无论串行执行还是虚拟并行执行,在计算相同任务时,新算法耗用时间少且解的价值更高.不仅如此,在实验中,文中的新算法获得了ORLIB中测试算例5.250-22的两个"新"解.     

On Enforced Convergence of ACO and its Implementation on the Reconfigurable Mesh Architecture Using Size Reduction Tasks

In this paper we show that size reduction tasks can be used for executing iterative randomized metaheuristics on runtime reconfigurable architectures so that an improved throughput and better solution qualities are obtained compared to conventional architectures that do not allow runtime reconfiguration. In particular, the problem of executing ant colony optimization (ACO) algorithms on a dynamically reconfigurable mesh architecture is studied. It is shown how ACO can be implemented such that the convergence behavior of the algorithm can be used to dynamically reduce the size of the submesh that is needed for execution. Furthermore we propose a method to enforce the convergence of ACO leading to a faster reduction process. This increases the throughput of ACO algorithms on runtime reconfigurable meshes. The increased throughput is used for repeated runs of ACO algorithms on a given set of problem instances which significantly improves the obtained solution quality.     

基于选路优化的改进蚁群算法

蚁群算法在处理大规模优化问题时效率很低。为此对蚁群算法提出了基于选路优化的两点改进:(1)引入选路优化策略,减少了算法中蚁群的选路次数,显著提高了算法的执行效率。(2)在选路操作中,只根据当前城市的前C个距离最近的且未经过城市为候选城市计算选择概率,从而减少单个蚂蚁选路的计算量。尤其对于以往较难处理的大规模TSP问题,改进算法在执行效率上有明显的优势。模拟实验结果表明改进算法较之基本蚁群算法在收敛速度有明显提高。     

An effective ant colony optimization algorithm for multi-objective job-shop scheduling with equal-size lot-splitting

This paper proposes several novel hybrid ant colony optimization (ACO)-based algorithms to resolve multi-objective job-shop scheduling problem with equal-size lot splitting. The main issue discussed in this paper is lot-splitting of jobs and tradeoff between lot-splitting costs and makespan. One of the disadvantages of ACO is its uncertainty on time of convergence. In order to enrich search patterns of ACO and improve its performance, five enhancements are made in the proposed algorithms including: A new type of pheromone and greedy heuristic function; Three new functions of state transition rules; A nimble local search algorithm for the improvements of solution quality; Mutation mechanism for divisive searching; A particle swarm optimization (PSO)-based algorithm for adaptive tuning of parameters. The objectives that are used to measure the quality of the generated schedules are weighted-sum of makespan, tardiness of jobs and lot-splitting cost. The developed algorithms are analyzed extensively on real-world data obtained from a printing company and simulated data. A mathematical programming model is developed and paired-samples t-tests are performed between obtained solutions of mathematical programming model and proposed algorithms in order to verify effectiveness of proposed algorithms.     

A fast two-stage ACO algorithm for robotic path planning

Ant colony optimization (ACO) algorithms are often used in robotic path planning; however, the algorithms have two inherent problems. On one hand, the distance elicitation function and transfer function are usually used to improve the ACO algorithms, whereas, the two indexes often fail to balance between algorithm efficiency and optimization effect; On the other hand, the algorithms are heavily affected by environmental complexity. Based on the scent pervasion principle, a fast two-stage ACO algorithm is proposed in this paper, which overcomes the inherent problems of traditional ACO algorithms. The basic idea is to split the heuristic search into two stages: preprocess stage and path planning stage. In the preprocess stage, the scent information is broadcasted to the whole map and then ants do path planning under the direction of scent information. The algorithm is tested in maps of various complexities and compared with different algorithms. The results show the good performance and convergence speed of the proposed algorithm, even the high grid resolution does not affect the quality of the path found.     

A novel two-stage hybrid swarm intelligence optimization algorithm and application

This paper presents a novel two-stage hybrid swarm intelligence optimization algorithm called GA–PSO–ACO algorithm that combines the evolution ideas of the genetic algorithms, particle swarm optimization and ant colony optimization based on the compensation for solving the traveling salesman problem. In the proposed hybrid algorithm, the whole process is divided into two stages. In the first stage, we make use of the randomicity, rapidity and wholeness of the genetic algorithms and particle swarm optimization to obtain a series of sub-optimal solutions (rough searching) to adjust the initial allocation of pheromone in the ACO. In the second stage, we make use of these advantages of the parallel, positive feedback and high accuracy of solution to implement solving of whole problem (detailed searching). To verify the effectiveness and efficiency of the proposed hybrid algorithm, various scale benchmark problems from TSPLIB are tested to demonstrate the potential of the proposed two-stage hybrid swarm intelligence optimization algorithm. The simulation examples demonstrate that the GA–PSO–ACO algorithm can greatly improve the computing efficiency for solving the TSP and outperforms the Tabu Search, genetic algorithms, particle swarm optimization, ant colony optimization, PS–ACO and other methods in solution quality. And the experimental results demonstrate that convergence is faster and better when the scale of TSP increases.     

Makespan minimization on single batch-processing machine via ant colony optimization

This paper investigates the problem of minimizing makespan on a single batch-processing machine, and the machine can process multiple jobs simultaneously. Each job is characterized by release time, processing time, and job size. We established a mixed integer programming model and proposed a valid lower bound for this problem. By introducing a definition of waste and idle space (WIS), this problem is proven to be equivalent to minimizing the WIS for the schedule. Since the problem is NP-hard, we proposed a heuristic and an ant colony optimization (ACO) algorithm based on the theorems presented. A candidate list strategy and a new method to construct heuristic information were introduced for the ACO approach to achieve a satisfactory solution in a reasonable computational time. Through extensive computational experiments, appropriate ACO parameter values were chosen and the effectiveness of the proposed algorithms was evaluated by solution quality and run time. The results showed that the ACO algorithm combined with the candidate list was more robust and consistently outperformed genetic algorithm (GA), CPLEX, and the other two heuristics, especially for large job instances.     

基于差分进化生物地理学优化的多层感知器训练方法

针对生物地理学优化训练多层感知器存在的早熟收敛以及初始化灵敏等问题,提出一种基于差分进化生物地理学优化的多层感知器训练方法。将生物地理学优化（Biogeography-based Optimization,BBO）与差分进化(Differential Evolution,DE)算法相结合,形成改进的混合DE_BBO算法;采用改进的DE_BBO来训练多层感知器（Multi-Layer Perceptron,MLP）,并应用于虹膜、乳腺癌、输血、钞票验证等4类数据分类。与BBO、PSO、GA、ACO、ES、PBIL等6种主流启发式算法的实验结果进行比较表明,DE_BBO_MLP算法在分类精度和收敛速度等方面优于已有方法。     

基于多蚁群的并行ACO算法

通过改变蚁群优化(ACO)算法行为,提出一种新的ACO并行化策略——并行多蚁群ACO算法。针对蚁群算法存在停滞现象的缺点,改进选择策略,实现具有自适应并行机制的选择和搜索策略,以加强其全局搜索能力。并行处理采用数据并行的手段,能减少处理器间的通信时间并获得更好的解。以对称TSP测试集为对象进行比较实验,结果表明,该算法相对于串行算法及现有的并行算法具有一定的优势。     

基于混合遗传—蚁群算法的MRO服务调度研究

随着设备的维修、维护和大修（Maintenance, Repair& Overhaul,MRO）规模扩大,设备的维修和维护越来越难,成本越来越高,MRO服务企业需要更加科学合理地调配资源,这就带来了MRO服务调度问题。为此本文提出了一种基于混合遗传-蚁群算法的MRO调度方法。建立了维修服务调度问题数学模型,采用混合遗传-蚁群算法对模型求解,以综合适应值最小为优化目标,得出最优调度方案,解决了MRO服务调度问题。最后,以某航天企业的10个维修任务为例,比较了本文提出的基于混合遗传-蚁群算法的调度方法与常规遗传算法、蚁群算法的优化结果,结果表明两种算法结果一致,且基于遗传-蚁群算法的调度方法收敛速度更快,从而验证了本文方法的可行性。     

自适应路由蚁群算法在导弹残骸搜索中的应用

防空导弹飞行试验后弹目残骸有着重要价值.根据残骸搜索的实际需求,把残骸落点纳入到路网中,结合自适应路由算法,改进了基本蚁群算法,解决了靶场残骸搜索的最优路径问题.蚁群算法有收敛性较差、易于过早陷入局部最优等不足,通过构建蚁群、引入信息素约束条件、调整信息素初始值、自适应改变信息素增量等技术,增强了蚁群搜索能力,改善了算法收敛速度.仿真表明该算法易于编程实现,时延小,鲁棒性强,实用性好.     

基于新型信息素更新策略的蚁群算法*

深入研究了蚁群优化算法（ACO）的路径搜索及参数控制策略,分析了其存在的缺陷。为了提高ACO算法的解题能力,提出一种新型信息素更新策略（PACS）,然后将PACS算法与其他蚁群算法分别应用于旅行商问题（TSP）进行仿真实验。仿真结果表明,PACS算法具有优良的全局优化性能,可抑制算法过早收敛于次优解,有效防止了停滞现象,收敛速度也大大加快。     

A hybrid ant colony optimization algorithm for optimal multiuser detection in DS-UWB system

A hybrid ant colony optimization algorithm is proposed by introducing extremal optimization local-search algorithm to the ant colony optimization (ACO) algorithm, and is applied to multiuser detection in direct sequence ultra wideband (DS-UWB) communication system in this paper. ACO algorithms have already successfully been applied to combinatorial optimization; however, as the pheromone accumulates, we may not get a global optimum because it can get stuck in a local minimum resulting in a bad steady state. Extremal optimization (EO) is a recently developed local-search heuristic method and has been successfully applied to a wide variety of optimization problems. Hence in this paper, a hybrid ACO algorithm, named ACO-EO algorithm, is proposed by introducing EO to ACO to improve the local-search ability of the algorithm. The ACO-EO algorithm is applied to multiuser detection in DS-UWB communication system, and via computer simulations it is shown that the proposed hybrid ACO algorithm has much better performance than other ACO algorithms and even equal to the optimal multiuser detector.     

基于并行ACO算法的DNA杂交测序

针对求解DNA杂交测序（SBH）问题的相关算法存在解的精度不高及收敛速度慢等问题,建立SBH问题的数学模型,从中抽取启发式信息,提出一种改进的并行蚁群优化算法（IPACO）,并将其应用到DNA杂交测序问题中。仿真实验结果表明,该算法解的精度和收敛速度均优于普通串行蚁群算法、禁忌搜索算法和进化算法。     

A comparative study of the improvement of performance using a PSO modified by ACO applied to TSP

Swarm-inspired optimization has become very popular in recent years. Particle swarm optimization (PSO) and Ant colony optimization (ACO) algorithms have attracted the interest of researchers due to their simplicity, effectiveness and efficiency in solving complex optimization problems. Both ACO and PSO were successfully applied for solving the traveling salesman problem (TSP). Performance of the conventional PSO algorithm for small problems with moderate dimensions and search space is very satisfactory. As the search, space gets more complex, conventional approaches tend to offer poor solutions. This paper presents a novel approach by introducing a PSO, which is modified by the ACO algorithm to improve the performance. The new hybrid method (PSO–ACO) is validated using the TSP benchmarks and the empirical results considering the completion time and the best length, illustrate that the proposed method is efficient.     

AN ENHANCED ANT COLONY OPTIMIZATION METAHEURISTIC FOR THE MINIMUM DOMINATING SET PROBLEM

This paper proposes an enhanced Ant Colony Optimization (ACO) metaheuristic called ACO-TS to attack the minimum dominating set (MDS) problem. One of the recognized difficulties faced by ACO in its original form is premature convergence, which produces less satisfactory solutions. We propose a way to encourage a higher degree of exploration of the search space by incorporating a technique based on a concept borrowed from genetic algorithms called tournament selection. Instead of always following the standard mechanism for selecting the next solution component, an ant would make its decision based on the outcome of a tournament between randomly selected allowable components. The frequency of the tournament selection is controlled by a probability measure. The use of tournament selection is coupled with an iteration-best pheromone update. To evaluate the enhanced ACO, we consider the MDS problem formulated from ad hoc network clustering. A comparison with its original form shows that the enhanced ACO produces better solutions using fewer number of cycles. We also empirically demonstrate that the proposed ACO produces better solutions than a genetic algorithm. Finally, we argue, based on empirical results, why the tournament selection approach is preferable to a pure random selection method.