Runtime Analysis of an Ant Colony Optimization Algorithm for TSP Instances

Ant colony optimization (ACO) is a relatively new random heuristic approach for solving optimization problems. The main application of the ACO algorithm lies in the field of combinatorial optimization, and the traveling salesman problem (TSP) is the first benchmark problem to which the ACO algorithm has been applied. However, relatively few results on the runtime analysis of the ACO on the TSP are available. This paper presents the first rigorous analysis of a simple ACO algorithm called (1 + 1) MMAA (Max-Min ant algorithm) on the TSP. The expected runtime bounds for (1 + 1) MMAA on two TSP instances of complete and non-complete graphs are obtained. The influence of the parameters controlling the relative importance of pheromone trail versus visibility is also analyzed, and their choice is shown to have an impact on the expected runtime.     

VERY STRONGLY CONSTRAINED PROBLEMS: AN ANT COLONY OPTIMIZATION APPROACH

Ant Colony Optimization (ACO) is a class of metaheuristic algorithms sharing the common approach of constructing a solution on the basis of information provided both by a standard constructive heuristic and by previously constructed solutions. This article is composed of three parts. The first one frames ACO in current trends of research on metaheuristics for combinatorial optimization. The second outlines some current research within the ACO community, reporting recent results obtained on different problems, while the third part focuses on a particular research line, named ANTS, providing some details on the algorithm and presenting results recently obtained on a prototypical strongly constrained problem: the set partitioning problem.     

A biased random-key genetic algorithm for the capacitated minimum spanning tree problem

This paper focuses on the capacitated minimum spanning tree (CMST) problem. Given a central processor and a set of remote terminals with specified demands for traffic that must flow between the central processor and terminals, the goal is to design a minimum cost network to carry this demand. Potential links exist between any pair of terminals and between the central processor and the terminals. Each potential link can be included in the design at a given cost. The CMST problem is to design a minimum-cost network connecting the terminals with the central processor so that the flow on any arc of the network is at most Q. A biased random-key genetic algorithm (BRKGA) is a metaheuristic for combinatorial optimization which evolves a population of random vectors that encode solutions to the combinatorial optimization problem. This paper explores several solution encodings as well as different strategies for some steps of the algorithm and finally proposes a BRKGA heuristic for the CMST problem. Computational experiments are presented showing the effectiveness of the approach: Seven new best-known solutions are presented for the set of benchmark instances used in the experiments.     

The quadratic minimum spanning tree problem: A lower bounding procedure and an efficient search algorithm

In this paper we consider the quadratic minimum spanning tree problem (QMSTP) which is known to be NP-hard. Given a complete graph, the QMSTP consists of finding a minimum spanning tree (MST) where interaction costs between pairs of edges are prescribed. A Lagrangian relaxation procedure is devised and an efficient local search algorithm with tabu thresholding is developed. Computational experiments are reported on standard test instances, randomly generated test instances and quadratic assignment problem (QAP) instances from the QAPLIB by using a transformation scheme. The local search heuristic yields very good performance and the Lagrangian relaxation procedure gives the tightest lower bounds for all instances when compared to previous lower bounding approaches.     

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.     

Beam-ACO—hybridizing ant colony optimization with beam search: an application to open shop scheduling

Ant colony optimization (ACO) is a metaheuristic approach to tackle hard combinatorial optimization problems. The basic component of ACO is a probabilistic solution construction mechanism. Due to its constructive nature, ACO can be regarded as a tree search method. Based on this observation, we hybridize the solution construction mechanism of ACO with beam search, which is a well-known tree search method. We call this approach Beam-ACO. The usefulness of Beam-ACO is demonstrated by its application to open shop scheduling (OSS). We experimentally show that Beam-ACO is a state-of-the-art method for OSS by comparing the obtained results to the best available methods on a wide range of benchmark instances.     

Savings based ant colony optimization for the capacitated minimum spanning tree problem

The problem of connecting a set of client nodes with known demands to a root node through a minimum cost tree network, subject to capacity constraints on all links is known as the capacitated minimum spanning tree (CMST) problem. As the problem is NP-hard, we propose a hybrid ant colony optimization (ACO) algorithm to tackle it heuristically. The algorithm exploits two important problem characteristics: (i) the CMST problem is closely related to the capacitated vehicle routing problem (CVRP), and (ii) given a clustering of client nodes that satisfies capacity constraints, the solution is to find a MST for each cluster, which can be done exactly in polynomial time. Our ACO exploits these two characteristics of the CMST by a solution construction originally developed for the CVRP. Given the CVRP solution, we then apply an implementation of Prim's algorithm to each cluster to obtain a feasible CMST solution. Results from a comprehensive computational study indicate the efficiency and effectiveness of the proposed approach.     

基于变异和信息素扩散的多维背包问题的蚁群算法

针对蚁群算法在求解大规模多维背包问题时存在的迭代次数过多、精度不高的不足,提出一种新的高性能的蚁群求解算法.算法将信息素更新和随机搜索机制的改进相融合.首先,基于对较优解的偏爱,采用Top-k策略从每次迭代的k个解中挖掘出对象间的关联距离;其次,以对象为信源借助关联距离建立信息素的扩散模型,通过信息素扩散的耦合补偿,强化了蚂蚁间的协作和交流;最后,利用一种简单的变异策略对迭代的结果进行优化.在通用数据集上的大量实验表明:与最新的蚁群算法相比,新算法不仅能获得更好的最优解,而且收敛速度有显著的提高.     

A rough set approach to feature selection based on ant colony optimization

Rough set theory is one of the effective methods to feature selection, which can preserve the meaning of the features. The essence of rough set approach to feature selection is to find a subset of the original features. Since finding a minimal subset of the features is a NP-hard problem, it is necessary to investigate effective and efficient heuristic algorithms. Ant colony optimization (ACO) has been successfully applied to many difficult combinatorial problems like quadratic assignment, traveling salesman, scheduling, etc. It is particularly attractive for feature selection since there is no heuristic information that can guide search to the optimal minimal subset every time. However, ants can discover the best feature combinations as they traverse the graph. In this paper, we propose a new rough set approach to feature selection based on ACO, which adopts mutual information based feature significance as heuristic information. A novel feature selection algorithm is also given. Jensen and Shen proposed a ACO-based feature selection approach which starts from a random feature. Our approach starts from the feature core, which changes the complete graph to a smaller one. To verify the efficiency of our algorithm, experiments are carried out on some standard UCI datasets. The results demonstrate that our algorithm can provide efficient solution to find a minimal subset of the features.     

Degree constrained minimum spanning tree problem: a learning automata approach

Degree-constrained minimum spanning tree problem is an NP-hard bicriteria combinatorial optimization problem seeking for the minimum weight spanning tree subject to an additional degree constraint on graph vertices. Due to the NP-hardness of the problem, heuristics are more promising approaches to find a near optimal solution in a reasonable time. This paper proposes a decentralized learning automata-based heuristic called LACT for approximating the DCMST problem. LACT is an iterative algorithm, and at each iteration a degree-constrained spanning tree is randomly constructed. Each vertex selects one of its incident edges and rewards it if its weight is not greater than the minimum weight seen so far and penalizes it otherwise. Therefore, the vertices learn how to locally connect them to the degree-constrained spanning tree through the minimum weight edge subject to the degree constraint. Based on the martingale theorem, the convergence of the proposed algorithm to the optimal solution is proved. Several simulation experiments are performed to examine the performance of the proposed algorithm on well-known Euclidean and non-Euclidean hard-to-solve problem instances. The obtained results are compared with those of best-known algorithms in terms of the solution quality and running time. From the results, it is observed that the proposed algorithm significantly outperforms the existing method.     

Solving software project scheduling problems with ant colony optimization

Software project scheduling problem (SPSP) is one of the important and challenging problems faced by the software project managers in the highly competitive software industry. As the problem is becoming an NP-hard problem with the increasing numbers of employees and tasks, only a few algorithms exist and the performance is still not satisfying. To design an effective algorithm for SPSP, this paper proposes an ant colony optimization (ACO) approach which is called ACS-SPSP algorithm. Since a task in software projects involves several employees, in this paper, by splitting tasks and distributing dedications of employees to task nodes we get the construction graph for ACO. Six domain-based heuristics are designed to consider the factors of task efforts, allocated dedications of employees and task importance. Among these heuristic strategies, the heuristic of allocated dedications of employees to other tasks performs well. ACS-SPSP is compared with a genetic algorithm to solve the SPSP on 30 random instances. Experimental results show that the proposed algorithm is promising and can obtain higher hit rates with more accuracy compared to the previous genetic algorithm solution.     

Multi-satellite control resource scheduling based on ant colony optimization

The multi-satellite control resource scheduling problem (MSCRSP) is a kind of large-scale combinatorial optimization problem. As the solution space of the problem is sparse, the optimization process is very complicated. Ant colony optimization as one of heuristic method is wildly used by other researchers to solve many practical problems. An algorithm of multi-satellite control resource scheduling problem based on ant colony optimization (MSCRSP–ACO) is presented in this paper. The main idea of MSCRSP–ACO is that pheromone trail update by two stages to avoid algorithm trapping into local optima. The main procedures of this algorithm contain three processes. Firstly, the data get by satellite control center should be preprocessed according to visible arcs. Secondly, aiming to minimize the working burden as optimization objective, the optimization model of MSCRSP, called complex independent set model (CISM), is developed based on visible arcs and working periods. Ant colony algorithm can be used directly to solve CISM. Lastly, a novel ant colony algorithm, called MSCRSP–ACO, is applied to CISM. From the definition of pheromone and heuristic information to the updating strategy of pheromone is described detailed. The effect of parameters on the algorithm performance is also studied by experimental method. The experiment results demonstrate that the global exploration ability and solution quality of the MSCRSP–ACO is superior to existed algorithms such as genetic algorithm, iterative repair algorithm and max–min ant system.     

Improved heuristics for the bounded-diameter minimum spanning tree problem

Given an undirected, connected, weighted graph and a positive integer k, the bounded-diameter minimum spanning tree (BDMST) problem seeks a spanning tree of the graph with smallest weight, among all spanning trees of the graph, which contain no path with more than k edges. In general, this problem is NP-Hard for 4 ≤ k < n − 1, where n is the number of vertices in the graph. This work is an improvement over two existing greedy heuristics, called randomized greedy heuristic (RGH) and centre-based tree construction heuristic (CBTC), and a permutation-coded evolutionary algorithm for the BDMST problem. We have proposed two improvements in RGH/CBTC. The first improvement iteratively tries to modify the bounded-diameter spanning tree obtained by RGH/CBTC so as to reduce its cost, whereas the second improves the speed. We have modified the crossover and mutation operators and the decoder used in permutation-coded evolutionary algorithm so as to improve its performance. Computational results show the effectiveness of our approaches. Our approaches obtained better quality solutions in a much shorter time on all test problem instances considered.     

赋权有向图的最小生成树算法

针对赋权有向图最小生成树问题存在可行解的情况,根据树节点入度最大值为1的性质,提出赋权有向图最小生成树性质。采用反证法,调整生成树根节点到弧头的路径来证明赋权有向图MST性质的正确性。基于赋权有向图MST性质,给出改进的Prim和Kruskal算法及其时间复杂度分析。实验给出构造某赋权有向图实例最小生成树的具体步骤,表明这2种算法能正确有效地构造赋权有向图最小生成树。     

A learning automata-based heuristic algorithm for solving the minimum spanning tree problem in stochastic graphs

During the last decades, a host of efficient algorithms have been developed for solving the minimum spanning tree problem in deterministic graphs, where the weight associated with the graph edges is assumed to be fixed. Though it is clear that the edge weight varies with time in realistic applications and such an assumption is wrong, finding the minimum spanning tree of a stochastic graph has not received the attention it merits. This is due to the fact that the minimum spanning tree problem becomes incredibly hard to solve when the edge weight is assumed to be a random variable. This becomes more difficult if we assume that the probability distribution function of the edge weight is unknown. In this paper, we propose a learning automata-based heuristic algorithm to solve the minimum spanning tree problem in stochastic graphs wherein the probability distribution function of the edge weight is unknown. The proposed algorithm taking advantage of learning automata determines the edges that must be sampled at each stage. As the presented algorithm proceeds, the sampling process is concentrated on the edges that constitute the spanning tree with the minimum expected weight. The proposed learning automata-based sampling method decreases the number of samples that need to be taken from the graph by reducing the rate of unnecessary samples. Experimental results show the superiority of the proposed algorithm over the well-known existing methods both in terms of the number of samples and the running time of algorithm.     

Assigning real-time tasks to heterogeneous processors by applying ant colony optimization

The problem of determining whether a set of periodic tasks can be assigned to a set of heterogeneous processors without deadline violations has been shown, in general, to be NP-hard. This paper presents a new algorithm based on ant colony optimization (ACO) metaheuristic for solving this problem. A local search heuristic that can be used by various metaheuristics to improve the assignment solution is proposed and its time and space complexity is analyzed. In addition to being able to search for a feasible assignment solution, our extended ACO algorithm can optimize the solution by lowering its energy consumption. Experimental results show that both the prototype and the extended version of our ACO algorithm outperform major existing methods; furthermore, the extended version achieves an average of 15.8% energy saving over its prototype.     

关于最大团问题的一种新算法

最大团问题是图论中重要的NP完全问题,目前求解最大团问题的方法只适合某些特殊的图,活则消耗时间长,求解效率低。该文提出了一种新的算法,蚁群算法来解决最大团问题。蚁群优化算法是一种基于自然启发的算法,是一种解决组合优化问题的有效方法。实验结果显示,算法的有效性。     

蚁群算法在求解旅行商问题中的应用综述

旅行商问题作为组合优化研究中最具挑战的问题之一, 自被提出以来就引起了学术界的广泛关注并提出了大量的方法来解决它. 蚁群算法是求解复杂组合优化问题的一种启发式仿生进化算法, 是求解旅行商问题的有效手段. 本文分别介绍蚁群算法中几个有代表性的算法, 综述了蚁群算法的改进、融合和应用的文献研究进展, 以评价近年来不同版本的蚁群算法为解决旅行商问题的发展和研究成果, 并针对改进蚁群算法结构框架、算法参数的设置及优化、信息素优化和混合算法等方面, 对现被提出的改进算法进行了分类综述. 对蚁群算法在未来对旅行商问题及其他不同领域的研究内容和研究热点的进一步发展提供了展望和依据.     

Fast Ant Colony Optimization on Runtime Reconfigurable Processor Arrays

Ant Colony Optimization (ACO) is a metaheuristic used to solve combinatorial optimization problems. As with other metaheuristics, like evolutionary methods, ACO algorithms often show good optimization behavior but are slow when compared to classical heuristics. Hence, there is a need to find fast implementations for ACO algorithms. In order to allow a fast parallel implementation, we propose several changes to a standard form of ACO algorithms. The main new features are the non-generational approach and the use of a threshold based decision function for the ants. We show that the new algorithm has a good optimization behavior and also allows a fast implementation on reconfigurable processor arrays. This is the first implementation of the ACO approach on a reconfigurable architecture. The running time of the algorithm is quasi-linear in the problem size n and the number of ants on a reconfigurable mesh with n ² processors, each provided with only a constant number of memory words.     

A hybrid meta-heuristic algorithm for optimization of crew scheduling

Crew scheduling problem is the problem of assigning crew members to the flights so that total cost is minimized while regulatory and legal restrictions are satisfied. The crew scheduling is an NP-hard constrained combinatorial optimization problem and hence, it cannot be exactly solved in a reasonable computational time. This paper presents a particle swarm optimization (PSO) algorithm synchronized with a local search heuristic for solving the crew scheduling problem. Recent studies use genetic algorithm (GA) or ant colony optimization (ACO) to solve large scale crew scheduling problems. Furthermore, two other hybrid algorithms based on GA and ACO algorithms have been developed to solve the problem. Computational results show the effectiveness and superiority of the proposed hybrid PSO algorithm over other algorithms.