Ants can solve constraint satisfaction problems

We describe a novel incomplete approach for solving constraint satisfaction problems (CSPs) based on the ant colony optimization (ACO) metaheuristic. The idea is to use artificial ants to keep track of promising areas of the search space by laying trails of pheromone. This pheromone information is used to guide the search, as a heuristic for choosing values to be assigned to variables. We first describe the basic ACO algorithm for solving CSPs and we show how it can be improved by combining it with local search techniques. Then, we introduce a preprocessing step, the goal of which is to favor a larger exploration of the search space at a lower cost, and we show that it allows ants to find better solutions faster. Finally, we evaluate our approach on random binary problems     

奖惩蚁群算法

由于传统蚁群算法所采用的是随机概率搜索策略,收敛速度慢是其主要问题。为了提高算法的收敛速度,这里提出一种带奖惩策略的蚁群算法（PPACO）。新算法中,每次循环中发现的较优解都被挑选出来加以奖励,而普通解则被惩罚,这样就加快了较优路径和普通路径上信息素的差异;另外,为了不使这种差异对算法产生过多的影响,所有路径上的信息素都被限制在一定的范围[τmin,τmax]内,同时,信息素的挥发系数被设为相对较高值。通过典型模拟实验证明,新算法对解决复杂组合优化问题非常有效。     

Guidance-solution based ant colony optimization for satellite control resource scheduling problem

An ant colony optimization (ACO) approach for the satellite control resource scheduling problem is presented. Based on the observation that the solution space of the problem is sparse, this ACO approach is combined with a guidance solution based pheromone updating method to avoid trapping in local optima. The basic idea of this method is to change the distribution of pheromone trails by updating them with a guidance solution once the algorithm stagnates. We compare the proposed algorithm with several other heuristics. The experimental results demonstrate that our approach possesses strong competitive advantage in exploring global best solutions.     

An ACO-RFD hybrid method to solve NP-complete problems

In this paper we hybridize ant colony optimization (ACO) and river formation dynamics (RFD), two related swarm intelligence methods. In ACO, ants form paths (problem solutions) by following each other’s pheromone trails and reinforcing trails at best paths until eventually a single path is followed. On the other hand, RFD is based on copying how drops form rivers by eroding the ground and depositing sediments. In a rough sense, RFD can be seen as a gradient-oriented version of ACO. Several previous experiments have shown that the gradient orientation of RFD makes this method solve problems in a different way as ACO. In particular, RFD typically performs deeper searches, which in turn makes it find worse solutions than ACO in the first execution steps in general, though RFD solutions surpass ACO solutions after some more time passes. In this paper we try to get the best features of both worlds by hybridizing RFD and ACO. We use a kind of ant-drop hybrid and consider both pheromone trails and altitudes in the environment. We apply the hybrid method, as well as ACO and RFD, to solve two NP-hard problems where ACO and RFD fit in a different manner: the traveling salesman problem (TSP) and the problem of the minimum distances tree in a variable-cost graph (MDV). We compare the results of each method and we analyze the advantages of using the hybrid approach in each case.     

基于重要解成分的信息素更新策略

蚁群优化算法通过信息素记录搜索过程中获取的知识,并基于信息素搜索新的解,因此好的信息素更新策略对蚁群优化算法至关重要。针对不同解成分的贡献不同的特点,提出了新的信息素更新策略:首先识别候选解的重要成分,然后在更新信息素时只允许重要的解成分得到加强。基于新的更新策略更新的信息素更好地反映了优质解的特点,从而加快了信息的正反馈过程。以4阶欺骗问题为例,验证了新算法的有效性。     

一种求解TSP问题的ACO&SS算法设计

提出一种求解旅行商(TSP)问题的新型分散搜索算法.将蚁群算法(ACO)的构解方法引入分散搜索(SS)算法,在搜索过程中既考虑解的质量,又考虑解的分散性.采用一种将蚁群算法的信息素更新技术与分散搜索的组合机制相结合的新型子集组合成新解的构解机制,同时采用动态更新参考集与临界准则策略来加快收敛速度.实验结果表明,该算法优于其他现有的方法,获得了较好的结果.     

Reliability optimization of a series system with multiple-choice and budget constraints using an efficient ant colony approach

This paper deals with a reliability optimization problem for a series system with multiple-choice and budget constraints. The objective is to choose one technology for each subsystem in order to maximize the reliability of the whole system subject to the available budget. This problem is NP-hard and could be formulated as a binary integer programming problem with a nonlinear objective function. In this paper, an efficient ant colony optimization (ACO) approach is developed for the problem. In the approach, a solution is generated by an ant based on both pheromone trails modified by previous ants and heuristic information considered as a fuzzy set. Constructed solutions are not guaranteed to be feasible; consequently, applying an appropriate procedure, an infeasible solution is replaced by a feasible one. Then, feasible solutions are improved by a local search. The proposed approach is compared with the existing metaheuristic available in the literature. Computational results demonstrate that the approach serves to be a better performance for large problems.     

Superior/Inferior Segment-Discriminated Ant System for combinatorial optimization problems

The Ant Colony Optimization method is a heuristic algorithm for solving various optimization problems, particularly the combinatorial optimization problems. Traditional ant-optimization methods might encounter search stagnation owing to a biased pheromone map that is dominated by local optimal trails. To overcome this drawback and lower the number of solution constructions for finding the optima, this paper presents an improving ant-optimization system, the Superior/Inferior Segment-Discriminated Ant System (SDAS). This system proposes a segment-based pheromone update strategy to deposit pheromone on superior segments and withdraw pheromone from inferior ones. The method uses the control-chart technique to define superior and inferior limits to partition the constructed solutions into superior, inferior, and ordinary solutions. Inferior and superior segments are then extracted from the superior and inferior solutions by stochastic set operations. Since the pheromone map is not easily dominated by any local optimal trail, the solution search is more efficient and effective. Several benchmarks from the TSP-LIB and OR-LIB were used as sample problems to test the proposed system against other ant-optimization systems, including the AS, ACS, AS_rank, AS_elite, and MMAS. Numerical results indicated that the SDAS obtains solutions that are similar to or better than others. Maturity index for the pheromone map was discussed and experimental results showed that the proposed method was able to prolong the time for the map to maturity to avoid earlier search stagnation.     

一种新的求解多维背包问题的分散算法

为了避免蚁群算法在优化搜索过程中易陷入局部最优和早熟收敛,提出一种求解多维背包问题的新型分散搜索算法。该算法是把蚁群算法的构解方法引入到分散搜索算法中,在搜索过程中,既考虑解的质量,又考虑解的分散性。同时,该分散算法还采用了动态更新参考集与阈值接收算法的阈值参数,以控制搜索空间来加快收敛速度。通过选取国际通用MDKP实例库中的多个实例进行测试表明,该算法可以避免陷入局部最优解,能提高全局寻优能力,其结果优于其他现有的方法,并获得了较好的结果。     

Ant colony optimization for resource-constrained project scheduling

An ant colony optimization (ACO) approach for the resource-constrained project scheduling problem (RCPSP) is presented. Several new features that are interesting for ACO in general are proposed and evaluated. In particular, the use of a combination of two pheromone evaluation methods by the ants to find new solutions, a change of the influence of the heuristic on the decisions of the ants during the run of the algorithm, and the option that an elitist ant forgets the best-found solution are studied. We tested the ACO algorithm on a set of large benchmark problems from the Project Scheduling Library. Compared to several other heuristics for the RCPSP, including genetic algorithms, simulated annealing, tabu search, and different sampling methods, our algorithm performed best on average. For nearly one-third of all benchmark problems, which were not known to be solved optimally before, the algorithm was able to find new best solutions     

Communication-aware task scheduling and voltage selection for total energy minimization in a multiprocessor system using Ant Colony Optimization

Energy consumption is a key parameter when highly computational tasks should be performed in a multiprocessor system. In this case, in order to reduce total energy consumption, task scheduling and low-power methodology should be combined in an efficient way. This paper proposes an algorithm for off-line communication-aware task scheduling and voltage selection using Ant Colony Optimization. The proposed algorithm minimizes total energy consumption of an application executing on a homogeneous multiprocessor system. The artificial agents explore the search space based on stochastic decision-making using global heuristic information with total energy consumption and local heuristic information with interprocessor communication volume. In search space exploration, both voltage selection and the dependencies between tasks are considered. The pheromone trails are updated by normalizing the total energy consumption. The pheromone trails represent the global heuristic information in order to utilize all entire energy consumption information from previous evaluated solutions. Experimental results show that the proposed algorithm outperforms traditional communication-aware task scheduling and task scheduling using genetic algorithms in terms of total energy consumption.     

Search bias in ant colony optimization: on the role of competition-balanced systems

One of the problems encountered when applying ant colony optimization (ACO) to combinatorial optimization problems is that the search process is sometimes biased by algorithm features such as the pheromone model and the solution construction process. Sometimes this bias is harmful and results in a decrease in algorithm performance over time, which is called second-order deception. In this work, we study the reasons for the occurrence of second-order deception. In this context, we introduce the concept of competition-balanced system (CBS), which is a property of the combination of an ACO algorithm with a problem instance. We show by means of an example that combinations of ACO algorithms with problem instances that are not CBSs may suffer from a bias that leads to second-order deception. Finally, we show that the choice of an appropriate pheromone model is crucial for the success of the ACO algorithm, and it can help avoid second-order deception.     

Two-stage updating pheromone for invariant ant colony optimization algorithm

Ant colony optimization (ACO) is a metaheuristic approach for combinatorial optimization problems. With the introduction of hypercube framework, invariance property of ACO algorithms draws more attention. In this paper, we propose a novel two-stage updating pheromone for invariant ant colony optimization (TSIACO) algorithm. Compared with standard ACO algorithms, TSIACO algorithm uses solution order other than solution itself as independent variable for quality function. In addition, the pheromone trail is updated with two stages: in one stage, the first r iterative optimal solutions are employed to enhance search capability, and in another stage, only optimal solution is used to accelerate the speed of convergence. And besides, the pheromone value is limited to an interval. We prove that TSIACO not only has the property of linear transformational invariance but also has translational invariance. We also prove that the pheromone trail can limit to the interval (0, 1]. Computational results on the traveling salesman problem show the effectiveness of TSIACO algorithm.     

基于聚类分析的增强型蚁群算法

针对蚁群算法存在的早熟收敛、搜索时间长等不足,提出一种增强型蚁群算法.该算法构建了一优解池,保存到当前迭代为止获得的若干优解,并提出一种基于邻域的聚类算法,通过对优解池中的元素聚类,捕获不同的优解分布区域.该算法交替使用不同簇中的优解更新信息素,兼顾考虑了搜索的强化性和分散性.针对典型的旅行商问题进行仿真实验,结果表明该算法获得的解质量高于已有的蚁群算法.     

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 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.     

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.     

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.     

A modified ant system to achieve better balance between intensification and diversification for the traveling salesman problem

This paper presents a new variant of Ant Colony Optimization (ACO) for the Traveling Salesman Problem (TSP). ACO has been successfully used in many combinatorial optimization problems. However, ACO has a problem in reaching the global optimal solutions for TSPs, and the algorithmic performance of ACO tends to deteriorate significantly as the problem size increases. In the proposed modification, adaptive tour construction and pheromone updating strategies are embedded into the conventional Ant System (AS), to achieve better balance between intensification and diversification in the search process. The performance of the proposed algorithm is tested on randomly generated data and well-known existing data. The computational results indicate the proposed modification is effective and efficient for the TSP and competitive with Ant Colony System (ACS), Max-Min Ant System (MMAS), and Artificial Bee Colony (ABC) Meta-Heuristic.     

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.