Flow shop scheduling to minimize the total completion time with a permanently present operator: Models and ant colony optimization metaheuristic

This paper studies the one-operator m-machine flow shop scheduling problem with the objective of minimizing the total completion time. In this problem, the processing of jobs and setup of machines require the continuous presence of a single operator. We compare three different mathematical formulations and propose an ant colony optimization based metaheuristic to solve this flow shop scheduling problem. A series of experiments are carried out to compare the properties of three formulations and to investigate the performance of the proposed ant colony optimization metaheuristic. The computational results show that (1) an assignment-based formulation performs best, and (2) the ant colony optimization based metaheuristic is a computationally efficient algorithm.     

Evolutionary truss topology optimization using a graph-based parameterization concept

A novel parameterization concept for the optimization of truss structures by means of evolutionary algorithms is presented. The main idea is to represent truss structures as mathematical graphs and directly apply genetic operators, i.e., mutation and crossover, on them. For this purpose, new genetic graph operators are introduced, which are combined with graph algorithms, e.g., Cuthill–McKee reordering, to raise their efficiency. This parameterization concept allows for the concurrent optimization of topology, geometry, and sizing of the truss structures. Furthermore, it is absolutely independent from any kind of ground structure normally reducing the number of possible topologies and sometimes preventing innovative design solutions. A further advantage of this parameterization concept compared to traditional encoding of evolutionary algorithms is the possibility of handling individuals of variable size. Finally, the effectiveness of the concept is demonstrated by examining three numerical examples.     

一个蚁群优化模型的期望性能分析

用蚁群优化求解组合优化问题时, 信息素模型及其规则可能使问题的各组件之间的竞争失衡, 从而有可能使蚁群搜索停滞在最差解。 研究了蚁群优化求解k-最小生成树问题时的信息素模型及其更新规则对性能的影响,对原有的信息素模型作出了新的解释:直接表示k-最小生成树问题的边被选择的概率。基于新的信息素模型设计了一种新的解的构造过程,这种过程不仅产生可行解, 也产生不可行解;同时研究了使用可行解和全部解更新信息素模型时算法的迭代期望质量随时间的增减情况,其结果表明, 只使用可行解时迭代期望质量随时间连续降低, 而使用全     

蚁群优化算法在求解随机组合优化问题中的应用综述*

不确定条件下的优化问题更贴近真实世界环境,因而日益受到广泛关注。综述了蚁群优化在求解一组不确定条件下的组合优化问题,即随机组合优化问题方面的应用。首先介绍了不确定条件下组合优化问题的概念分类模型,给出了随机组合优化问题的一般定义;然后指出了其与求解传统确定性组合优化问题的不同之处,即目标函数的计算存在不确定性,并详细论述了目前解决方法的进展;最后分析了该领域值得重点关注的几个研究方向,并对其未来发展进行了展望。     

求解自适应组合优化蚁群算法的研究

传统的组合优化蚁群算法在求解过程中要消耗大量的时间,极易陷入局部最优化求解等弊端,同时还会产生大量无用的冗余迭代码,运算效率低。对此,提出了自适应组合优化蚁群算法。通过对改变信息素的迭代、参数选择的分析和增加对信息素局部更新方式,提高了整个系统运算速度及收敛速度,扩充了优化的范围,克服了无用迭代码的产生,减少了停滞现象的出现。通过该算法对旅行商问题进行仿真实验,其结果表明了该算法的可行性和有效性。     

Optimization under uncertainty with applications to design of truss structures

Many real-world engineering design problems are naturally cast in the form of optimization programs with uncertainty-contaminated data. In this context, a reliable design must be able to cope in some way with the presence of uncertainty. In this paper, we consider two standard philosophies for finding optimal solutions for uncertain convex optimization problems. In the first approach, classical in the stochastic optimization literature, the optimal design should minimize the expected value of the objective function with respect to uncertainty (average approach), while in the second one it should minimize the worst-case objective (worst-case or min–max approach). Both approaches are briefly reviewed in this paper and are shown to lead to exact and numerically efficient solution schemes when the uncertainty enters the data in simple form. For general uncertainty dependence however, the problems are numerically hard. In this paper, we present two techniques based on uncertainty randomization that permit to solve efficiently some suitable probabilistic relaxation of the indicated problems, with full generality with respect to the way in which the uncertainty enters the problem data. In the specific context of truss topology design, uncertainty in the problem arises, for instance, from imprecise knowledge of material characteristics and/or loading configurations. In this paper, we show how reliable structural design can be obtained using the proposed techniques based on the interplay of convex optimization and randomization.     

多目标优化问题的蚁群算法研究

将离散空间问题求解的蚁群算法引入连续空间,针对多目标优化问题的特点,提出一种用于求解带有约束条件的多目标函数优化问题的蚁群算法.该方法定义了连续空间中信息量的留存方式和蚂蚁的行走策略,并将信息素交流和基于全局最优经验指导两种寻优方式相结合,用以加速算法收敛和维持群体的多样性.通过3组基准函数来测试算法性能,并与NSGAII算法进行了仿真比较.实验表明该方法搜索效率高,向真实Pareto前沿逼近的效果好,获得的解的散布范围广,是一种求解多目标优化问题的有效方法.     

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。     

An elitist self-adaptive step-size search for structural design optimization

This paper presents a method for optimal sizing of truss structures based on a refined self-adaptive step-size search (SASS) algorithm. An elitist self-adaptive step-size search (ESASS) algorithm is proposed wherein two approaches are considered for improving (i) convergence accuracy, and (ii) computational efficiency. In the first approach an additional randomness is incorporated into the sampling step of the technique to preserve exploration capability of the algorithm during the optimization. Furthermore, an adaptive sampling scheme is introduced to enhance quality of the final solutions. In the second approach computational efficiency of the technique is accelerated through avoiding unnecessary analyses throughout the optimization process using the so-called upper bound strategy (UBS). The numerical results indicate the efficiency of the proposed ESASS algorithm.     

蚁群算法研究与应用的新进展

蚁群算法是一种源于大自然生物界的仿生进化算法,具有自组织性、正反馈性、较强的鲁棒性和分布式计算等特性,且易于与其它算法相结合,在众多的复杂组合优化领域中有着广阔的应用前景。首先对蚁群算法的理论及其重要参数进行了阐述,继而分析了其在参数优化和智能融合方面的改进与应用;然后对其在车间作业调度问题、车辆路径问题、图像处理、电力系统优化等领域的应用进展进行了综述;最后对其理论研究和应用领域可能存在的问题及对策进行了探讨和展望。     

Water wave optimization: A new nature-inspired metaheuristic

Nature-inspired computing has been a hot topic in scientific and engineering fields in recent years. Inspired by the shallow water wave theory, the paper presents a novel metaheuristic method, named water wave optimization (WWO), for global optimization problems. We show how the beautiful phenomena of water waves, such as propagation, refraction, and breaking, can be used to derive effective mechanisms for searching in a high-dimensional solution space. In general, the algorithmic framework of WWO is simple, and easy to implement with a small-size population and only a few control parameters. We have tested WWO on a diverse set of benchmark problems, and applied WWO to a real-world high-speed train scheduling problem in China. The computational results demonstrate that WWO is very competitive with state-of-the-art evolutionary algorithms including invasive weed optimization (IWO), biogeography-based optimization (BBO), bat algorithm (BA), etc. The new metaheuristic is expected to have wide applications in real-world engineering optimization problems.     

Structural topology optimization using ant colony optimization algorithm

The ant colony optimization (ACO) algorithm, a relatively recent bio-inspired approach to solve combinatorial optimization problems mimicking the behavior of real ant colonies, is applied to problems of continuum structural topology design. An overview of the ACO algorithm is first described. A discretized topology design representation and the method for mapping ant's trail into this representation are then detailed. Subsequently, a modified ACO algorithm with elitist ants, niche strategy and memory of multiple colonies is illustrated. Several well-studied examples from structural topology optimization problems of minimum weight and minimum compliance are used to demonstrate its efficiency and versatility. The results indicate the effectiveness of the proposed algorithm and its ability to find families of multi-modal optimal design.     

化学反应蚁群优化算法

针对化学反应优化对反馈信息利用不足导致后期求解效率低的问题,提出化学反应蚁群优化算法.该算法利用化学反应优化生成较优解,通过信息素转换策略将较优解转换为蚁群算法的初始信息素,最后由蚁群算法累积更新信息素得到最优解.以TSP为例进行仿真,结果表明,与化学反应优化、蚁群算法、模拟退火算法相比,所提算法具有更高的寻优能力、收敛效率和计算效率.     

Scalable platforms using ant colony optimization

Mass customization necessitates increased product variety at the customers’ end but comparatively lesser part variety at the manufacturer’s end. Product platform concepts have been successful to achieve this goal at large. One of the popular methods for product platform formation is to scale one or more design variables called the scaling variables. Effective optimization methods are needed to identify proper values of the scaling variables. This paper presents a graph-based optimization method called the scalable platforms using ant colony optimization (SPACO) method for identifying appropriate values of the scaling variables. In the graph-based representation, each node signifies a sub-range of values for a design variable. This application includes the concept of multiplicity in node selection because there are multiple nodes corresponding to the discretized values of a given design variable. In the SPACO method, the overall decision is a result of the cumulative decisions, made by simple computing agents called the ants, over a number of iterations. The space search technique initially starts as a random search technique over the entire search space and progressively turns into an autocatalytic (positive feedback) probabilistic search technique as the solution matures. We use a family of universal electric motors, widely cited in the literature, to test the effectiveness of the proposed method. Our simulation results, when compared to the results reported in the literature, prove that SPACO method is a viable optimization method for determining the values of design variables for scalable platforms.     

Using a style-based ant colony system for adaptive learning

Adaptive learning provides an alternative to the traditional “one size fits all” approach and has driven the development of teaching and learning towards a dynamic learning process for learning. Therefore, exploring the adaptive paths to suit learners personalized needs is an interesting issue. This paper proposes an extended approach of ant colony optimization, which is based on a recent metaheuristic method for discovering group patterns that is designed to help learners advance their on-line learning along an adaptive learning path. The investigation emphasizes the relationship of learning content to the learning style of each participant in adaptive learning. An adaptive learning rule was developed to identify how learners of different learning styles may associate those contents which have the higher probability of being useful to form an optimal learning path. A style-based ant colony system is implemented and its algorithm parameters are optimized to conform to the actual pedagogical process. A survey was also conducted to evaluate the validity and efficiency of the system in producing adaptive paths to different learners. The results reveal that both the learners and the lecturers agree that the style-based ant colony system is able to provide useful supplementary learning paths.     

On solving permutation scheduling problems with ant colony optimization

A new approach for solving permutation scheduling problems with ant colony optimization (ACO) is proposed in this paper. The approach assumes that no precedence constraints between the jobs have to be fulfilled. It is tested with an ACO algorithm for the single-machine total weighted deviation problem. In the new approach the ants allocate the places in the schedule not sequentially, as in the standard approach, but in random order. This leads to a better utilization of the pheromone information. It is shown by experiments that adequate combinations between the standard approach which can profit from list scheduling heuristics and the new approach perform particularly well.     

基于文化的连续蚂蚁优化算法的研究*

针对蚂蚁优化算法在求解连续空间问题方面的缺陷,提出一种基于文化的连续蚂蚁优化算法。该算法将蚂蚁优化算法纳入文化算法的框架,组成基于蚂蚁优化算法的主群体和信念的两大空间。在知识和群体层面使用双重进化机制支持问题的求解和知识的提取,从而充分利用精英蚂蚁所携带的特征信息,在很大程度上提高了收敛速度,增强了搜索的多样性。实验结果表明,该算法求解速度快、寻优成功率高,是一种提高蚂蚁优化算法性能的有效算法。     

Binary-coding-based ant colony optimization and its convergence

Ant colony optimization (ACO for short) is a meta-heuristics for hard combinatorial optimization problems. It is a population-based approach that uses exploitation of positive feedback as well as greedy search. In this paper, genetic algorithm's (GA for short) ideas are introduced into ACO to present a new binary-coding based ant colony optimization. Compared with the typical ACO, the algorithm is intended to replace the problem's parameter-space with coding-space, which links ACO with GA so that the fruits of GA can be applied to ACO directly. Furthermore, it can not only solve general combinatorial optimization problems, but also other problems such as function optimization. Based on the algorithm, it is proved that if the pheromone remainder factor ρ is under the condition of ρ≥1, the algorithm can promise to converge at the optimal, whereas if 0<ρ<1, it does not. This work is supported by the Science Foundation of Shanghai Municipal Commission of Science and Technology under Grant No.00JC14052. Tian-Ming Bu received the M.S. degree in computer software and theory from Shanghai University, China, in 2003. And now he is a Ph.D. candidate of Fudan University in the same area of theory computer science. His research interests include algorithms, especially, heuristic algorithms and heuristic algorithms and parallel algorithms, quantum computing and computational complexity. Song-Nian Yu received the B.S. degree in mathematics from Xi'an University of Science and Technology, Xi'an, China, in 1981, the Ph.D. degree under Prof. L. Lovasz's guidance and from Lorand University, Budapest, Hungary, in 1990. Dr. Yu is a professor in the School of Computer Engineering and Science at Shanghai University. He was a visiting professor as a faculty member in Department of Computer Science at Nelson College of Engineering, West Virginia University, from 1998 to 1999. His current research interests include parallel algorithms' design and analyses, graph theory, combinatorial optimization, wavelet analyses, and grid computing. Hui-Wei Guan received the B.S. degree in electronic engineering from Shanghai University, China, in 1982, the M.S. degree in computer engineering from China Textile University, China, in 1989, and the Ph.D. degree in computer science and engineering from Shanghai Jiaotong University, China, in 1993. He is an associate professor in the Department of Computer Science at North Shore Community College, USA. He is a member of IEEE. His current research interests are parallel and distributed computing, high performance computing, distributed database, massively parallel processing system, and intelligent control.     

相位编码量子蚁群算法及在连续优化中的应用*

针对蚁群算法只适用于离散优化问题的局限性和收敛速度慢的问题,提出一种适合连续优化的量子蚁群算法。该方法直接采用量子位的相位对蚂蚁编码。首先根据基于信息素强度和可见度构造的选择概率,选择蚂蚁的前进目标;然后采用量子旋转门更新描述蚂蚁位置的量子比特,完成蚂蚁移动,并采用Pauli-Z门实现蚂蚁的变异增加位置的多样性;最后根据移动后的新位置完成蚁群信息素强度和可见度的更新。由于优化过程统一在空间［0,2π］n进行,而与具体问题无关,对不同尺度空间的优化问题具有良好的适应性。以函数极值优化和控制器参数优化为例,     

Diversity control in ant colony optimization

Optimization inspired by cooperative food retrieval in ants has been unexpectedly successful and has been known as ant colony optimization (ACO) in recent years. One of the most important factors to improve the performance of the ACO algorithms is the complex trade-off between intensification and diversification. This article investigates the effects of controlling the diversity by adopting a simple mechanism for random selection in ACO. The results of computer experiments have shown that it can generate better solutions stably for the traveling salesmen problem than AS_rank which is known as one of the newest and best ACO algorithms by utilizing two types of diversity.