量子进化算法研究进展

在介绍量子进化算法(QEA)的原理、特点和基本流程的基础上,重点综述QEA的改进,包括改进基本算子、引入新算子、改变种群规模、扩展为并行算法和构造新型算法框架等.介绍了QEA的应用研究,进而提出了QEA在理论、算法、组合优化、多目标优化与约束优化、不确定优化及应用方面的若干进一步的研究内容.     

Algorithmic analysis of a basic evolutionary algorithm for continuous optimization

In practical optimization, applying evolutionary algorithms has nearly become a matter of course. Their theoretical analysis, however, is far behind practice. So far, theorems on the runtime are limited to discrete search spaces; results for continuous search spaces are limited to convergence theory or even rely on validation by experiments, which is unsatisfactory from a theoretical point of view.     

A two‐phase harmony search algorithm for continuous optimization

Harmony search (HS) algorithm is inspired by the music improvisation process in which a musician searches for the best harmony and continues to polish the harmony to improve its aesthetics. The efficiency of evolutionary algorithms depends on the extent of balance between diversification and intensification during the course of the search. An ideal evolutionary algorithm must have efficient exploration in the beginning and enhanced exploitation toward the end. In this paper, a two‐phase harmony search (TPHS) algorithm is proposed that attempts to strike a balance between exploration and exploitation by concentrating on diversification in the first phase using catastrophic mutation and then switches to intensification using local search in the second phase. The performance of TPHS is analyzed and compared with 4 state‐of‐the‐art HS variants on all the 30 IEEE CEC 2014 benchmark functions. The numerical results demonstrate the superiority of the proposed TPHS algorithm in terms of accuracy, particularly on multimodal functions when compared with other state‐of‐the‐art HS variants; further comparison with state‐of‐the‐art evolutionary algorithms reveals excellent performance of TPHS on composition functions. Composition functions are combined, rotated, shifted, and biased version of other unimodal and multimodal test functions and mimic the difficulties of real search spaces by providing a massive number of local optima and different shapes for different regions of the search space. The performance of the TPHS algorithm is also evaluated on a real‐life problem from the field of computer vision called camera calibration problem, ie, a 12‐dimensional highly nonlinear optimization problem with several local optima.     

A robust real-coded evolutionary algorithm with toroidal search space conversion

This paper presents a robust Real-coded evolutionary algorithm. Real-coded evolutionary algorithms (RCEAs), such as real-coded genetic algorithms and evolution strategies, are known as effective methods for function optimization. However, they often fail to find the optimum in case the objective function is multimodal, discrete or high-dimensional. It is also reported that most crossover (or recombination) operators for RCEAs has sampling bias that prevents to find the optimum near the boundary of search space. They like to search the center of search space much more than the other. Therefore, they will not work on functions that have their optima near the boundary of search space. In this paper, we apply two methods, genetic algorithm with search area adaptation (GSA) and toroidal search space conversion (TSC), to the function optimization for improving the robustness of RCEAs. The former method searches adaptively and the latter one removes the sampling bias. Through several experiments, we have confirmed that GSA works adaptively and it shows higher performance, and RCEAs with TSC show effectiveness to find the optima near the boundary of search space.     

Cognitive behavior optimization algorithm for solving optimization problems

Nature-based algorithms have become popular in recent fifteen years and have been widely applied in various fields of science and engineering, such as robot control, cluster analysis, controller design, dynamic optimization and image processing. In this paper, a new swarm intelligence algorithm named cognitive behavior optimization algorithm (COA) is introduced, which is used to solve the real-valued numerical optimization problems. COA has a detailed cognitive behavior model. In the model of COA, the common phenomenon of foraging food source for population is summarized as the process of exploration–communication–adjustment. Matching with the process, three main behaviors and two groups in COA are introduced. Firstly, cognitive population uses Gaussian and Levy flight random walk methods to explore the search space in the rough search behavior. Secondly, the improved crossover and mutation operator are used in the information exchange and share behavior between the two groups: cognitive population and memory population. Finally, the intelligent adjustment behavior is used to enhance the exploitation of the population for cognitive population. To verify the performance of our approach, both the classic and modern complex benchmark functions considered as the unconstrained functions are employed. Meanwhile, some well-known engineering design optimization problems are used as the constrained functions in the literature. The experimental results, considering both convergence and accuracy simultaneously, demonstrate the effectiveness of COA for global numerical and engineering optimization problems.     

基于自适应机制的多宇宙并行量子衍生进化算法

进化参量的选取对量子衍生进化算法(QEA)的优化性能有极大的影响,传统QEA在选择进化参量时并未考虑种群中个体间的差异,种群中所有个体采用相同的进化参量完成更新,导致算法在解决组合优化问题中存在收敛速度慢、容易陷入局部最优解等问题。针对这一问题,采用自适应机制调整QEA的旋转角步长和量子变异概率,算法中任意一代的任一个体的进化参量均由该个体自身适应度确定,从而保证尽可能多的进化个体能够朝着最优解方向不断靠近。此外,由于自适应量子进化算法需要评估个体的适应度,导致运算时间较长,针对这一问题则采用多宇宙机制将算法分布于多个宇宙中并行实现,从而提高算法的执行效率。通过搜索多峰函数最优解和求解背包问题测试算法性能,结果表明,与传统QEA相比,所提出算法在收敛速度、搜索全局最优解及执行速度方面具有较好的表现。     

改进的多宇宙并行量子进化算法

通过设计一种新的量子个体更新策略,提出了改进的多宇宙并行量子进化算法,并对算法的收敛性进行了分析探讨,从理论上证明了该算法的有效性,最后将该算法用于多目标0/1背包问题。仿真结果表明：改进方法能够找到接近Pareto最优前端的更好的解,同时维持解分布的均匀性。     

求解多目标优化问题的分级变异量子进化算法

分析量子进化算法和免疫算子的特点,提出一种分级变异的量子进化算法,用于求解多目标优化问题,算法主要基于两个策略:首先,利用快速非受控排序和密度距离计算种群抗原-抗体的亲和度;然后,基于亲和度排序将个体进行分级,最优分级中的个体作为算法中的最优个体,大部分实施量子旋转更新和免疫操作,而剩余分级中的个体实施免疫交叉操作以获得新的个体补充种群,求解多目标0/1背包问题的实验结果表明了该算法的有效性.     

基于网格的一种新的动态演化算法

近年来,越来越多的演化计算研究者对动态优化问题产生了很大的兴趣,并产生了很多解决动态优化问题的方法。提出一种新的动态演化算法,与传统的演化算法有所不同,它是建立在划分网格基础上的,故而称它为网格优化算法。通过测试典型的动态优化问题,并与经典的SOS算法进行比较,证明了算法的有效性。     

函数优化的一种高效演化算法

提出了一个求解函数优化问题的高效演化算法,其设计思想由混合选择策略与分类变异簟略构成。该算法使用锦标赛选择、轮盘选择相结合的混合选择策略。变异运算分为三类进行：对最好个体实施模式搜索。对适应值排名靠前的三分之一的个体采用柯西变异,而其它个体使用普通变异算子。针对15个测试函数的实验取得了相当好的效果,实验结果表明该算法不仅收敛速度快．而且所求得的解达到或者以相当高的精度逼近最优解。     

Parallel quantum-inspired evolutionary algorithms for community detection in social networks

The world around us may be viewed as a network of entities interconnected via their social, economic, and political interactions. These entities and their interactions form a social network. A social network is often modeled as a graph whose nodes represent entities, and edges represent interactions between these entities. These networks are characterized by the collective latent behavior that does not follow trivially from the behaviors of the individual entities in the network. One such behavior is the existence of hierarchy in the network structure, the sub-networks being popularly known as communities. Discovery of the community structure in a social network is a key problem in social network analysis as it refines our understanding of the social fabric. Not surprisingly, the problem of detecting communities in social networks has received substantial attention from the researchers.In this paper, we propose parallel implementations of recently proposed community detection algorithms that employ variants of the well-known quantum-inspired evolutionary algorithm (QIEA). Like any other evolutionary algorithm, a quantum-inspired evolutionary algorithm is also characterized by the representation of the individual, the evaluation function, and the population dynamics. However, individual bits called qubits, are in a superposition of states. As chromosomes evolve individually, the quantum-inspired evolutionary algorithms (QIEAs) are intrinsically suitable for parallelization.In recent years, programmable graphics processing units — GPUs, have evolved into massively parallel environments with tremendous computational power. NVIDIA® compute unified device architecture (CUDA®) technology, one of the leading general-purpose parallel computing architectures with hundreds of cores, can concurrently run thousands of computing threads. The paper proposes novel parallel implementations of quantum-inspired evolutionary algorithms in the field of community detection on CUDA-enabled GPUs.The proposed implementations employ a single-population fine-grained approach that is suited for massively parallel computations. In the proposed approach, each element of a chromosome is assigned to a separate thread. It is observed that the proposed algorithms perform significantly better than the benchmark algorithms. Further, the proposed parallel implementations achieve significant speedup over the serial versions. Due to the highly parallel nature of the proposed algorithms, an increase in the number of multiprocessors and GPU devices may lead to a further speedup.     

A new real-coded stochastic Bayesian optimization algorithm for continuous global optimization

Estimation of distribution algorithms are considered to be a new class of evolutionary algorithms which are applied as an alternative to genetic algorithms. Such algorithms sample the new generation from a probabilistic model of promising solutions. The search space of the optimization problem is improved by such probabilistic models. In the Bayesian optimization algorithm (BOA), the set of promising solutions forms a Bayesian network and the new solutions are sampled from the built Bayesian network. This paper proposes a novel real-coded stochastic BOA for continuous global optimization by utilizing a stochastic Bayesian network. In the proposed algorithm, the new Bayesian network takes advantage of using a stochastic structure (that there is a probability distribution function for each edge in the network) and the new generation is sampled from the stochastic structure. In order to generate a new solution, some new structure, and therefore a new Bayesian network is sampled from the current stochastic structure and the new solution will be produced from the sampled Bayesian network. Due to the stochastic structure used in the sampling phase, each sample can be generated based on a different structure. Therefore the different dependency structures can be preserved. Before the new generation is generated, the stochastic network’s probability distributions are updated according to the fitness evaluation of the current generation. The proposed method is able to take advantage of using different dependency structures through the sampling phase just by using one stochastic structure. The experimental results reported in this paper show that the proposed algorithm increases the quality of the solutions on the general optimization benchmark problems.     

Comparisons of several variants of continuous quantum-inspired evolutionary algorithms

Abstract

In this study, an extensive numerical analysis is carried out to investigate the effects of different quantum-based operators on the performance of continuous quantum-inspired evolutionary algorithms (QEAs). In this context, different variants of quantum-inspired evolutionary operators are adopted for numerical simulations. Furthermore, some novel chaos-enhanced QEAs are proposed and their performances are evaluated through the numerical comparative study. Based on evaluating the accuracy, robustness, convergence, scalability and sensitivity to initialisation of the rival methods, it is indicated that the algorithmic structure of QEAs is prone to being combined with chaotic maps. The results demonstrate that chaotically implemented QEAs can effectively explore/exploit the solution spaces of different landscapes and dimensionality, and finally, converge to acceptable regions within the solution domain.     

改进型复杂过程全局进化算法在热连轧负荷分配中的应用

为实现热连轧精轧机组负荷分配的优化设定,提出一种具有柔性框架结构的改进型复杂过程全局进化算法.该算法部分地借用了分散搜索原则,在通用框架中嵌入具有搜索机制的子方法;利用无限折叠映射混沌模型和局部搜索法,分别对初始种群的生成和"超越"深度搜索进行改进以提高最优解的求解效率.实验结果表明,该算法能够使用较少的参数完成负荷分配优化问题的可行解搜索,具有较好的时效性,是局部和全局搜索的有机体.     

A simple and efficient real-coded genetic algorithm for constrained optimization

This paper presents a simple and efficient real-coded genetic algorithm (RCGA) for constrained real-parameter optimization. Different from some conventional RCGAs that operate evolutionary operators in a series framework, the proposed RCGA implements three specially designed evolutionary operators, named the ranking selection (RS), direction-based crossover (DBX), and the dynamic random mutation (DRM), to mimic a specific evolutionary process that has a parallel-structured inner loop. A variety of benchmark constrained optimization problems (COPs) are used to evaluate the effectiveness and the applicability of the proposed RCGA. Besides, some existing state-of-the-art optimization algorithms in the same category of the proposed algorithm are considered and utilized as a rigorous base of performance evaluation. Extensive comparison results reveal that the proposed RCGA is superior to most of the comparison algorithms in providing a much faster convergence speed as well as a better solution accuracy, especially for problems subject to stringent equality constraints. Finally, as a specific application, the proposed RCGA is applied to optimize the GaAs film growth of a horizontal metal-organic chemical vapor deposition reactor. Simulation studies have confirmed the superior performance of the proposed RCGA in solving COPs.     

一种新颖的函数优化进化算法

进化算法在求解全局优化问题时易陷入局部最优且收敛速度慢. 为了解决这一问题, 设计了一个基于下降尺度函数的杂交算子, 利用下降尺度函数与种群的关系来寻找实值函数的下降方向. 为了提高非均匀变异算子在进化后期的搜索能力, 通过均衡算子的局部搜索和全局搜索能力使其在算法后期仍能跳出局部最优. 在此基础上给出了一种新的进化算法. 最后将其与9个现有的算法进行了比较, 数值实验表明新算法快速有效.     

Sum-of-squares-based fuzzy controller design using quantum-inspired evolutionary algorithm

In the field of fuzzy control, control gains are obtained by solving stabilisation conditions in linear-matrix-inequality-based Takagi–Sugeno fuzzy control method and sum-of-squares-based polynomial fuzzy control method. However, the optimal performance requirements are not considered under those stabilisation conditions. In order to handle specific performance problems, this paper proposes a novel design procedure with regard to polynomial fuzzy controllers using quantum-inspired evolutionary algorithms. The first contribution of this paper is a combination of polynomial fuzzy control and quantum-inspired evolutionary algorithms to undertake an optimal performance controller design. The second contribution is the proposed stability condition derived from the polynomial Lyapunov function. The proposed design approach is dissimilar to the traditional approach, in which control gains are obtained by solving the stabilisation conditions. The first step of the controller design uses the quantum-inspired evolutionary algorithms to determine the control gains with the best performance. Then, the stability of the closed-loop system is analysed under the proposed stability conditions. To illustrate effectiveness and validity, the problem of balancing and the up-swing of an inverted pendulum on a cart is used.     

一种新的求解TSP的混合量子进化算法

在分析量子进化基本概念的基础上,提出了一种新的求解TSP的混合量子进化算法（MQEA）。该算法将三段优化局部搜索算法融入量子进化机制,采用一种基于边的编码方法,应用最近邻规则设置初始参数,并设计了排序交叉算子以扩展种群的搜索范围。通过选取国际通用旅行商问题（TSP）实例库(TSPLIB)中的多个实例进行测试,表明新算法具有高的精确度和鲁棒性,即使对于中大规模问题（城市数大于500）,也能以很小的种群和微小的相对误差求得满意解。     

An evolutionary method for complex-process optimization

In this paper we present a new evolutionary method for complex-process optimization. It is partially based on the principles of the scatter search methodology, but it makes use of innovative strategies to be more effective in the context of complex-process optimization using a small number of tuning parameters. In particular, we introduce a new combination method based on path relinking, which considers a broader area around the population members than previous combination methods. We also use a population-update method which improves the balance between intensification and diversification. New strategies to intensify the search and to escape from suboptimal solutions are also presented. The application of the proposed evolutionary algorithm to different sets of both state-of-the-art continuous global optimization and complex-process optimization problems reveals that it is robust and efficient for the type of problems intended to solve, outperforming the results obtained with other methods found in the literature.