Properties of Symmetric Fitness Functions

The properties of symmetric fitness functions are investigated. We show that the search spaces obtained from symmetric functions have the zero-correlation structures between fitness and distance. It is also proven that symmetric functions induce a class of the hardest problems in terms of the epistasis variance and its variants. These analyses suggest that the existing quantitative measures cannot discriminate among symmetric functions, which reveals critical limitations of the measures. To take a closer look at the symmetric functions, additional analyses are performed from other viewpoints including additive separability and boundedness. It is shown that additive separability in a symmetric function is closely related to the symmetry of its subfunctions. This elucidates why most of the well-known symmetric fitness functions are additively inseparable. The properties of two-bounded symmetric functions are investigated and they are utilized in designing an efficient algorithm to check additive separability for the two-bounded functions. Throughout this paper, we heavily use the generalized Walsh transform over multary alphabets. Our results have an independent interest as a nontrivial application of the generalized Walsh analysis.     

对遗传算法困难度测量的基因关联法的研究

针对基因关联测度法的本质及意义进行了详细的理论剖析和实证研究.首先分析了反映遗传算法基因关联程度的标准化的基因关联方差与基因关联相关系数,进一步归纳出两个基本定理,并给予了严格的数学证明.最后用一些初等函数及NNK-模型对这一方法进行了实证分析,实验结果表明,对于困难问题该方法能够给予准确的判别,而对于某些较为容易的问题可能产生误判.     

A note on problem difficulty measures in black-box optimization: classification, realizations and predictability

Various methods have been defined to measure the hardness of a fitness function for evolutionary algorithms and other black-box heuristics. Examples include fitness landscape analysis, epistasis, fitness-distance correlations etc., all of which are relatively easy to describe. However, they do not always correctly specify the hardness of the function. Some measures are easy to implement, others are more intuitive and hard to formalize. This paper rigorously defines difficulty measures in black-box optimization and proposes a classification. Different types of realizations of such measures are studied, namely exact and approximate ones. For both types of realizations, it is proven that predictive versions that run in polynomial time in general do not exist unless certain complexity-theoretical assumptions are wrong.     

基于混合遗传算法和点面距离测度的深度像配准*

提出一种利用改进的遗传算法和点面距离作为误差测度的深度像精确配准算法。与现有ICP框架下的迭代算法不同,将深度像配准视为高维空间的一个优化问题,通过在遗传算法中加入退火选择、爬山法以及参数空间的动态退化来加速寻找最优的位置转换关系。同时,采用一种新的基于点面距离的适应函数来计算配准误差,使得算法具有更强的鲁棒性。实验结果表明,该算法不需要初始的运动参数估计,具有较高的配准精度,收敛速度快且抗噪声能力强。     

并行混合遗传算法在深度像配准中的应用研究

实现了基于并行混合遗传算法的深度像精确配准,并比较了四种不同测度下算法的收敛速度和配准精度。根据进程数将种群划分为相应数量的子种群,每一个进程维护一个子种群的交叉、变异和选择,并通过采用环状的最优个体迁移策略和退火选择算子,实现了基于粗粒度并行混合遗传算法的深度像精确配准。此外,还比较了点对均值、中值、点面距离以及表面间平均体积四种测度下算法的性能和优劣。实验结果表明,并行计算技术的应用能够有效加速遗传算法的收敛,减少算法的运行时间。     

Evolutionary algorithm enhancement for model predictive control and real-time decision support

Effective decision support and model predictive control of real-time environmental systems require that evolutionary algorithms operate more efficiently. A suite of model predictive control (MPC) genetic algorithms are developed and tested offline to explore their value for reducing combined sewer overflow (CSO) volumes during real-time use in a deep-tunnel sewer system. MPC approaches include the micro-GA, the probability-based compact GA, and domain-specific GA methods that reduce the number of decision variable values analyzed within the sewer hydraulic model, thus reducing algorithm search space. Minimum fitness and constraint values achieved by all GA approaches, as well as computational times required to reach the minimum values, are compared to large population sizes with long convergence times. Optimization results for a subset of the Chicago combined sewer system indicate that genetic algorithm variations with a coarse decision variable representation, eventually transitioning to the entire range of decision variable values, are best suited to address the CSO control problem. Although diversity-enhancing micro-GAs evaluate a larger search space and exhibit shorter convergence times, these representations do not reach minimum fitness and constraint values. The domain-specific GAs prove to be the most efficient for this case study. Further MPC algorithm developments are suggested to continue advancing computational performance of this important class of problems with dynamic strategies that evolve as the external constraint conditions change.     

A novel genetic algorithm with different structure selection for circuit design optimization

In the traditional GA, the tournament selection for crossover and mutation is based on the fitness of individuals. This can make convergence easy, but some useful genes may be lost. In selection, as well as fitness, we consider the different structure of each individual compared with an elite one. Some individuals are selected with many different structures, and then crossover and mutation are performed from these to generate new individuals. In this way, the GA can increase diversification into search spaces so that it can find a better solution. One promising application of GA is evolvable hardware (EHW), which is a new research field to synthesize an optimal circuit. We propose an optimal circuit design by using a GA with a different structure selection (GAdss), and with a fitness function composed of circuit complexity, power, and signal delay. Its effectiveness is shown by simulations. From the results, we can see that the best elite fitness, the average fitness value of correct circuits, and the number of correct circuits with GAdss are better than with GA. The best case of optimal circuits generated by GAdss is 8.1% better in evaluation value than that by traditional GA.     

Genetic drift in genetic algorithm selection schemes

A method for calculating genetic drift in terms of changing population fitness variance is presented. The method allows for an easy comparison of different selection schemes and exact analytical results are derived for traditional generational selection, steady-state selection with varying generation gap, a simple model of Eshelman's CHC algorithm (1991), and (μ+λ) evolution strategies. The effects of changing genetic drift on the convergence of a GA are demonstrated empirically     

基于改进遗传算法的餐厅服务机器人路径规划

针对遗传算法（GA）易产生早熟现象和收敛速度慢的问题,提出了一种基于传统遗传算法（TGA）的改进遗传算法——HLGA,用于实际餐厅服务机器人的路径规划。首先,通过基于编辑距离的相似度方法对拟随机序列产生的初始种群进行优化;其次,采用自适应算法的改进交叉概率和变异概率调整公式,对选择操作后的个体进行交叉、变异操作;最后,计算具有安全性评价因子函数的个体适应度值,进一步对比、迭代得到全局最优解。理论分析和Matlab仿真表明,与TGA和基于个体相似度改进的自适应遗传算法（ISAGA）相比,HLGA的运行时间分别缩短了6.92 s和1.79 s,且规划的实际路径更具有安全性和平滑性。实验结果表明HLGA在实际应用中能有效提高路径规划质量,同时缩小搜索空间、减少规划时间。     

Measuring fuzzy uncertainty

First, this paper reviews several well known measures of fuzziness for discrete fuzzy sets. Then new multiplicative and additive classes are defined. We show that each class satisfies five well-known axioms for fuzziness measures, and demonstrate that several existing measures are relatives of these classes. The multiplicative class is based on nonnegative, monotone increasing concave functions. The additive class requires only nonnegative concave functions. Some relationships between several existing and the new measures are established, and some new properties are derived. The relative merits and drawbacks of different measures for applications are discussed. A weighted fuzzy entropy which is flexible enough to incorporate subjectiveness in the measure of fuzziness is also introduced. Finally, we comment on the construction of measures that may assess all of the uncertainties associated with a physical system     

结合SVM的交互式遗传算法及其应用

交互式遗传算法在人机交互过程中．用户对每代的所有个体都要进行评估。针对个体数量较大．进化代数较多．用户容易疲劳这一问题。提出了一种改进算法。充分利用遗传初始阶段用户所选择的正例和反例信息．采用支持向量机构造分类器．在整个图像库中找出更多符合分类器的图像加入到遗传过程．以扩大遗传操作中好个体的个数．加速算法收敛．从而减轻用户疲劳；同时交互中不断扩大的样本集也使支持向量机分类器更加准确．从而建立比较完善的个性化的情感模型。本文将该算法应用于服装图像的个性化情感检索。实验结果表明．所提出的方法可以较好地减轻用户疲劳，检索出的图像较好地体现用户的个性化情感。     

基于种群多样度的变参数遗传算法的研究

该文针对基本遗传算法（SGA）所存在的缺陷——早熟现象进行了分析，并在此基础上提出了基于种群多样度的变参数遗传算法（VPGA）。该算法从概率角度分析了遗传操作算子的作用，搜索范围以及多样性的影响，依据种群的多样度对遗传算法的参数进行自动调节，抑制早熟现象。并应用两种遗传算法对评价遗传算法性能的四个著名测试函数进行了仿真测试，仿真结果表明该算法相对于基本遗传算法的优越性和抑制早熟现象的有效性。     

Learning Finite-State Transducers: Evolution Versus Heuristic State Merging

Finite-state transducers (FSTs) are finite-state machines (FSMs) that map strings in a source domain into strings in a target domain. While there are many reports in the literature of evolving FSMs, there has been much less work on evolving FSTs. In particular, the fitness functions required for evolving FSTs are generally different from those used for FSMs. In this paper, three string distance-based fitness functions are evaluated, in order of increasing computational complexity: string equality, Hamming distance, and edit distance. The fitness-distance correlation (FDC) and evolutionary performance of each fitness function is analyzed when used within a random mutation hill-climber (RMHC). Edit distance has the strongest FDC and also provides the best evolutionary performance, in that it is more likely to find the target FST within a given number of fitness function evaluations. Edit distance is also the most expensive to compute, but in most cases this extra computation is more than justified by its performance. The RMHC was compared with the best known heuristic method for learning FSTs, the onward subsequential transducer inference algorithm (OSTIA). On noise-free data, the RMHC performs best on problems with sparse training sets and small target machines. The RMHC and OSTIA offer similar performance for large target machines and denser data sets. When noise-corrupted data is used for training, the RMHC still performs well, while OSTIA performs poorly given even small amounts of noise. The RMHC is also shown to outperform a genetic algorithm. Hence, for certain classes of FST induction problem, the RMHC presented in this paper offers the best performance of any known algorithm     

An information-theoretic analysis on the interactions of variables in combinatorial optimization problems

In optimization problems, the contribution of a variable to fitness often depends on the states of other variables. This phenomenon is referred to as epistasis or linkage. In this paper, we show that a new theory of epistasis can be established on the basis of Shannon's information theory. From this, we derive a new epistasis measure called entropic epistasis and some theoretical results. We also provide experimental results verifying the measure and showing how it can be used for designing efficient evolutionary algorithms.     

A novel hybrid algorithm of gravitational search algorithm with genetic algorithm for multi-level thresholding

The multi-level thresholding is a popular method for image segmentation. However, the method is computationally expensive and suffers from premature convergence when level increases. To solve the two problems, this paper presents an advanced version of gravitational search algorithm (GSA), namely hybrid algorithm of GSA with genetic algorithm (GA) (GSA-GA) for multi-level thresholding. In GSA-GA, when premature convergence occurred, the roulette selection and discrete mutation operators of GA are introduced to diversify the population and escape from premature convergence. The introduction of these operators therefore promotes GSA-GA to perform faster and more accurate multi-level image thresholding. In this paper, two common criteria (1) entropy and (2) between-class variance were utilized as fitness functions. Experiments have been performed on six test images using various numbers of thresholds. The experimental results were compared with standard GSA and three state-of-art GSA variants. Comparison results showed that the GSA-GA produced superior or comparative segmentation accuracy in both entropy and between-class variance criteria. Moreover, the statistical significance test demonstrated that GSA-GA significantly reduce the computational complexity for all of the tested images.     

改进粒子群优化算法的移动机器人路径规划

针对单一智能优化算法求解机器人路径规划时易陷入局部误区的问题,提出改进粒子群优化算法(GB_PSO)用于机器人路径规划.该算法以粒子群优化算法(particle swarm optimization,PSO)为主体,由于遗传算法(genetic algorithm,GA)和细菌觅食算法(bacterial foraging optimization algorithm,BFO)更新策略所受环境影响的不同,拟合两种环境参数;然后计算粒子与不同环境参数之间的相关性将粒子群划分为两类,分别通过GA的选择、交叉、变异算子和BFO的趋化操作并行加强局部优化;最后通过改进的粒子群更新公式对粒子进行更新,实现机器人全局和局部路径的优化.实验结果表明,改进粒子群优化算法进行路径规划提高了局部和整体的搜索能力,路径规划速度快且路径距离短,同时具备更强的鲁棒性.     

Inductive genetic programming with decision trees

This article proposes a study of inductive Genetic Programming with Decision Trees (GPDT). The theoretical underpinning is an approach to the development of fitness functions for improving the search guidance. The approach relies on analysis of the global fitness landscape structure with a statistical correlation measure. The basic idea is that the fitness landscape could be made informative enough to enable efficient search navigation. We demonstrate that by a careful design of the fitness function the global landscape becomes smoother, its correlation increases, and facilitates the search. Another claim is that the fitness function has not only to mitigate navigation difficulties, but also to guarantee maintenance of decision trees with low syntactic complexity and high predictive accuracy.     

Quantifying and mapping biodiversity and ecosystem services: Utility of a multi-season NDVI based Mahalanobis distance surrogate

There is an urgent need for techniques to rapidly and periodically measure biodiversity and ecosystem services over large landscapes. Conventional vegetation classification and mapping approaches are based on discrete arbitrary classes which do not capture gradual changes in forest type (and corresponding biodiversity and ecosystem services values) from site to site. We developed a simple multi-date NDVI based Mahalanobis distance measure (called eco-climatic distance) that quantifies forest type variability across a moisture gradient for complex tropical forested landscapes on a single ecologically interpretable, continuous scale. This Mahalanobis distance, unlike other distance measures takes into account the variability in the reference class and shared information amongst bands as it is based on the covariance matrix, and therefore is most useful to summarize ecological distance of a pixel to a reference class in multi-band remotely sensed space In this study we successfully apply this measure as a surrogate for tree biodiversity and ecosystem services at two nested scales for the Western Ghats Bio-diversity hotspot. Data from over 500 tree-plots and forest type maps was used to test the ability of this remotely sensed distance to be a surrogate for abundance based tree-species compositional turn-over and as a continuous measure of forest type and ecosystem services. Our results suggest a strong but scale dependant relationship between the remotely-sensed distance measure and floristic distance between plots. The multi-date NDVI distance measure emerges as very good quantitative surrogate for forest type and is a useful complement to existing forest classification systems. This surrogate quantifies forest type variability on a single, continuous quantitative scale and has important applications in conservation planning and mapping and monitoring of hydrologic and carbon storage and sequestration services.     

实数与二进制编码GA种群多样性统一数学模型

针对GA早熟收敛问题研究中存在的种群多样性定义缺乏统一性和普适性问题,基于GA基因层次种群多样性的本质,建立了实数和二进制编码的GA层次多样性的统一数学模型。首先,将实数编码GA的种群矩阵等效变换成与二进制编码GA种群矩阵相同的形式。其次,定义了类随机变量的概念及其特性指标:数学期望、偏离度以及方差;在此基础上建立了适于两种编码的种群多样性的统一模型,并给出了该模型的进化矩阵和图形化两种表示方法。对GA测试函数的仿真分析表明,该模型可以有效地体现和分析GA进化过程中种群多样性的变化趋势以及各基因位的收敛过程和收敛结果。最后,指出了进一步的分析思路和方向。     

基于遗传算法的多传感器网络中目标定位算法

应用于目标定位的多传感器网络系统中,测距定位是一种常用手段,但是由于系统设备和环境干扰等因素的影响,使得测距数据产生误差,影响定位精度。提出了一种基于最小二乘法和遗传算法的一种组合定位算法,首先利用最小二乘法,拟合出目标点的初始概位,并对各节点到初始概位的距离与测量数据的相对误差的绝对值进行排序,根据确定的剔除比例系数,剔除明显异常的测距数据后,再利用遗传算法对目标点进行定位。仿真实验表明,该算法简单易于实现,可有效提高定位精度。