Toward minimal restriction of genetic encoding and crossovers for the two-dimensional Euclidean TSP

In the field of evolutionary algorithms (EAs), many operators have been introduced for the traveling salesman problem (TSP). Most encoding schemes have various restrictions that often result in a loss of information contained in problem instances. We suggest a new chromosomal encoding scheme that pursues minimal information loss and a crossover scheme with minimal restriction for the two-dimensional (2D) Euclidean TSP. The most notable feature of the suggested crossover is that it uses the 2D tour images themselves for chromosomal cutting. We prove the theoretical validity of the new crossover by an equivalence-class analysis. The proposed encoding/crossover pair outperformed both distance-preserving crossover and edge-assembly crossover, which represent two state-of-the-art crossovers in the literature. We also tested its performance on a mixed framework that incorporates a large-step Markov chain technique into the framework of a traditional EA.     

Geometric crossovers for multiway graph partitioning

Geometric crossover is a representation-independent generalization of the traditional crossover defined using the distance of the solution space. By choosing a distance firmly rooted in the syntax of the solution representation as a basis for geometric crossover, one can design new crossovers for any representation. Using a distance tailored to the problem at hand, the formal definition of geometric crossover allows us to design new problem-specific crossovers that embed problem-knowledge in the search. The standard encoding for multiway graph partitioning is highly redundant: each solution has a number of representations, one for each way of labeling the represented partition. Traditional crossover does not perform well on redundant encodings. We propose a new geometric crossover for graph partitioning based on a labeling-independent distance that filters out the redundancy of the encoding. A correlation analysis of the fitness landscape based on this distance shows that it is well suited to graph partitioning. A second difficulty with designing a crossover for multiway graph partitioning is that of feasibility: in general recombining feasible partitions does not lead to feasible offspring partitions. We design a new geometric crossover for permutations with repetitions that naturally suits partition problems and we test it on the graph partitioning problem. We then combine it with the labeling-independent crossover and obtain a much superior geometric crossover inheriting both advantages.     

基于多目标遗传算法的仿人机器人中枢神经运动控制器的设计

针对多自由度仿人机器人的运动控制,从神经生理学和机器人学的角度研究了基于中 枢模式生成器（CPGs）的仿人运动控制策略．提出了一种将多目标遗传算法应用于(CPGs)参 数优化的方法．首先构造用于仿人机器人运动控制的(CPGs)的结构,其参数通过遗传算法按 相应的评价函数得到优化．     

Semantically-based crossover in genetic programming: application to real-valued symbolic regression

We investigate the effects of semantically-based crossover operators in genetic programming, applied to real-valued symbolic regression problems. We propose two new relations derived from the semantic distance between subtrees, known as semantic equivalence and semantic similarity. These relations are used to guide variants of the crossover operator, resulting in two new crossover operators—semantics aware crossover (SAC) and semantic similarity-based crossover (SSC). SAC, was introduced and previously studied, is added here for the purpose of comparison and analysis. SSC extends SAC by more closely controlling the semantic distance between subtrees to which crossover may be applied. The new operators were tested on some real-valued symbolic regression problems and compared with standard crossover (SC), context aware crossover (CAC), Soft Brood Selection (SBS), and No Same Mate (NSM) selection. The experimental results show on the problems examined that, with computational effort measured by the number of function node evaluations, only SSC and SBS were significantly better than SC, and SSC was often better than SBS. Further experiments were also conducted to analyse the perfomance sensitivity to the parameter settings for SSC. This analysis leads to a conclusion that SSC is more constructive and has higher locality than SAC, NSM and SC; we believe these are the main reasons for the improved performance of SSC.     

Genetic algorithms for communications network design - an empiricalstudy of the factors that influence performance

We explore the use of GAs for solving a network optimization problem, the degree-constrained minimum spanning tree problem. We also examine the impact of encoding, crossover, and mutation on the performance of the GA. A specialized repair heuristic is used to improve performance. An experimental design with 48 cells and ten data points in each cell is used to examine the impact of two encoding methods, three crossover methods, two mutation methods, and four networks of varying node sizes. Two performance measures, solution quality and computation time, are used to evaluate the performance. The results obtained indicate that encoding has the greatest effect on solution quality, followed by mutation and crossover. Among the various options, the combination of determinant encoding, exchange mutation, and uniform crossover more often provides better results for solution quality than other combinations. For computation time, the combination of determinant encoding, exchange mutation, and one-point crossover provides better results     

An alternative model of genetic algorithms as learning machines

In this paper we report some results related to the use of genetic algorithms as learning machines (GLM) via a new regeneration/crossover model. In the past GAs have been applied as learning systems in traditional classifier systems. An alternative method to learning is the one where GAs are treated as computing devices where the genetic structure encodes some sort of automaton. That such an approach is theoretically possible results directly from Turing's thesis. We discuss a new model where the standard regeneration mechanism via biased individual survival and random crossover is replaced by a deterministic crossover scheme; furthermore, standard crossover is replaced by ring crossover. We statistically establish that such a genetic process results, indeed, in systems which learn. We also report on the way that crossover probabilities affect the learning convergence of such systems. After a statistical analysis, we found that GLMs, after being trained, show predictive behavior. Finally, we conclude from a statistical analysis, that the probability that a GLM shows a predictive behavior is better that 0.97, proving conclusively their viability as trainable learning systems.     

Subtree semantic geometric crossover for genetic programming

The semantic geometric crossover (SGX) proposed by Moraglio et al. has achieved very promising results and received great attention from researchers, but has a significant disadvantage in the exponential growth in size of the solutions. We propose a crossover operator named subtree semantic geometric crossover (SSGX), with the aim of addressing this issue. It is similar to SGX but uses subtree semantic similarity to approximate the geometric property. We compare SSGX to standard crossover (SC), to SGX, and to other recent semantic-based crossover operators, testing on several symbolic regression problems. Overall our new operator out-performs the other operators on test data performance, and reduces computational time relative to most of them. Further analysis shows that while SGX is rather exploitative, and SC rather explorative, SSGX achieves a balance between the two. A simple method of further enhancing SSGX performance is also demonstrated.     

Dynamic and heuristic fuzzy connectives-based crossover operators for controlling the diversity and convergence of real-coded genetic algorithms

Genetic algorithms are adaptive methods which may be used as approximation heuristic for search and optimization problems. Genetic algorithms process a population of search space solutions with three operations: selection, crossover, and mutation. A great problem in the use of genetic algorithms is the premature convergence, a premature stagnation of the search caused by the lack of diversity in the population and a disproportionate relationship between exploitation and exploration. The crossover operator is considered one of the most determinant elements for solving this problem. In this article we present two types of crossover operators based on fuzzy connectives for real-coded genetic algorithms. The first type is designed to keep a suitable sequence between the exploration and the exploitation along the genetic algorithm's run, the dynamic fuzzy connectives-based crossover operators, the second, for generating offspring near to the best parents in order to offer diversity or convergence in a profitable way, the heuristic fuzzy connectives-based crossover operators. We combine both crossover operators for designing dynamic heuristic fuzzy connectives-based crossover operators that show a robust behavior. © 1996 John Wiley & Sons, Inc.     

A formal analysis of the role of multi-point crossover in genetic algorithms

On the basis of early theoretical and empirical studies, genetic algorithms have typically used 1 and 2-point crossover operators as the standard mechanisms for implementing recombination. However, there have been a number of recent studies, primarily empirical in nature, which have shown the benefits of crossover operators involving a higher number of crossover points. From a traditional theoretical point of view, the most surprising of these new results relate to uniform crossover, which involves on the averageL/2 crossover points for strings of lengthL. In this paper we extend the existing theoretical results in an attempt to provide a broader explanatory and predictive theory of the role of multi-point crossover in genetic algorithms. In particular, we extend the traditional disruption analysis to include two general forms of multi-point crossover:n-point crossover and uniform crossover. We also analyze two other aspects of multi-point crossover operators, namely, their recombination potential and exploratory power. The results of this analysis provide a much clearer view of the role of multi-point crossover in genetic algorithms. The implications of these results on implementation issues and performance are discussed, and several directions for further research are suggested.     

基于加速度信号和进化RBF神经网络的人体行为识别*

针对基于加速度信号的人体行为识别,采用递阶遗传算法(HGA)训练径向基函数(RBF)神经网络,获得满意的识别正确率.设计适应度函数,利用四分位数间距改进HGA中参数基因的交叉方式,给出自动确定子代生成区域的方法,省去以往同类算法中的经验性设定,并结合算术交叉选择优秀子代,然后对比均匀变异和非均匀变异子代的适应值,实现对RBF网络结构和参数的联合优化.在基于加速度信号的行为识别系统中,与基本HGA和其他常用的训练方法相比,文中算法训练的RBF分类器可获得更低的输出误差和更高的测试样本识别正确率.     

ptGAs--genetic algorithms evolving noncoding segments by means of promoter/terminator sequences

In this article we present work on chromosome structures for genetic algorithms (GAs) based on biological principles. Mainly, the influence of noncoding segments on GA behavior and performance is investigated. We compare representations with noncoding sequences at predefined, fixed locations with "junk" code induced by the use of promoter/terminator sequences (ptGAs) that define start and end of a coding sequence, respectively. As one of the advantages of noncoding segments a few researchers have identified the reduction of the disruptive effects of crossover, and we solidify this argument by a formal analysis of crossover disruption probabilities for noncoding segments at fixed locations. The additional use of promoter/terminator sequences not only enables evolution of parameter values, but also allows for adaptation of number, size, and location of genes (problem parameters) on an artificial chromosome. Randomly generated chromosomes of fixed length carry different numbers of promoter/terminator sequences resulting in genes of varying size and location. Evolution of these ptGA chromosomes drives the number of parameters and their values to (sub)optimal solutions. Moreover, the formation of tightly linked building blocks is enhanced by self-organization of gene locations. We also introduce a new, nondisruptive crossover operator emerging from the ptGA gene structure with adaptive crossover rate, location, and number of crossover sites. For experimental comparisons of this genetic operator to conventional crossover in GAs, as well as properties of different ptGA chromosome structures, an artificial problem from the literature is utilized. Finally, the potential of ptGA is demonstrated on an NP-complete combinatorial optimization problem.     

求解武器—目标分配问题的混合编码差异演化算法*

提出一种混合编码差异演化求解武器—目标分配优化问题。在差异演化算法中增加违反边界约束处理操作,确保由变异和交叉操作生成的每个新个体满足边界约束条件;对差异演化算法中的选择操作重新定义,使其可以直接处理约束条件。基于编码映射的方法构建一种新的混合编码差异演化算法。利用武器—目标分配问题对该算法进行了仿真实验,结果表明该算法的有效性与适用性。混合编码差异演化算法是求解离散约束优化问题的一种有效方法。     

Crossover in Grammatical Evolution

We present an investigation into crossover in Grammatical Evolution that begins by examining a biologically-inspired homologous crossover operator that is compared to standard one and two-point operators. Results demonstrate that this homologous operator is no better than the simpler one-point operator traditionally adopted.An analysis of the effectiveness of one-point crossover is then conducted by determining the effects of this operator, by adopting a headless chicken-type crossover that swaps randomly generated fragments in place of the evolved strings. Experiments show detrimental effects with the utility of the headless chicken operator.Finally, the mechanism of crossover in GE is analysed and termed ripple crossover, due to its defining characteristics. An experiment is described where ripple crossover is applied to tree-based genetic programming, and the results show that ripple crossover is more effective in exploring the search space of possible programs than sub-tree crossover by examining the rate of premature convergence during the run. Ripple crossover produces populations whose fitness increases gradually over time, slower than, but to an eventual higher level than that of sub-tree crossover.     

An empirical study on the synergy of multiple crossover operators

Typical evolutionary algorithms (EAs) exploit the different space-search properties of variation operators, such as crossover, mutation and local optimization. There are also various operators in each element. This paper provides an extensive empirical study on the synergy among multiple crossover operators. We choose a number of different crossover operators in an EA and investigate whether or not their combinations outperform the sole usage of the best crossover operator. The traveling salesman problem and the graph bisection problem were chosen for experimentation. Strong synergy effects were observed in both problems     

一种改进的基于交叉矩阵统计的软件故障定位技术

故障定位是软件调试过程中一项耗时耗力的工作,而自动故障定位技术能够很好地与自动测试技术相结合,对于提高软件调试效率具有重要的现实意义。提出了一种改进的基于交叉矩阵统计的软件故障定位技术。该方法在故障定位前先对所有的成功执行轨迹序列和失败执行轨迹序列进行聚类约减,以消除执行轨迹冗余;然后将消除冗余后的执行轨迹存储到交叉矩阵中;最后通过Crosstab算法计算出各语句的可疑度并对语句进行可疑度排序,进而产生故障报告。在西门子测试程序集上做了执行轨迹聚类约减前后的性能对比实验,实验结果验证了本文方法的有效性。     

Automatic grey level thresholding through index of fuzziness and entropy

Algorithms for automatic thresholding of grey levels (without reference to histogram) are described using the terms ‘index of fuzziness’ and ‘entropy’ of a fuzzy set. Their values are seen to be minimum when the crossover point of an S-function corresponds to boundary levels among different regions in image space. The effectiveness of the algorithms is demonstrated for images having both bimodal and multimodal grey level distributions.     

Crossover and evolutionary stability in the prisoner's dilemma

We examine the role played by crossover in a series of genetic algorithm-based evolutionary simulations of the iterated prisoner's dilemma. The simulations are characterized by extended periods of stability, during which evolutionarily meta-stable strategies remain more or less fixed in the population, interrupted by transient, unstable episodes triggered by the appearance of adaptively targeted predators. This leads to a global evolutionary pattern whereby the population shifts from one of a few evolutionarily metastable strategies to another to evade emerging predator strategies. While crossover is not particularly helpful in producing better average scores, it markedly enhances overall evolutionary stability. We show that crossover achieves this by (1) impeding the appearance and spread of targeted predator strategies during stable phases, and (2) greatly reducing the duration of unstable epochs, presumably by efficient recombination of building blocks to rediscover prior metastable strategies. We also speculate that during stable phases, crossover's operation on the persistently heterogeneous gene pool enhances the survival of useful building blocks, thus sustaining long-range temporal correlations in the evolving population. Empirical support for this conjecture is found in the extended tails of probability distribution functions for stable phase lifetimes.     

Theory of Genetic Algorithms II: models for genetic operators over the string-tensor representation of populations and convergence to global optima for arbitrary fitness function under scaling

We present a theoretical framework for an asymptotically converging, scaled genetic algorithm which uses an arbitrary-size alphabet and common scaled genetic operators. The alphabet can be interpreted as a set of equidistant real numbers and multiple-spot mutation performs a scalable compromise between pure random search and neighborhood-based change on the alphabet level. We discuss several versions of the crossover operator and their interplay with mutation. In particular, we consider uniform crossover and gene-lottery crossover which does not commute with mutation. The Vose–Liepins version of mutation-crossover is also integrated in our approach. In order to achieve convergence to global optima, the mutation rate and the crossover rate have to be annealed to zero in proper fashion, and unbounded, power-law scaled proportional fitness selection is used with logarithmic growth in the exponent. Our analysis shows that using certain types of crossover operators and large population size allows for particularly slow annealing schedules for the crossover rate. In our discussion, we focus on the following three major aspects based upon contraction properties of the mutation and fitness selection operators: (i) the drive towards uniform populations in a genetic algorithm using standard operations, (ii) weak ergodicity of the inhomogeneous Markov chain describing the probabilistic model for the scaled algorithm, (iii) convergence to globally optimal solutions. In particular, we remove two restrictions imposed in Theorem 8.6 and Remark 8.7 of (Theoret. Comput. Sci. 259 (2001) 1) where a similar type of algorithm is considered as described here: mutation need not commute with crossover and the fitness function (which may come from a coevolutionary single species setting) need not have a single maximum.     

Linear analysis of genetic algorithms

We represent simple and fitness-scaled genetic algorithms by Markov chains on probability distributions over the set of all possible populations of a fixed finite size. Analysis of this formulation yields new insight into the geometric properties of the three phase mutation, crossover, and fitness selection of a genetic algorithm by representing them as stochastic matrices acting on the state space. This indicates new methods using mutation and crossover as the proposal scheme for simulated annealing. We show by explicit estimates that for small mutation rates a genetic algorithm asymptotically spends most of its time in uniform populations regardless of crossover rate. The simple genetic algorithm converges in the following sense: there exists a fully positive limit probability distribution over populations. This distribution is independent of the choice of initial population. We establish strong ergodicity of the underlying inhomogeneous Markov chain for genetic algorithms that use any of a large class of fitness scaling methods including linear fitness scaling, sigma-truncation, and power law scaling. Our analysis even allows for variation in mutation and crossover rates according to a pre-determined schedule, where the mutation rate stays bounded away from zero. We show that the limit probability distribution of such a process is fully positive at all populations of uniform fitness. Consequently, genetic algorithms that use the above fitness scalings do not converge to a population containing only optimal members. This answers a question of G. Rudolph (IEEE Trans. on Neural Networks 5 (1994) 96–101). For a large set of fitness scaling methods, the limit distribution depends on the pre-order induced by the fitness function f, i.e. c c′ f(c) f(c′) on possible creatures c and c′, and not on the particular values assumed by the fitness function.     

Evolutionary dynamics and the coding structure of sequences: Multiple coding as a consequence of crossover and high mutation rates

In this paper we explore the influence of the dynamics of evolution on coding structures of sequences. We show that, in systems with crossover, high mutation rates cause the most conserved subsequences to be preferentially used as recognition sites for newly evolving sequences. In other words: “multiple coding” evolves in these systems. Multiple coding often does not increase the fitness of the population; nevertheless it is selected. By contrast, in systems without crossover, a low mutation rate causes multiple coding to be avoided, so that only single coding evolves. Again this “choice” is not reflected in the fitness of the population, but is dictated by the evolutionary dynamics. We conclude that the genetic operator crossover turns evolutionary processes in pattern detectors rather than optimizers.