Hybrid crossover operators for real-coded genetic algorithms: an experimental study

Most real-coded genetic algorithm research has focused on developing effective crossover operators, and as a result, many different types have been proposed. Some forms of crossover operators are more suitable to tackle certain problems than others, even at the different stages of the genetic process in the same problem. For this reason, techniques which combine multiple crossovers have been suggested as alternative schemes to the common practice of applying only one crossover model to all the elements in the population. Therefore, the study of the synergy produced by combining the different styles of the traversal of solution space associated with the different crossover operators is an important one. The aim is to investigate whether or not the combination of crossovers perform better than the best single crossover amongst them. In this paper we have undertaken an extensive study in which we have examined the synergetic effects among real-parameter crossover operators with different search biases. This has been done by means of hybrid real-parameter crossover operators, which generate two offspring for every pair of parents, each one with a different crossover operator. Experimental results show that synergy is possible among real-parameter crossover operators, and in addition, that it is responsible for improving performance with respect to the use of a single crossover operator.     

Robust confidence intervals applied to crossover operator for real-coded genetic algorithms

In this work we propose a new approach to crossover operators for real-coded genetic algorithms based on robust confidence intervals. These confidence intervals are an alternative to standard confidence intervals. In this paper, they are used for localising the search regions where the best individuals are placed. Robust confidence intervals use robust localization and dispersion estimators that are highly recommendable when the distribution of the random variables is not known or is distorted. Both situations are likely when we are dealing with the best individuals of the population, especially if the problem under study is multimodal. The performance of the crossovers based on robust intervals is evaluated using a well characterised set of optimisation problems. We have chosen problems with different features of modality, separability, regularity, and correlation among their variables. The results show that the performance of the crossovers based on robust confidence intervals is less dependent on the problem than the performance of the crossovers based on Gaussian confidence intervals. We have also made comparisons between several standard crossovers that show very interesting results, which support the idea underlying the defined operators.     

Adaptive directed mutation for real-coded genetic algorithms

Adaptive directed mutation (ADM) operator, a novel, simple, and efficient real-coded genetic algorithm (RCGA) is proposed and then employed to solve complex function optimization problems. The suggested ADM operator enhances the abilities of GAs in searching global optima as well as in speeding convergence by integrating the local directional search strategy and the adaptive random search strategies. Using 41 benchmark global optimization test functions, the performance of the new algorithm is compared with five conventional mutation operators and then with six genetic algorithms (GAs) reported in literature. Results indicate that the proposed ADM-RCGA is fast, accurate, and reliable, and outperforms all the other GAs considered in the present study.     

Adaptive crossover,mutation and selection using fuzzy system for genetic algorithms

Genetic algorithms use a tournament selection or a roulette selection to choice better population. But these selections couldn’t use heuristic information for specific problem. Fuzzy selection system by heuristic rule base help to find optimal solution efficiently. And adaptive crossover and mutation probabilistic rate is faster than using fixed value. In this paper, we want fuzzy selection system for genetic algorithms and adaptive crossover and mutation rate fuzzy system. This work was presented in part and awarded as Young Author Award at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Using real-coded genetic algorithms for Weibull parameter estimation

Genetic algorithms (GAs) represent a class of adaptive search techniques based on a direct analogy to Darwinian natural selection and mutations in biological systems. “Standard” GAs have emphasized the utilization of binary codes. However, recent empirical results have indicated that a chromosome representation which utilizes real values have enhanced the performance of these GAs in certain engineering problems. A real-valued Genetic Algorithm method described in this paper estimates the parameter values from an unconstrained population of data points for a Weibull distribution function using a simultaneous random search function by integrating the principles of the Genetic Algorithm and the method of Maximum Likelihood Estimation. The results of the real-coded GA technique for parameter estimation are compared to the results of the Newton-Raphson Algorithm.     

Hybrid crossover operators with multiple descendents for real‐coded genetic algorithms: Combining neighborhood‐based crossover operators

Most real‐coded genetic algorithm research has focused on developing effective crossover operators, and as a result, many different types of crossover operators have been proposed. Some forms of crossover operators are more suitable to tackle certain problems than others, even at the different stages of the genetic process in the same problem. For this reason, techniques that combine multiple crossovers, called hybrid crossover operators, have been suggested as alternative schemes to the common practice of applying only one crossover model to all the elements in the population. On the other hand, there are operators with multiple offsprings, more than two descendants from two parents, which present a better behavior than the operators with only two descendants, and achieve a good balance between exploration and exploitation. © 2009 Wiley Periodicals, Inc.     

一种择优配种的实数编码遗传算法*

模拟生物学家在优秀种子间进行杂交得到更好基因种子的方式,对实数编码遗传算法的种群进行优选,只在优选后的种群间杂交,可使算法快速收敛于极优值;同时,每代都加入新的随机种子,保持种群多样化。实验表明,该算法达到最优值的速度明显快于基本实数编码遗传算法。     

A comparison study of self-adaptation in evolution strategies and real-coded genetic algorithms

This paper discusses the self-adaptive mechanisms of evolution strategies (ES) and real-coded genetic algorithms (RCGA) for optimization in continuous search spaces. For multi-membered evolution strategies, a self-adaptive mechanism of mutation parameters has been proposed by Schwefel. It introduces parameters such as standard deviations of the normal distribution for mutation into the genetic code and lets them evolve by selection as well as the decision variables. In the RCGA, crossover or recombination is used mainly for search. It utilizes information on several individuals to generate novel search points, and therefore, it can generate offspring adaptively according to the distribution of parents without any adaptive parameters. The present paper discusses characteristics of these two self-adaptive mechanisms through numerical experiments. The self-adaptive characteristics such as translation, enlargement, focusing, and directing of the distribution of children generated by the ES and the RCGA are examined through experiments.     

Balancing meals using fuzzy arithmetic and heuristic search algorithms

This paper aims at showing how well-known ideas in the fields of fuzzy arithmetic and heuristic search have been combined in an educational software in nutrition in order to provide not only a better mathematical modeling, but also significant functional improvements for end-users, comparing to other nutrition programs. This software, called Nutri-Expert, helps patients to improve their nutritional habits, by analyzing in detail their food intakes, and by suggesting changes that result in well-balanced meals. Fuzzy arithmetic is used to model the input and database data, and for all computations. A fuzzy pattern matching is performed between total amounts of nutrients and different norm patterns, and the results are displayed using a galvanometer metaphor. A heuristic search algorithm is used to find out minimal sets of pertinent actions to perform on a meal in order to make it well balanced. The search is guided by an evaluation function based on fuzzy pattern matching indexes. The different versions of the algorithm have been benchmarked against a test database of real meals. Finally, the medical efficacy of Nutri-Expert and its acceptance by end-users have been demonstrated in several medical studies, the main results of which are presented.     

Local convergence of the fuzzy c-Means algorithms

Much understanding has recently been gained concerning global convergence properties of the fuzzy c-Means (FCM) family of clustering algorithms. These global convergence properties, which hold for all iteration sequences, guarantee that every FCM iteration sequence converges, at least along a subsequence, to a stationary point of an FCM objective function. In this paper we prove a local convergence property, that is, a property pertaining to iteration sequences started near a solution. Specifically, a simple result is proved which shows that whenever an FCM algorithm is started sufficiently near a minimizer of the corresponding objective function, then the iteration sequence must converge to that particular minimizer. The result guarantees that once captured by the local neighborhood of a minimizer, the succeeding iterate sequence will not escape—thus, infinite oscillation of such a sequence cannot occur. The rate of convergence of the sequence to such a point is also discussed.     

A study on the convergence of genetic algorithms

This paper extends genetic algorithms to achieve fast solutions to difficult problem. To accomplish this, we present empirical results on the terminated condition by bias and the functionized model of mutation rate in genetic algorithms. The terminated condition by bias enable to reducing computation time(CPU time) according to limitted and pre-estimated number of generations. The functionized model of mutation operator reducing computation time and improving solution should be accomplished by applying quite low mutation rate on the continuing generation with remaining 95 percentage of bias.     

遗传算法的平均收敛速度及其估计

给出了独立于表示的变异算子和交叉算子的数学描述, 建立了遗传算法种群的精确马尔可夫链模型, 导出了种群中最佳个体的马尔可夫链及其随机矩阵, 将遗传算法的平均收敛速度定义为最佳个体转移至吸收态的平均吸收时间的数学期望, 提出了应用最佳个体的随机矩阵估计遗传算法平均收敛速度的理论方法和计算步骤.     

RGFGA: an efficient representation and crossover for grouping genetic algorithms

There is substantial research into genetic algorithms that are used to group large numbers of objects into mutually exclusive subsets based upon some fitness function. However, nearly all methods involve degeneracy to some degree.We introduce a new representation for grouping genetic algorithms, the restricted growth function genetic algorithm, that effectively removes all degeneracy, resulting in a more efficient search. A new crossover operator is also described that exploits a measure of similarity between chromosomes in a population. Using several synthetic datasets, we compare the performance of our representation and crossover with another well known state-of-the-art GA method, a strawman optimisation method and a well-established statistical clustering algorithm, with encouraging results.     

遗传交叉和变异对种群多样性的影响

首先,定义了群体的算术交叉扩展子空间、寻优空间和基因位直方图概念,并分析了交叉在解空间的扩展性．然后,证明了在二进制编码中,交叉不能改变基因层次上的多样性;而在实数编码中,在一定条件下,算术交叉可改变基因层次上的多样性,但以扩大寻优空间、产生无用解为代价．随后,证明了交叉可改变个体层次上的多样性,而变异可改变以上两个层次上的多样性．最后,分析了所得结论对遗传算法的改进和应用具有的指导意义,并通过仿真加以验证．     

Theoretical basis of parameter tuning for finding optima near the boundaries of search spaces in real-coded genetic algorithms

Studies on parameter tuning in evolutionary algorithms are essential for achieving efficient adaptive searches. This paper discusses parameter tuning in real-valued crossover operators theoretically. The theoretical analysis is devoted to improving robustness of real-coded genetic algorithms (RCGAs) for finding optima near the boundaries of bounded search spaces, which can be found in most real-world applications. The proposed technique for crossover-parameter tuning is expressed mathematically, and thus enables us to control the dispersion of child distribution quantitatively. The universal applicability and effect have been confirmed theoretically and verified empirically with five crossover operators. Statistical properties of several practical RCGAs are also investigated numerically. Performance comparison with various parameter values has been conducted on test functions with the optima placed not only at the center but also in a corner of the search space. Although the parameter-tuning technique is fairly simple, the experimental results have shown the great effectiveness.     

基于异位交叉的遗传算法的研究

针对目前遗传算法搜索速度较慢的问题，对提高遗传算法收敛速度的不同方法进行了分析。提出一种加快收敛速度的异位交叉算子，并给出算法仿其实验。仿真结果表明，这种交叉算子可比一般的对等位交叉算子更有效地提高收敛速度，且不易陷入局部最优解。具有实现简单、易于应用及鲁捧性强的特点。     

遗传算法在模糊设计中的应用

构造了CAD系统模糊设计的一种具体解决方案: 其环境为收集到的现场数据; 学习环节采用基于遗传算法的模糊优化算法; 知识库由设计准则构成; 执行部件为设计单元. 建立了回归方程的模糊优化学习算法, 并构造了该算法的流程. 然后利用该模糊设计系统获得了飞边尺寸设计准则, 且应用实例对该算法的稳定性进行了校验. 为评估该算法的性能, 将其与最小二乘法和免疫遗传算法进行了比较, 结果表明, 该算法速度快, 精度高, 稳定性好.     

提高多目标进化算法分布性的动态调整机制

为提高多目标进化算法的分布性,提出一种基于极坐标的动态调整机制。在极坐标下,根据解集的拥挤程度,计算个体解的缩放系数。在进化过程中利用该缩放系数动态调整解集支配关系,适当提高分布性好的解在支配关系中的地位以改善解的分布。对测试函数的仿真试验结果表明,将该机制应用于经典算法能显著提高算法的分布性,同时保持良好的收敛性。     

Phase transitions and symmetry breaking in genetic algorithms with crossover

In this paper, we consider the role of the crossover operator in genetic algorithms. Specifically, we study optimisation problems that exhibit many local optima and consider how crossover affects the rate at which the population breaks the symmetry of the problem. As an example of such a problem, we consider the subset sum problem. In doing so, we demonstrate a previously unobserved phenomenon, whereby the genetic algorithm with crossover exhibits a critical mutation rate, at which its performance sharply diverges from that of the genetic algorithm without crossover. At this critical mutation rate, the genetic algorithm with crossover exhibits a rapid increase in population diversity. We calculate the details of this phenomenon on a simple instance of the subset sum problem and show that it is a classic phase transition between ordered and disordered populations. Finally, we show that this critical mutation rate corresponds to the transition between the genetic algorithm accelerating or preventing symmetry breaking and that the critical mutation rate represents an optimum in terms of the balance of exploration and exploitation within the algorithm.     

Optimization of fuzzy partitions for inductive reasoning using genetic algorithms

Fuzzy Inductive Reasoning (FIR) is a data-driven methodology that uses fuzzy and pattern recognition techniques to infer system models and to predict their future behavior. It is well known that variations on fuzzy partitions have a direct effect on the performance of the fuzzy-rule-based systems. The FIR methodology is not an exception. The performance of the model identification and prediction processes of FIR is highly influenced by the discretization parameters of the system variables, i.e. the number of classes of each variable and the membership functions that define its semantics. In this work, we design two new genetic fuzzy systems (GFSs) that improve this modeling and simulation technique. The main goal of the GFSs is to learn the fuzzification parameters of the FIR methodology. The new approaches are applied to two real modeling problems, the human central nervous system and an electrical distribution problem.