An Improved Genetic Algorithm with Average-bound Crossover and Wavelet Mutation Operations

This paper presents a real-coded genetic algorithm (RCGA) with new genetic operations (crossover and mutation). They are called the average-bound crossover and wavelet mutation. By introducing the proposed genetic operations, both the solution quality and stability are better than the RCGA with conventional genetic operations. A suite of benchmark test functions are used to evaluate the performance of the proposed algorithm. Application examples on economic load dispatch and tuning an associative-memory neural network are used to show the performance of the proposed RCGA.     

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.     

一种改进的TSP启发交叉算子

旅行商问题（TSP,Traveling Salesman Problem）是一种经典的NP组合优化问题。遗传算法在求解这类组合问题方面明显优于传统算法,同时也提出了许多求解较好路径的交叉算子。在对比分析唐立新提出的两种启发式交叉算法的基础上,提出了一种新的交叉算子。该算子通过判断父代的城市是否相邻来保存有效基因片断,通过加入一个移动的窗口来加快算法收敛。实验结果表明了该算子的有效性。     

Nonconvex economic load dispatch using an efficient real-coded genetic algorithm

An efficient optimisation procedure based on real-coded genetic algorithm (RCGA) is proposed for the solution of economic load dispatch (ELD) problem with continuous and nonsmooth/nonconvex cost function and with various constraints being considered. The effectiveness of the proposed algorithm has been demonstrated on different systems considering the transmission losses and valve point loading effect in thermal units. The proposed algorithm is equipped with an effective constraint handling technique, which eliminates the need for penalty parameters. For the purpose of comparison, the same problem has also been solved using binary-coded genetic algorithm (BCGA) and three other popular RCGAs. In the proposed RCGA, simulated binary crossover and polynomial mutation are used against the single point crossover and bit-flipping mutation in BCGA. It has been observed from the test results that the proposed RCGA is more efficient in terms of thermal cost minimisation and execution time for ELD problem with continuous search space than BCGA and some other popular RCGAs.     

Parameter estimation in mathematical models using the real coded genetic algorithms

In this study, parameter estimation in mathematical models using the real coded genetic algorithms (RCGA) approach is presented. Although the RCGA is similar with the binary coded genetic algorithms (BCGA) in terms of genetic process, it has few advantages such as high precision, non-existence of Hamming’s cliff etc., over the BCGA. In this approach, creating initial population and selection procedure are almost the same with the BCGA, but crossover and mutation operations. The proposed approach is implemented on the second order ordinary differential equations modeling the enzyme effusion problem and it is compared with previous approaches. The results indicate that the proposed approach produced better estimated results with respect to previous findings.     

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.     

自交叉算子

研究表明交叉算子对染色体具有破坏和重构的双重作用,从而在进化代数增加的时候能够使模式内部各基因趋于独立,并且只要组成模式的各个基因都存在,则该模式一定能够被搜索到,此时模式的极限概率就等于组成该模式各基因的初始概率（也就是基因的极限概率）的乘积,与模式的定义长度无关,在对交叉算子性能深入认识的基础上,我们提出了一种新的交叉算子-自交叉算子,实际的算例显示算法的性能得到明显改善。     

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.     

求解TSP的启发式顺序交叉算子

旅行商问题是经典的NP难组合优化问题之一.在用遗传算法求解旅行商问题时,顺序交叉算子是一种较为常用的遗传交叉算子.使用顺序交叉算子时的交叉点位置是随机指定的,不能反映关键遗传信息,导致算法执行效率较低.在顺序交叉算子的基础上,提出了一种启发式顺序交叉算子.该算子结合顺序交叉算子和启发式算法以得到双亲中交叉点位置,保留了双亲中关键的城市顺序信息.该算子改善了使用顺序交叉算子执行效率低的问题.实验结果表明了该算子的有效性.     

交叉算子的搜索能力

文中对遗传算法中常用的交叉算子的搜索能力进行了讨论,综合考虑了交叉算子对染色体的双重作用,给出了染色体在交叉算子作用下数量和分布范围的变化规律,得到了模式变化的极限性能,证明了交叉算子在演化代数增加的时候能够使模式内部各基因趋于独立,并且只要组成模式的各个基因都存在,则该模式一定能够被搜索到,此时模式的极限概率等于组成该模式各基因的初始概率（也就是基因的极限概率）的乘积,并且与模式的定义长度无关,说明了交叉算子使群体分布扩散的特性,从而可以进一步改善遗传算法的性能     

Investigation of self-organizing map for genetic algorithm

This paper describes self-organizing maps for genetic algorithm (SOM-GA) which is the combinational algorithm of a real-coded genetic algorithm (RCGA) and self-organizing map (SOM). The self-organizing maps are trained with the information of the individuals in the population. Sub-populations are defined by the help of the trained map. The RCGA is performed in the sub-populations. The use of the sub-population search algorithm improves the local search performance of the RCGA. The search performance is compared with the real-coded genetic algorithm (RCGA) in three test functions. The results show that SOM-GA can find better solutions in shorter CPU time than RCGA. Although the computational cost for training SOM is expensive, the results show that the convergence speed of SOM-GA is accelerated according to the development of SOM training.     

一种变形杂交算子——轮转杂交算子

杂交算子是遗传算法的三个基本算子之一,它在改进解群质量方面发挥着重要作用。现有遗传算法的杂交算子通常选择两个个体组成母本进行杂交运算。该文提出了一种选择三个个体组成母本进行轮转杂交的思想,文章称这种新的杂交算子为轮转杂交算子。首先通过理论分析证明,它能够扩大遗传算子搜索子空间,使收敛结果更趋于最优解。然后将其用于分布式系统任务调度问题,模拟结果说明是可行的。     

A new crossover operator in genetic programming for object classification.

The crossover operator has been considered "the centre of the storm" in genetic programming (GP). However, many existing GP approaches to object recognition suggest that the standard GP crossover is not sufficiently powerful in producing good child programs due to the totally random choice of the crossover points. To deal with this problem, this paper introduces an approach with a new crossover operator in GP for object recognition, particularly object classification. In this approach, a local hill-climbing search is used in constructing good building blocks, a weight called looseness is introduced to identify the good building blocks in individual programs, and the looseness values are used as heuristics in choosing appropriate crossover points to preserve good building blocks. This approach is examined and compared with the standard crossover operator and the headless chicken crossover (HCC) method on a sequence of object classification problems. The results suggest that this approach outperforms the HCC, the standard crossover, and the standard crossover operator with hill climbing on all of these problems in terms of the classification accuracy. Although this approach spends a bit longer time than the standard crossover operator, it significantly improves the system efficiency over the HCC method.     

有导向交叉算子的研究

为了更有效地处理建筑块,提出有导向的交叉算子。首先反复运行快速演化算法找到多个局部最优解,然后识别这些局部最优解中的重要基因位,将其标识为潜在的建筑块,然后应用有导向的交叉算子,组合父代中的建筑块。基于4阶欺骗问题验证了新算法的可行性。     

An Efficient Adaptive Real Coded Genetic Algorithm to Solve the Portfolio Choice Problem Under Cumulative Prospect Theory

Cumulative prospect theory (CPT) has become one of the most popular approaches for evaluating the behavior of decision makers under conditions of uncertainty. Substantial experimental evidence suggests that human behavior may significantly deviate from the traditional expected utility maximization framework when faced with uncertainty. The problem of portfolio selection should be revised when the investor’s preference is for CPT instead of expected utility theory. However, because of the complexity of the CPT function, little research has investigated the portfolio choice problem based on CPT. In this paper, we present an operational model for portfolio selection under CPT, and propose a real-coded genetic algorithm (RCGA) to solve the problem of portfolio choice. To overcome the limitations of RCGA and improve its performance, we introduce an adaptive method and propose a new selection operator. Computational results show that the proposed method is a rapid, effective, and stable genetic algorithm.     

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.     

New Real-Coded Genetic Algorithm Operators for Minimization of Molecular Potential Energy Function

The global minimum of the potential energy of a molecule corresponds to its most stable conformation and it dictates most of its properties. Due to the extensive search space and the massive number of local minima that propagate exponentially with molecular size, determining the global minimum of a potential energy function could prove to be significantly challenging. This study demonstrates the application of newly designed real-coded genetic algorithm (RCGA) called RX-STPM, which incorporates the use of Rayleigh crossover (RX) and scale-truncated Pareto mutator (STPM) as defined earlier for minimizing molecular potential energy functions. Computational results for problems with up to 100 degrees of freedom are compared with five other existing methods from the literature. The numerical results indicate the underlying reliability (robustness) and efficiency of the proposed approach compared to other existing algorithms with low computational costs.     

柔性作业车间调度中的组合遗传优化研究

针对柔性作业车间调度问题,提出一种组合遗传算法。该算法在种群初始化、选择、交叉、变异各阶段,组合使用各种不同的策略。针对机器编码部分的交叉,提出一种基于工件的机器交叉算子,用以改进机器分配部分随机交叉引起的对父代优秀基因继承不足的缺陷。通过对典型算例的计算以及与其他文献的研究成果比较,证明该算法的优良性能。     

交叉算子的极限一致性

交叉算子是遗传算法的主要操作算子之一，它使遗传算法具有了其它传统方法所没有的特性，并于它的理论研究对深入理解遗传算法具有重要意义，该文对遗传算法中常用的交叉算子（一点交叉算子、两点交叉算子、多点交叉算子和一致交叉算子）的性质进行了分析，综合考虑了交叉算子色全的双重作用，给了染色体在各种交叉算子作用下的变化规律，并得到了模式变化的极限性能，证明了这些交叉算子的极限一致性，即这些交叉算子在演化代数趋于无穷时对染色体的作用结果是一致的，同时对各自不同的收敛特点进行了分析，这些分析结果不仅UMDA等算法提供了一定的理论依据。也为今后的研究工作提供了基础。     

交叉位置非等概率选取的遗传算法

以遗传算法应用中普遍采用的二进制编码为前提，分析了交叉位置等概率选取交叉操作对遗传算法寻优的不利影响，并提出交叉位置非等概率选取的交叉操作方法，利用该交叉操作算子的遗传算法具有较好的收敛性能。