运用遗传规划解决异或问题的新方法*

介绍了一种用遗传规划这种新的搜索优化技术解决经典异或问题的新途径.遗传规划实质是使用广义的计算机程序来描述问题,并且可以根据环境状况动态改变计算机程序的结构.根据遗传规划特征,引入两种思路、三种方法对异或问题进行求解,取得了很好的效果.与神经网络相比,遗传规划可以动态进化学习并取得显式的数学表达式.     

Genetic algorithm-based fuzzy goal programming for class of chance-constrained programming problems

This paper presents a procedure for solving a multiobjective chance-constrained programming problem. Random variables appearing on both sides of the chance constraint are considered as discrete random variables with a known probability distribution. The literature does not contain any deterministic equivalent for solving this type of problem. Therefore, classical multiobjective programming techniques are not directly applicable. In this paper, we use a stochastic simulation technique to handle randomness in chance constraints. A fuzzy goal programming formulation is developed by using a stochastic simulation-based genetic algorithm. The most satisfactory solution is obtained from the highest membership value of each of the membership goals. Two numerical examples demonstrate the feasibility of the proposed approach.     

求解一类特殊的双层规划问题的遗传算法

主要研究上层函数及其约束函数不要求具有凸性和可微性,下层是关于下层决策变量是凸二次规划的双层规划模型,通过Karush-Kuhn-Tucher 条件转化为一个单层规划,利用下层是正定二次规划,将下层的决策变量表示为关于 Lagrangian乘子的表达式,从而降低了搜索空间的维数,设计了遗传算法,并通过数值实验表明该遗传算非常有效。     

Multi-stage genetic programming: A new strategy to nonlinear system modeling

This paper presents a new multi-stage genetic programming (MSGP) strategy for modeling nonlinear systems. The proposed strategy is based on incorporating the individual effect of predictor variables and the interactions among them to provide more accurate simulations. According to the MSGP strategy, an efficient formulation for a problem comprises different terms. In the first stage of the MSGP-based analysis, the output variable is formulated in terms of an influencing variable. Thereafter, the error between the actual and the predicted value is formulated in terms of a new variable. Finally, the interaction term is derived by formulating the difference between the actual values and the values predicted by the individually developed terms. The capabilities of MSGP are illustrated by applying it to the formulation of different complex engineering problems. The problems analyzed herein include the following: (i) simulation of pH neutralization process, (ii) prediction of surface roughness in end milling, and (iii) classification of soil liquefaction conditions. The validity of the proposed strategy is confirmed by applying the derived models to the parts of the experimental results that were not included in the analyses. Further, the external validation of the models is verified using several statistical criteria recommended by other researchers. The MSGP-based solutions are capable of effectively simulating the nonlinear behavior of the investigated systems. The results of MSGP are found to be more accurate than those of standard GP and artificial neural network-based models.     

多下层分式双层规划问题的改进遗传算法

针对一类具有多个线性下层问题的分式双层规划, 提出一种基于新编码方式的遗传算法。 首先,利用对偶理论,将问题化为单层非线性规划;接着,利用下层对偶问题的可行基编码,针对任意编码个体,解出对偶变量值,使得单层规划变为线性分式规划;最后,求解产生的线性分式规划,其目标值作为个体的适应度值。 这种编码方式及适应度的计算有效提高了遗传算法的效率。 通过对4个算例的计算,验证了算法的有效性。     

遗传编程运行期个体多样性分析方法及应用

文中根据遗传算法理论分析了遗传编程中种群多样性对算法收敛特性的影响,提出了一种可行的种群多样性跟踪评测方法,同时提出了优选父代个体的改进方法。以求解旅行商问题为例,通过统计性实验数据验证了改进后的算法较采用同样局部优化的常规遗传算法具有更好的收敛速度和优化解,同时也对改进后算法的相关控制参数选择进行了实验分析,结论为改进算法能获得更好的收敛性能。     

遗传进化算法在时间序列建模中的应用

该文把时间序列建模看作是模型结构和参数的优化搜索过程,将遗传规划与遗传算法结合起来对结构和参数共存且相互影响的复杂解空间进行全局最优搜索实现模型结构和参数的共同识别。实例分析表明该方法建立的预测模型具有较高的精度和推广预测能力。     

A linear goal programming approach to determining the relative importance weights of customer requirements in quality function deployment

Quality function deployment (QFD) is a planning tool used in new product development and quality management. It aims at achieving maximum customer satisfaction by listening to the voice of customers. To implement QFD, customer requirements (CRs) should be identified and assessed first. The current paper proposes a linear goal programming (LGP) approach to assess the relative importance weights of CRs. The LGP approach enables customers to express their preferences on the relative importance weights of CRs in their preferred or familiar formats, which may differ from one customer to another but have no need to be transformed into the same format, thus avoiding information loss or distortion. A numerical example is tested with the LGP approach to demonstrate its validity, effectiveness and potential applications in QFD practice.     

A hyper-heuristic approach to automated generation of mutation operators for evolutionary programming

Evolutionary programming can solve black-box function optimisation problems by evolving a population of numerical vectors. The variation component in the evolutionary process is supplied by a mutation operator, which is typically a Gaussian, Cauchy, or Lévy probability distribution. In this paper, we use genetic programming to automatically generate mutation operators for an evolutionary programming system, testing the proposed approach over a set of function classes, which represent a source of functions. The empirical results over a set of benchmark function classes illustrate that genetic programming can evolve mutation operators which generalise well from the training set to the test set on each function class. The proposed method is able to outperform existing human designed mutation operators with statistical significance in most cases, with competitive results observed for the rest.     

Application of fuzzy goal programming approach to multi-objective linear fractional inventory model

In this paper, we propose a model and solution approach for a multi-item inventory problem without shortages. The proposed model is formulated as a fractional multi-objective optimisation problem along with three constraints: budget constraint, space constraint and budgetary constraint on ordering cost of each item. The proposed inventory model becomes a multiple criteria decision-making (MCDM) problem in fuzzy environment. This model is solved by multi-objective fuzzy goal programming (MOFGP) approach. A numerical example is given to illustrate the proposed model.