Prediction of mode I fracture toughness of rock using linear multiple regression and gene expression programming

Prediction of mode I fracture toughness (K_IC) of rock is of significant importance in rock engineering analyses. In this study, linear multiple regression (LMR) and gene expression programming (GEP) methods were used to provide a reliable relationship to determine mode I fracture toughness of rock. The presented model was developed based on 60 datasets taken from the previous literature. To predict fracture parameters, three mechanical parameters of rock mass including uniaxial compressive strength (UCS), Brazilian tensile strength (BTS), and elastic modulus (E) have been selected as the input parameters. A cluster of data was collected and divided into two random groups of training and testing datasets. Then, different statistical linear and artificial intelligence based nonlinear analyses were conducted on the training data to provide a reliable prediction model of K_IC. These two predictive methods were then evaluated based on the testing data. To evaluate the efficiency of the proposed models for predicting the mode I fracture toughness of rock, various statistical indices including coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE) were utilized herein. In the case of testing datasets, the values of R², RMSE, and MAE for the GEP model were 0.87, 0.188, and 0.156, respectively, while they were 0.74, 0.473, and 0.223, respectively, for the LMR model. The results indicated that the selected GEP model delivered superior performance with a higher R² value and lower errors.     

Generation expansion planning in electricity markets: A novel framework based on dynamic stochastic MPEC

This paper presents a novel framework for generation expansion planning (GEP) of restructured power systems under uncertainty in a multi-period horizon, which includes generation investment from a price maker perspective. The investment problem is modeled as a bi-level optimization problem. The first level problem includes decisions related to investment in order to maximize total profit in the planning horizon. The second level problem consists of maximizing social welfare where the power market is cleared. Rival uncertainties on offering and investment are modeled using sets of scenarios. The bi-level optimization problem is then converted to a dynamic stochastic MPEC and represented as a mixed integer linear program (MILP) after linearization. The proposed framework is examined on a typical six-bus power network, MAZANDARAN regional electric company (MREC) transmission network as an area of IRAN interconnected power system and IEEE RTS 24-bus network. Simulation results confirm that the proposed framework can be a useful tool for analyzing the behavior of investments in electricity markets.     

基于基因算法的焦炭质量预测模型的研究

选取干燥无灰基挥发分（Vdaf）、胶质层最大厚度（Y）和炭化室高宽比（L/B）作为自变量,通过基于基因表达式的克隆选择算法对4种不同类型焦炉的生产数据进行分析,并建立焦炭质量的预测模型。对比采用该方法与回归分析得到的预测模型,该方法所得焦炭质量的预测模型的误差要远小于后者,能够更好地满足实际生产需求,为焦化厂快速准确地得到配煤方案提供了理论依据。     

改进GEP方法在边坡非圆临界滑动面搜索中的应用

基因表达式编程(Genetic Expression Programming,简称GEP)是模拟生物遗传进化过程的一种新型优化方法,其结合遗传算法(GA)和遗传编程(GP)各自的优点,使编码更为方便、简单。为了进一步改善GEP方法的局部搜索能力和克服“早熟”现象,将局部搜索能力很强的单纯形法和回溯机制引入GEP中,提出了混合GEP方法。以安全系数为目标函数,将混合GEP法和不平衡推力法结合,提出确定非圆弧临界滑动面的新方法。2个经典算例的计算结果表明:该新方法可以准确地搜索到边坡非圆临界滑动面及相应的安全系数,且混合GEP方法的局部搜索精度和全局搜索能力均优于标准GEP方法,同时收敛速度得到明显提高。     

基于基因表达式编程算法的复杂网络社区结构划分

由于复杂网络的不确定性,传统的复杂网络社区结构划分算法易造成过早收敛,使精度降低,且由于计算量大,时间复杂度较高。为克服以上不足,利用基因表达式编程(GEP)的自适应性和全局搜索能力强以及具有并行性计算等特点,优化网络社区结构的划分,提出了一种基于GEP的复杂网络社区结构划分算法,并通过实验验证了新算法的有效性。新算法在无先验信息情况下,可较准确地完成对复杂网络的社区划分。     

基于IP和GEP算法的股票预测

采用免疫算法和基于基因表达式编程的混合算法建立了股票指数预测模型。实验结果显示,该模型能够以相当高的精度预测股票指数。     

基于EMD和GEP的软件可靠性预测模型

基于经验模态分解和基因表达式编程算法提出了一种软件可靠性预测模型。通过对软件失效数据序列进行经验模态分解得到不同频段的本征模态分量和剩余分量,消除失效数据中的噪声,运用基因表达式编程算法的灵活表达能力,把分解得到的不同频段的各本征模态分量及剩余分量中所对应的不同失效时间序列作为样本来分别进行预测,重构各本征模态分量和剩余分量中相对应的预测结果,将其作为软件失效的最终预测值。基于两组真实软件失效数据集,将所提出的方法与基于支持向量回归机以及单纯使用基因表达式编程的软件可靠性预测模型进行比较分析。结果表明,该软件可靠性预测模型具有更为显著的模型拟合能力与精确的预测效果。     

基于基因表达式编程的进化计算模式定理

基因表达式编程（GEP）从提出迄今尚无完整的理论体系,严重阻碍了GEP的发展。为解决该问题,本文从理论上深入的研究了GEP计算模型：定义了GEP基因模式及相关的概念,采用概率办法详细分析了单基因GEP应用实例在进化过程中各算子的作用,根据分析结果推导出GEP模式定理,通过详细的实验验证了GEP模式定理的正确性。GEP模式定理的提出,为GEP算法改进评估提供了量化的依据。     

基于RFID与基因表达式编程的经济统计时序挖掘

为解决基因表达式编程(GEP)在符号回归、RFID分类及经济领域中对时序数据的挖掘速度和精度还不够的问题,提出了统计基因、统计染色体和统计时序-适应度的定义,并针对传统GEP经济时序模型进行了综合改进;提出了新颖的单变量时序和多变量时序挖掘算法,提高了GEP统计时序挖掘的速度和精度;实验表明,与传统GEP、单变量GEP时序算法相比,多变量GEP时序算法挖掘速度快,其预测精度比单变量时序算法高出5%以上.该算法同样适用于RFID以及其他经济系统中的时序数据挖掘.     

基于多样化进化策略的基因表达式编程算法

针对传统GEP（Gene Expression Programming）算法的未成熟收敛以及陷入局部最优问题,提出一种基于多样化进化策略的基因表达式编程算法（DS-GEP：Gene Expression Programming based on diversified develop-ment strategy）。该算法通过基因空间均匀分布策略,自适应地交叉和变异算子以及淘汰算子等方法,对种群给予不同的进化策略,以保持种群的多样性,从而增强算法的寻优能力。通过对函数挖掘的实验证明,多样化进化策略各个部分均对改善挖掘效率发挥了作用,提高了DS-GEP函数挖掘算法的成功率。与传统GEP算法相比较,该算法的平均成功进化代数缩短了11%,成功进化时间缩短了8%,进化成功率提高了20%。