左智科 李一龙

摘 要：为准确预测城市自来水供水量，提出采用教与学优化算法（TLBO）优化的极限学习机预测方法。针对TLBO算法收敛精度低、易陷入局部最优的不足，提出一种改进的TLBO算法（ITLBO）。在ITLBO中，增加一个最差学生补习阶段，通过老师对该学生单独辅导或者采用一个反向学习策略快速提升学生成绩;在此基础上，采用一种干扰算子对老师进行扰动，增强种群跳出局部最优的动能;最后，将ITLBO算法用于优化调整极限学习机（ELM）模型的输入权值和隐层阈值参数，并构建ITLBO-ELM自来水供水量预测模型。将ITLBO-ELM模型用于上海市自来水供水量的预测实验，仿真结果表明该模型能够准确预测自来水供水量。

关键词：预测;极限学习机;教与学优化算法;反向学习;优化

Abstract：In order to predict the total amount of city tap water supply accurately， a predicting method of the extreme learning machine （ELM） optimized by teaching-learning-based optimization was proposed. An improved TLBO algorithm （ITLBO） was proposed to solve the problem of low convergence accuracy and easy to fall into local optimization. In ITLBO， an extra tutoring stage was added for the worst student， and the teacher could help the student individually or adopt the opposition-based learning strategy to quickly improve the student's performance. On this basis， a disturbance operator was used to perturb the teacher position， which increased the kinetic energy of the population to jump out of the local optimum. Finally， the improved ITLBO algorithm was used to optimize and adjust the input weight and hidden threshold parameters of ELM model， and the ITLBO-ELM water supply prediction model was built. ITLBO-ELM model was used to predict the tap water supply in Shanghai. The simulation results show that the model can accurately predict the tap water supply total amount.

Key words： prediction; extreme learning machine; teaching-learning-based optimization; opposition-based learning; optimization

水資源是人类社会基础性自然资源。随着人口规模和经济社会的持续发展，工业与居民自来水用水量增长，导致城市水资源供需矛盾日益激化。用水预测对于有效管理供水设施以满足城市日益增长的需求至关重要，准确预测城市需水可为供水环节优化调度提供重要决策依据[1-2]。高级机器学习技术可用于基于特征的预测，在水资源需求分析方面应用广泛[3-4]。极限学习机（ELM）是一种单隐层前馈神经网络，是由HUANG Guangbin等[5]根据Moore-Penrose Pseudoinverse广义逆矩阵提出的学习算法。很多研究者通过优化算法确定模型输入权重和隐层偏差来提升ELM算法的预测性能[6-8]。

教与学优化算法（TLBO）是一种元启发式优化方法[9]，具有结构简单、性能优良等特征，在解决许多科学和工程问题方面表现出卓越的性能[10-11]。……