一种多反向学习的教与学优化算法

针对原始教与学优化算法全局搜索和局部搜索协调不足、当前反向学习策略过于单一的问题，将多种反向学习策略同教与学优化算法相结合，提出一种基于多反向学习的教与学优化（MOTLBO）算法。首先，借鉴反向学习的思想，设计一种基于Sigmoid函数且随进化代数逐渐变化的非线性混合反向学习模型，模型综合考虑了问题的搜索边界信息和种群的历史搜索信息；其次，在原始教与学算法教和学两个阶段的基础上，增加了基于搜索边界指导的自学习阶段，增强了种群的多样性；最后，将混合反向学习模型与算法的各阶段相结合，根据各阶段的不同特征，设计了基于均值个体、随机个体和最优个体的反向解计算方法，充分吸收种群的历史搜索经验，提高算法的收敛精度和速度。采用具有不同特征的Benchmark测试函数对算法的非线性混合反向学习模型和收敛性能进行测试，实验结果表明：非线性混合反向学习模型相对于单一的边界信息反向学习或种群信息反向学习，具有更强的全局搜索和局部探测能力；而与原始教与学优化算法及其改进算法相比，MOTLBO算法在获得较高的收敛精度和稳定性的同时保持了更快的收敛速度，其综合性能得到较大提升。此外，对扩频雷达相位编码求解的实验结果进一步表明，MOTLBO算法能有效避免陷入局部最优，亦适用于求解实际的工程优化问题。

Multi-opposition Teaching-Learning-based Optimization

In order to address the problems that the original teaching-learning-based optimization (TLBO) cannot balance the global exploration and the local exploitation well, and the current opposition-based learning (OBL) strategies are too simple, a multi-opposition teaching-learning-based optimization (MOTLBO) was proposed by combining various opposition-based strategies with TLBO. Firstly, learning from the idea of OBL, a nonlinear mixed opposition-based learning model with a Sigmoid function and gradual evolution change was designed, in which the boundary search information and the population historical search information systematically were taken into account. Secondly, a self-learning stage guided by search boundary was added based on the existing teaching and learning stages, which can enhance the population diversity greatly. Finally, combining the mixed model with each stage of the algorithm, the calculation methods of opposition-based solutions according to mean individual, randomly selected individual, and optimal individual, respectively, were presented, which fully utilized the historical search experience of the population and hence improved the convergence precision and speed. The Benchmark test functions with different characteristics were used to test the nonlinear mixed opposition-based learning model and convergence performance of the proposed algorithm. The experimental results showed that the nonlinear mixed opposition-based learning model has stronger capability of global exploration and local exploitation than the one that only uses the boundary search information or population historical search information. By compared with the TLBO and some of its current outstanding variants, the proposed algorithm obtained high optimization accuracy and stability while guaranteeing the convergence speed, achieving great improvements on comprehensive performances. Moreover, the experimental results of the spread spectrum radar Polly phase code design demonstrated that the proposed algorithm can escape from local optimum effectively. Hence, the proposed algorithm can also be used to handle the real-word engineering optimization problems.