This study develops an adaptive multilevel prediction (AMLP) method to detect and track multiple global optima over time. First, it formulates a multilevel prediction approach in which a higher level prediction improves the accuracy of the lower level prediction to reduce the prediction error, enabling it to capture more complex patterns in the changes. However, a higher level prediction is more sensitive to input errors and the randomness in the pattern of the change. To overcome this challenge, this study employs an adaptive mechanism which can determine the near-optimal prediction level at each time step. At the same time, AMLP calculates the strength of the diversity introduced after a change based on the estimated prediction error. A successful static multimodal optimizer is augmented with AMLP, for which AMLP determines the location and the mutation strength of the initialized subpopulations. An existing dynamic benchmark generator is improved so that it can generate dynamic test problems with more complex patterns in their changes. In particular, this dynamic benchmark generator allows for controlling the randomness of the pattern in the change to simulate dynamic problems with different degrees of predictability. A few controlled experiments are first performed to provide insight into different components of AMLP. Then, AMLP is compared with some of the most successful prediction methods when they are incorporated into the developed dynamic multimodal optimization method. Eleven dynamic cases with different change severity, change frequency, predictability, problem dimensionality, and the number of global minima are considered. The numerical results show the superiority of AMLP over other prediction methods.

中文翻译：

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动态多模态优化的自适应多级预测方法

本研究开发了一种自适应多级预测 (AMLP) 方法，以随着时间的推移检测和跟踪多个全局最优值。首先，它制定了一种多层次预测方法，其中较高层次的预测提高了较低层次预测的准确性，以减少预测误差，使其能够捕捉变化中更复杂的模式。然而，更高级别的预测对输入错误和变化模式的随机性更敏感。为了克服这一挑战，本研究采用了一种自适应机制，可以在每个时间步确定接近最佳的预测水平。同时，AMLP根据估计的预测误差计算变化后引入的多样性的强度。AMLP 增强了一个成功的静态多模式优化器，AMLP 决定了初始化亚群的位置和突变强度。改进了现有的动态基准生成器，使其可以生成具有更复杂变化模式的动态测试问题。特别是，这个动态基准生成器允许控制变化中模式的随机性，以模拟具有不同程度可预测性的动态问题。首先进行一些受控实验以深入了解 AMLP 的不同组成部分。然后，将 AMLP 与一些最成功的预测方法结合到开发的动态多模态优化方法中时进行比较。考虑了具有不同变化严重性、变化频率、可预测性、问题维度和全局最小值数量的 11 个动态案例。