划分序乘积空间作为一种新的粒计算模型可以从多个视角和多个层次对问题进行描述和求解. 其解空间是由多个问题求解层组成的格结构, 其中每个问题求解层由多个单层次视角构成. 如何在划分序乘积空间中选择问题求解层是一个NP难问题. 为此, 提出一种两阶段自适应遗传算法TSAGA (two stage adaptive genetic algorithm)来寻找问题求解层. 首先, 采用实数编码对问题求解层进行编码, 然后根据问题求解层的分类精度和粒度定义适应度函数. 算法第1阶段基于经典遗传算法, 预选出一些优秀问题求解层作为第2阶段初始种群的一部分, 从而优化解空间. 算法第2阶段, 提出随当前种群进化迭代次数动态变化的自适应选择算子、自适应交叉算子以及自适应大变异算子, 从而在优化的解空间中进一步选择问题求解层. 实验结果证明了所提方法的有效性.
As a new granular computing model, partition order product space can describe and solve problems from multiple views and levels. Its problem solving space is a lattice structure composed of multiple problem solving levels, and each problem solving level is composed of multiple one-level views. How to choose the problem solving level in the partition order product space is an NP-hard problem. Therefore, this study proposes a two-stage adaptive genetic algorithm (TSAGA) to find the problem solving level. First, real encoding is used to encode the problem solving level, and then the fitness function is defined according to the classification accuracy and granularity of the problem solving level. The first stage of the algorithm is based on a classical genetic algorithm, and some excellent problem solving levels are pre-selected as part of the initial population of the second stage, so as to optimize the problem solving space. In the second stage of the algorithm, an adaptive selection operator, adaptive crossover operator, and adaptive large-mutation operator are proposed, which can dynamically change with the number of iterations of the current population evolution, so as to further select the problem solving level in the optimized problem solving space. Experimental results demonstrate the effectiveness of the proposed method.