Running-Time Analysis of Brain Storm Optimization Based on Average Gain Model.

The brain storm optimization (BSO) algorithm has received increased attention in the field of evolutionary computation. While BSO has been applied in numerous industrial scenarios due to its effectiveness and accessibility, there are few theoretical analysis results about its running time. Running-time analysis can be conducted through the estimation of the upper bounds of the expected first hitting time to evaluate the efficiency of BSO. This study estimates the upper bounds of the expected first hitting time on six single individual BSO variants (BSOs with one individual) based on the average gain model. The theoretical analysis indicates the following results. (1) The time complexity of the six BSO variants is O(n) in equal coefficient linear functions regardless of the presence or absence of the disrupting operator, where n is the number of the dimensions. Moreover, the coefficient of the upper bounds on the expected first hitting time shows that the single individual BSOs with the disrupting operator require fewer iterations to obtain the target solution than the single individual BSOs without the disrupting operator. (2) The upper bounds on the expected first hitting time of single individual BSOs with the standard normally distributed mutation operator are lower than those of BSOs with the uniformly distributed mutation operator. (3) The upper bounds on the expected first hitting time of single individual BSOs with the U-12,12 mutation operator are approximately twice those of BSOs with the U(-1,1) mutation operator. The corresponding numerical results are also consistent with the theoretical analysis results.

Causal Discovery Combining K2 with Brain Storm Optimization Algorithm.

Exploring and detecting the causal relations among variables have shown huge practical values in recent years, with numerous opportunities for scientific discovery, and have been commonly seen as the core of data science. Among all possible causal discovery methods, causal discovery based on a constraint approach could recover the causal structures from passive observational data in general cases, and had shown extensive prospects in numerous real world applications. However, when the graph was sufficiently large, it did not work well. To alleviate this problem, an improved causal structure learning algorithm named brain storm optimization (BSO), is presented in this paper, combining K2 with brain storm optimization (K2-BSO). Here BSO is used to search optimal topological order of nodes instead of graph space. This paper assumes that dataset is generated by conforming to a causal diagram in which each variable is generated from its parent based on a causal mechanism. We designed an elaborate distance function for clustering step in BSO according to the mechanism of K2. The graph space therefore was reduced to a smaller topological order space and the order space can be further reduced by an efficient clustering method. The experimental results on various real-world datasets showed our methods outperformed the traditional search and score methods and the state-of-the-art genetic algorithm-based methods.