# A Brain Storm and Chaotic Accelerated Particle Swarm Optimization Hybridization
## 1 Introduction
The most common approach is to encourage exploration during the initial iterations of the optimization process and exploitation during the later ones. This balance, also referred to as the exploration-exploitation trade-off, is one of the main points of focus when such a metaheuristic is fine tuned with respect to its own parameters. BSO has demonstrated better speed in its global exploration for a random initialization compared to PSO, with the latter, however, being more competent at local exploitation when given a predefined initialization [33]. BSO utilizes a clustering process that is impactful and necessary for the algorithm's update scheme, but, unfortunately, it can be computationally heavy. Considering the above facts, in this work, we hybridized BSO with CAPSO, which is computationally lighter than BSO and more simplistic than PSO. Our main aim was to create a hybrid that served as a possible improvement compared to BSO. The developed BSO-CAPSO hybrid initially ran as BSO, then it continued the optimization process as CAPSO. The two algorithms were used as simple building blocks, facilitating their development and application. Similarly, recent approaches can be found in [34; 35], where PSO is hybridized with strategies/algorithms considering exploration and exploitation characteristics and benefits. BSO-CAPSO was tested on seven benchmark functions of various characteristics for different numbers of dimensions. Results showed advantageous behavior when compared to stand-alone BSO and CAPSO. Particularly, the results provided demonstrated that the BSO-CAPSO hybrid achieved the following:  
1. It severely outperformed CAPSO for most types of optimization benchmarks that were tested. 2. It was more effective when optimizing unimodal functions compared to BSO. 3. It showed advantageous behavior in multimodal problems with various degrees of success compared to BSO. 4. It was noticeably computationally lighter than BSO, to around one third of its computation time. It led to high-quality local search areas within a short amount of iterations. Thus, the BSO-CAPSO hybrid could be successfully used to explore areas of complex optimization problems efficiently and provide useful solutions or local search areas. It could improve both of the stand-alone algorithms, while its application was not of greater complexity. The rest of the paper is outlined as follows. In Section 2, the theoretical bases of stand-alone BSO and CAPSO are presented in detail. In Section 3, we present the BSO-CAPSO hybrid as a concept; its parameters and hybridization method are demonstrated and explained. In Section 4, we expand on the experimental parameters and conditions while the benchmarking functions are also provided in detail. Information regarding the hybrid's parameter tuning is provided alongside a detailed presentation of the parameters used for our set of experiments. In Section 5, the results for all the experiments are provided. The BSO-CAPSO hybrid is compared to the stand-alone BSO and CAPSO algorithms for all the benchmarking functions and for different numbers of dimensions. Computation time is also accounted for. The results are accompanied by several convergence diagrams to visualize the differences of the algorithms' behaviors and efficiency. Finally, in Section 6, the observations regarding the results provided are organized and presented, and the benefits of the BSO-CAPSO hybrid are discussed. Additionally, further discussions regarding the applications of the proposed hybrid algorithm and future experimentation are included.