# A Brain Storm and Chaotic Accelerated Particle Swarm Optimization Hybridization
## 1 Introduction  
The constantly evolving families of evolutionary computation, swarm intelligence, metaheuristic and nature-inspired optimization algorithms have penetrated into various interdisciplinary scientific domains. Their applications to several optimization problems have offered a plethora of results and conclusions [1]. Recent studies have indicated that these optimization algorithms are here to stay since associated methodologies emerge rapidly. Interesting discourse and debate regarding the classification of metaheuristic and original nature-inspired algorithms have also been examined [2]. Thus, the need to evolve both the algorithms themselves as well as our own knowledge of them has arisen [3, 4]. Regarding the improvement of existing metaheuristics/nature-inspired algorithms and their better utilization, one well-established approach is hybridization. We refer to hybrid algorithms as a combination or augmentation of two or more algorithms (and/or heuristics and metaheuristics) in order for them to work together to find the solution of a problem more effectively. This synergy can be achieved in many fashions: algorithms can work in parallel, compete or cooperate, switch places once or multiple times, or augment each other by sharing techniques and knowledge. A hybrid method can be more competitive or cooperative in nature, this depends on the hybridization scheme and the algorithms chosen. In evolutionary optimization, hybridization seems to be very popular and successful since it allows the utilization of advantages of more than onealgorithms, while also combating some of their disadvantages. Many well-established nature-inspired algorithms have been incorporated into hybrids with other algorithms or techniques, resulting in many effective approaches which can also be utilized for diverse applications [5; 6; 7; 8; 9]. Brain storm optimization (BSO) is a relatively new nature-inspired evolutionary algorithm, which was originally introduced by [PERSON] [10]. BSO is considered a promising optimization method with several variants [11; 12; 13] and applications, e.g., in electromagnetic engineering [14]. BSO models the social behavior of brainstorming amongst a group of people with different characteristics and backgrounds. The goal of BSO is to consistently invent and improve ideas as solutions of a problem. On the other hand, particle swarm optimization (PSO) is an immensely popular nature-inspired optimization algorithm that efficiently models the behavior of a flock of birds in search of food. The group cooperates and shares some knowledge and alignment. Since its introduction and refinement by [PERSON], [PERSON] and [PERSON] in [15; 16], PSO has been used in a multitude of optimization problems and proven to be a robust and relatively simple method. There exist several PSO variants that expand on the algorithm's topologies, cooperation behaviors, problem domains, stochastic behaviors and more. The chaotic accelerated PSO (CAPSO) algorithm is such a variant [17], which utilizes chaotic maps, and has been successfully applied to different optimization problems, e.g., [18; 19; 20]. It constitutes an improvement of accelerated PSO (APSO), serving as a more exploitative and simplified PSO algorithm [21; 22]. It is worth noting that both BSO (e.g., [23; 24; 25; 26; 27]) and PSO (e.g., [28; 29; 30; 31; 32]) are popular hybridization candidates. For evolutionary global optimization algorithms, the importance of the exploration and exploitation phases is tremendous. Exploration ensures that the algorithm reaches different promising areas of the search space. Additionally, exploration serves the algorithm as a means to escape getting trapped into a local optimum. Exploitation allows the algorithm to effectively search a given promising area around a current solution. It is more comparable to local search behavior. The right balance between exploration and exploitation is necessary, but it is difficult to perfect.