# Adaptive Self-Scaling Brain-Storm Optimization via a Chaotic Search Mechanism
## 1 Introduction  
Meta-heuristic algorithms have attracted increasing attention in recent years due to their unique advantages in solving high-dimensional and complex optimization problems and have been successfully applied to communication, transportation, national defense, management and computer science [1; 2; 3; 4; 5]. Deterministic algorithms usually start from a similar initial point and obtain the same solution in the iterative process, but the search process can easily fall into local optima. The development of meta-heuristic algorithms has accelerated in the past few decades. These algorithms use random operators to start with random initialization, which can avoid local optima [6]. In addition to randomness, meta-heuristic algorithms can handle approximation and uncertainty and adapt to problems. These characteristics ensure that meta-heuristic algorithms can be developed freely for a variety of classifications. Several optimization algorithms have been created based on biological populations or population mechanisms, e.g., the differential evolution (DE) algorithm [7; 8; 9], particle swarm optimization (PSO) algorithm [10; 11; 12], gravitational search algorithm (GSA) [13; 14; 15], whale optimization algorithm (WOA) [16; 17; 18] and artificial bee colony (ABC) algorithm [19; 20]. All these variants have achieved great success in solving practical problems in many fields such as artificial neural network learning [21; 22; 23; 24], protein structure prediction [25; 26; 27], time series prediction [28; 29; 30], and dendritic neuron learning [31; 32]. Brain-storm optimization (BSO) is a swarm intelligence algorithm with broad application prospects in solving complicated problems [33; 34; 35]. BSO is inspired by human brainstorming, in which every thought produced by the human brain represents an individual in the search space. During brainstorming, people first generate rough ideasand then exchange and discuss these ideas with others, during which low-level ideas are eliminated and great ones are retained. The brainstorming process is repeated, and the ideas become increasingly mature. New ideas are constantly generated and added to the final list. Once the process is finished, a feasible and effective idea is presented. Since it was proposed in 2011, BSO has been a focus of swarm intelligence research due to its novelty and efficiency. BSO has been successfully applied to various scenarios such as function optimization, engineering optimization, and financial prediction [4; 36; 37; 38; 39]. However, as with other swarm intelligence optimization algorithms, BSO is prone to falling into local optima and premature convergence. Many variants have been proposed to improve various aspects of the performance of BSO. For example, the chaotic brain-storm optimization (CBSO) algorithm proposed by [PERSON] et al. effectively improves the search performance of BSO [40]. Because it does not use an adaptive strategy, the algorithm is not ideal when dealing with complex functions. For swarm intelligence optimization algorithms, the balance between convergence and divergence is of great significance; premature convergence leads to a low population diversity and poor-quality solutions, while overmutance convergence results in very slow search speeds. In references [40; 41], chaotic sequences were used as variables to initialize the population and to generate new individuals. Chaos, as a universal phenomenon of nonlinear dynamic systems, is unpredictable and non-repetitive. Hence, its randomicity and ergodicity can effectively improve the population diversity and solution quality of BSO. Reference [42] used 12 chaotic maps to generate chaotic variables for the chaotic local search (CLS) process and embedded this process into their algorithm according to different schemes; in addition, a multiple chaos embedded chaotic parallel gravitational search algorithm (CGSA-P) was proposed. However, during iteration, the individuals converged rapidly, and it was difficult to adjust the search range.