# Dynamic Heterogeneous Search-Mutation Structure-Based Equilibrium Optimizer
## 1 Introduction  
Optimization issues are widely encountered in scientific research and engineering application across fields such as transportation [1], manufacturing [2], and medicine [3]. Approaches to solving optimization issues can generally be categorized into two major groups: conventional optimization approaches and intelligent optimization approaches. As the process of the intelligent era advances, numerous complex optimization issues characterized by non-convexity, high nonlinearity, multimodality, and multiple variables have emerged in scientific research and engineering applications. These intricate features greatly hinder the capability of conventional optimization approaches to effectively solve such problems. Due to the merits of flexible application, an efficient optimization search, and easy implementation, intelligent optimization algorithms have gained widespread adoption in solving such complex optimization problems across diverse domains [4, 5, 6]. As intelligent optimization algorithms have shown strong superiority in tackling complex optimization issues, more and more researchers have started to invest in the research of this field and introduced various intelligent optimization algorithms, including the slime mold algorithm (SMA) [7], gray wolf optimizer (GWO) [8], Hunger Games search (HGS) [9], particle swarm optimization (PSO) [10], reptile search algorithm (RSA) [11], and differential evolution (DE) [12], etc. The equilibrium optimizer (EO) [13] is a novel intelligent optimization algorithm that was proposed by [PERSON] et al. in 2020. It was inspired by a mixed-dynamicmass-balance equation applied to a fixed control volume, which describes the fundamental physical principle of mass conservation during the processes of inflow, outflow, and generation within the control volume. The EO features a straightforward concept, a simple implementation mode, and a low computational load, which achieves successful applications in multiple kinds of fields, such as distribution systems [14], path-planning tasks [15], and microelectronic components [16]. To strengthen the optimization capability of EO for satisfying particular demands, researchers have further developed a series of EO variants. A comparative study for the EO variants is shown in Table 1. In [17], the accuracy of the algorithm was enhanced by incorporating a novel concentration-updating equation and opposition learning. In [18], a Gaussian distribution estimation method was incorporated, which strengthened optimization capability by leveraging population-advantage information to guide evolutionary processes. [PERSON] et al. [19] enhanced acceleration in convergence by updating the concentration of candidate solutions using a Laplace distribution-based random walk and accelerating exploitation with opposition learning. In [20], an adaptive decision-based modified concentration-updating equation was introduced, which enhanced the global search capability by increasing population diversity. [PERSON] et al. [21] constructed the dynamic multi-population mutation architecture to strengthen search capabilities and population multiformity. In [22], a modified EO variant was developed using a local minimum elimination mechanism and a linear diversity reduction mechanism, which enhanced the convergence of EO by moving the worst particles from the population towards the optimal particle. Although the aforementioned EO variants strengthened the search capability from different perspectives, these EO variants still face issues with population diversity attenuation, inadequate search efficiency, and vulnerability towards local optimum in solving complex optimization problems. Therefore, a dynamic heterogeneous search-mutation structure-based equilibrium optimizer (DHSMEO) was developed to further alleviate these issues, which strengthened the performance by adopting three improvement strategies to form a dynamic heterogeneous search-mutation structure.