## 1 Introduction
Multi-population technology is an effective method to enhance population diversity by partitioning the population into multiple sub-populations and utilizing each sub-population to independently search the optimization space [22]. Based on the above advantage, multi-population technology has been employed to improve diverse optimization algorithms in recent years, such as multi-population PSO [23], multi-population whale optimization algorithm (WOA) [24], multi-population sine cosine algorithm (SCA) [25], multi-population differential evolution (DE) [26], and so on. Multi-population technology assists the above multi-population algorithms to preserve the population diversity during the optimization process. However, multi-population technology has two main categories: dynamic architecture and static architecture. The dynamic architecture raises the cost of the algorithm, while the static architecture is ineffective for the convergence of the algorithm [27]. Therefore, how to design an efficient and simple multi-population architecture is still a challenging research topic. In EO, the iterative search for optimal solution is implemented based on equilibrium candidate generation and particle concentration updating. If the equilibrium candidates of EO are pooled together within the local optimum area, this search pattern may result in the problems of population diversity decline and premature convergence. This search pattern relies too much on the equilibrium candidates generated by the whole population and lacks the effective utilization of the sub-population structure and information within the population updating process. The above shortcomings of EO limit its search capability in the optimization space. To alleviate the above problems of EO, a dynamic multi-population mutation architecture-based equilibrium optimizer (DMMAEO) is proposed. By constructing a sub-population structure and using sub-population information, the particle concentration updating stage and equilibrium candidate generation stage of the DMMAEO are altered in the following way. At first, the sub-population structure and corresponding information interaction mode are constructed by introducing a dynamic multi-population guidance mechanism for enhancing population diversity. Then, the neighborhood space information of sub-population particle concentrations is used by integrating dynamic Gaussian mutation to strengthen the exploitation ability. Finally, the promising space information of sub-population equilibrium candidates is employed by combining dynamic Cauchy mutation to improve the exploration ability. To summarize, the major contributions from this study are shown below. 1. A dynamic multi-population guidance mechanism is constructed for the whole population, which can enhance the population diversity by utilizing the sub-population structure and information. 2. A dynamic Gaussian mutation-based sub-population concentration updating mechanism is introduced, which can improve the exploitation ability by using the neighborhood information of sub-population particle concentrations. 3. A dynamic Cauchy mutation-based sub-population equilibrium candidate generation mechanism is integrated, which can strengthen the exploration ability by extending the search space for sub-population equilibrium candidates. 4. The optimization performance of DMMAEO is analyzed through comparing it with multiple recent promising algorithms across 58 test functions. 5. The practicality of DMMAEO is further verified by applying the the DMMAEO to address six engineering design problems and a UGV multi-target path planning problem. Section 2 gives an overview of EO's structure. Section 3 offers a detailed explanation of the specifics regarding DMMAEO. Section 4 shows the test experiments and discussion of DMMAEO on 58 test functions. Section 5 presents the performance of DMMAEO in addressing engineering application problems.