# Dynamic Reconfiguration of Active Distribution Network Based on Improved Equilibrium Optimizer
## 1 Introduction
[15] employed an Adaptive Quantum-inspired Evolutionary Algorithm to optimize network reconfiguration with DG and capacitor allocation, achieving simultaneous power loss reduction and economic benefit maximization. [PERSON] and [PERSON] [16] utilized the dragonfly optimization algorithm for distribution network reconfiguration, demonstrating superior energy loss reduction through coordinated control of tap transformers and DG power factors. [PERSON] et al. [17] developed a dynamic simulated annealing particle swarm optimization (DSAPSO) algorithm for distribution network reconfiguration with DGs, effectively improving convergence speed and reducing power losses while enhancing voltage stability. [PERSON] et al. [18] proposed an improved salp swarm algorithm integrating differential evolution operators for simultaneous DG allocation and network reconfiguration, achieving notable reductions in power loss cost and reliability improvement expenses. Notably, the Equilibrium Optimizer (EO), introduced by [PERSON] et al. [19] in 2020, is inspired by the principle of mass balance in physics. [PERSON] and [PERSON] [20] conducted a comprehensive statistical comparison of metaheuristic algorithms for distribution network reconfiguration and demonstrated that the Equilibrium Optimizer consistently outperformed ten other methods in terms of loss reduction, voltage improvement, and reliability enhancement across multiple test systems. [PERSON] et al. [21] developed an improved equilibrium optimization algorithm (IEOA) incorporating a recycling strategy to enhance global search capability for the joint problem of network reconfiguration and distributed generation allocation. The method was validated on IEEE 33-bus, 69-bus, and 137-bus systems under multiple load levels, demonstrating significant reductions in active power losses and improvements in voltage profiles. Comparative analysis with other metaheuristics--including harmony search, genetic algorithm, and firefly algorithm--confirmed the superior robustness and effectiveness of the proposed approach in handling complex multi-objective optimization problems. Despite these successes, several limitations remain. Due to the stochastic nature of intelligent algorithms, they are prone to local optima. Furthermore, their randomness often results in the generation of a large number of infeasible or suboptimal solutions during the search process, expanding the solution space unnecessarily and increasing computational cost [22; 23]. A particularly critical requirement is ensuring that generated solutions adhere to the radial topology constraint of distribution networks. Thus, improving algorithm performance and reducing infeasibility remain pressing challenges. Recent studies have attempted to address these issues using advanced strategies such as multi-objective frameworks, scenario-based uncertainty modeling, and hybrid metaheuristics [24; 25; 26; 27; 28; 29]. However, most still lack dynamic adaptability and robust feasibility assurance mechanisms, particularly under time-varying load and DG outputs--gaps that this study aims to bridge. Therefore, the main contributions of this study are summarized as follows:  
1. Improved load period division: A fuzzy C-means clustering method is enhanced by incorporating time-weighted load similarity and optimal network topology similarity, resulting in more accurate and stable time segmentation. 2. Feasibility judgment innovation: An adaptive ordered loop-based feasibility model is proposed to rigorously eliminate infeasible and low-quality solutions by enforcing power balance and topological constraints. 3. Enhanced optimization algorithm: An improved Equilibrium Optimizer (IEO) is developed by incorporating Tent chaotic initialization, elite non-dominated sorting, stochastic mutation, and binomial crossover, significantly enhancing convergence and global search capabilities. 4.