## 1 Introduction
While these are crucial aspects affecting elevator performance, the optimization objective is not directly targeting the minimization of passenger waiting times. In [12], the authors address the energy crisis in elevator group control systems (EGCSs) by implementing and analyzing energy-saving strategies utilizing particle swarm optimization (PSO) and genetic algorithm (GA) metaheuristic algorithms, which remain limited despite their potential significance. However, the focus on energy saving mightadvertently prioritize energy efficiency over passenger waiting times. In [13], using modern sensors and computer vision, the proposed control system harnesses information from multiple monitoring agents to estimate the sizes of waiting passengers and their belongings in elevator halls, aiming for efficient dispatching and fair minimization of waiting times. One potential drawback in the study [13] is the reliance on sensor-based estimation of waiting passengers using modern technology such as computer vision. While the aim is to optimize dispatching and minimize waiting times fairly, relying solely on sensor-based estimations might introduce inaccuracies or limitations in real-time scenarios. The moth-flame optimization (MFO) algorithm [14; 15] is advantageous for calculating average waiting times in elevator systems due to its global exploration ability and rapid convergence toward optimal solutions. Inspired by moth behavior, MFO efficiently explores various configurations, aiding in identifying waiting-time reduction strategies across diverse scenarios. Its swift convergence speed accelerates the search for efficient solutions. However, MFO's performance can be sensitive to parameter settings, requiring careful calibration. Additionally, there is a risk of premature convergence to suboptimal solutions, potentially hindering its adaptability to dynamic passenger demands. Despite these considerations, MFO shows promise in swiftly identifying effective waiting-time reduction strategies for elevators, provided that its parameters are meticulously adjusted to suit the system's dynamics. The sparrow search algorithm (SSA) [16; 17] demonstrates specific advantages in computing average waiting times within elevator systems. Inspired by sparrows' foraging behavior, SSA efficiently explores solution spaces, enabling comprehensive analysis of various configurations to identify optimal settings for minimizing waiting times across diverse operational scenarios. SSA's dynamic adaptability, driven by its diversity mechanism, allows it to strike a balance between exploration and exploitation, which is particularly beneficial in handling fluctuating passenger demands for elevators. However, potential drawbacks include parameter sensitivity, necessitating precise calibration, and potential computational complexity when handling extensive or complex elevator configurations. Despite these considerations, SSA's strengths in efficient exploration and adaptability suggest promise in effectively minimizing waiting times, contingent on meticulous parameter tuning and management of computational complexities within elevator systems. The scheduling of group elevators represents a combinatorial optimization problem without an established method for polynomial time resolution. Efficiently determining an optimal schedule entails evaluating all possible schedule combinations, with a complexity in the problem search domain denoted as O(N\({}^{\text{P}}\)), where N signifies the number of operational cars and P represents the requests. This results in N\({}^{\text{P}}\) potential assignment combinations for the requests among the cars. However, evaluating the cost associated with each schedule, such as waiting times, would facilitate the selection of the lowest-cost schedule. Yet, with a scenario involving 30 requests for 4 elevators, the number of feasible schedules is equal to 430. This quantity exceeds the computational feasibility of scanning and identifying the minimum cost schedule within a specified time limit even with advanced computer systems.