## 1 Introduction
Therefore, algorithms are required that can identify effective and satisfactory, but not necessarily optimal, schedules. In terms of waiting-time criteria, ensuring acceptable waiting time for each passenger is important. A passenger's dissatisfaction usually increases with a longer waiting time; however, there is a threshold beyond which passengers find difficult to tolerate additional delays. When a passenger's wait time exceeds this threshold, that person's dissatisfaction increases rapidly. Therefore, our system is designed to maintain a tolerable waiting time to mitigate passenger dissatisfaction. This paper investigates various methods for controlling elevator-car dispatching in response to hall calls, focusing on minimizing passenger waiting time and optimizing elevator movement. Our study begins by establishing a representation of the elevator group control system as a finite-state machine to understand its dynamic behavior. We then analyze two primary heuristic approaches:  
1. Directional Continuity Heuristic: This heuristic prioritizes maintaining the current direction of movement unless the highest or lowest floor is reached
2. Final Call Heuristic: This heuristic allows direction changes upon completing the final call in the current direction, regardless of floor extremes. While these heuristics demonstrate some effectiveness, we identify areas for improvement and explore two optimization methodologies: the genetic algorithm (GA) and simulated annealing (SA). GA and SA have emerged as preferred optimization methods for elevator control systems due to their unique abilities to respond to the complexity of this problem. GA excels in exploring a wide range of solution spaces and iteratively exploiting solutions. For elevator systems, this means considering many configurations, from elevator allocation to time scheduling strategies, which is crucial to addressing the multifaceted challenge of minimizing passenger waiting time. Its parallel-processing capacity fits well with scenarios requiring coordination among several elevators. On the other hand, SA's strength lies in navigating complex landscapes by probabilistically accepting suboptimal solutions, enabling the exploration of various configurations crucial for dealing with the nonlinear, nonconvex spaces inherent in the optimization of waiting time. SA's adaptability via a temperature parameter allows it to dynamically adjust the elevator control parameters, essential for optimizing scheduling policies to minimize waiting times. GA and SA provide flexibility and efficiency in dealing with the dynamic, nonlinear nature of elevator optimization problems, making them favorable choices among the multitude of available optimization techniques. The computation of fitness for each solution, whether in the context of GA or SA, adheres to the method outlined in reference [18]. However, GA and SA often lead to prolonged computational durations, primarily attributed to the significant number of iterations they undergo. To optimize their performance in minimizing average waiting time within elevator systems, meticulous parameter optimization becomes imperative. This optimization focuses on fine-tuning the basic parameters of GA and SA to strike a balance between solution quality and computational efficiency, ensuring the attainment of optimal results swiftly amidst the complex optimization landscape inherent in elevator systems. Through extensive simulations, we determine the optimal parameter values for both GA and SA and conduct a comparative analysis to identify the most effective method among all approaches investigated. Our research findings contribute significantly to the advancement of elevator group control systems by:  
* Establishing a comprehensive understanding of the system dynamics through finite state machine representation;
* Evaluating existing heuristic methods and identifying their limitations;
* Proposing novel optimization approaches using GA and SA;
* Conducting a rigorous comparison of various dispatching algorithms.