# Exploring Evolutionary Algorithms for Multi-Objective Optimization in Seismic Structural Design
## 2 Background
### Nature-Inspired Algorithms  
Nature-inspired algorithms employ metaheuristics inspired by biological, ecological, and other natural processes [63]. These algorithms have been widely applied to find efficient solutions, especially for multi-objective optimization problems. Nature-inspired algorithms include genetic algorithms, ant colony optimization, particle swarm optimization, bee algorithms, and other evolutionary strategies. These algorithms are distinguished by their ability to find Pareto-optimal solutions to complex and multidimensional optimization problems [41].  
Nature-inspired algorithms have been widely applied to multi-objective optimization problems. The main advantage of these algorithms is their ability to efficiently explore a large solution space. Methods such as genetic algorithms and PSO can produce Pareto-optimal solutions while optimizing multiple conflicting objectives. These algorithms iteratively improve solutions using evolutionary strategies to converge to the global optimum. The mathematical structures of these algorithms enable the exploration of the Pareto front in multi-objective optimization. For example, the elitism and ranking strategies of genetic algorithms offer a wide range of solutions to multi-objective problems. Similarly, PSO's speed and position updates allow for Pareto-optimal solutions by balancing between different objectives.  
Nature-inspired algorithms provide powerful and flexible solution methods for multi-objective optimization problems. These algorithms are inspired by biological and natural processes and are capable of exploring a large solution space and finding Pareto-optimal solutions. Methods such as genetic algorithms, PSO and ACO provide efficient solutions in multi-objective optimization and can be used in a wide range of applications. In the scientific literature, the success of nature-inspired algorithms in multi-objective optimization is recognized as an important part of this field.  
The computational cost of evolutionary algorithms as well as of nature-inspired algorithms used in multi-objective optimization problems is an important factor, especially in practical engineering applications. The computational efficiency of the selected algorithm can directly affect the total time and resource consumption of the optimization process. Genetic algorithms explore a large solution space using a population-based approach, but this exploration process can require high computational costs. For example, when large population sizes or a large number of generations are used, the computational time of GAs increases significantly. [PERSON] (2001) and [PERSON] (2002) emphasized that running GAs for a large number of generations on large problem domains can lead to high computational costs (6; 7). The computational cost of PSO is directly related to the position and velocity updates of each particle. PSO generally requires less computational resources because particles can reach the solution faster using the experience of their neighbors. This makes PSO more computationally efficient, especially for optimization problems with high dimensions and large datasets (55). Simulated annealing, although an algorithm that aims to reach a global optimum, involves random movements in the solution space, which can increase the computational cost in some cases. However, this cost can be reduced through the careful selection of parameters such as initial temperatures and cooling rates. [PERSON] and [PERSON] et al. emphasized the importance of certain parameter settings for the effective implementation of SA (56).