# Exploring Evolutionary Algorithms for Multi-Objective Optimization in Seismic Structural Design
## 2 Background
### Multi-Objective Optimization
The objective space for multi-objective optimization is significantly larger and higher than that of the single-objective function, whose objective space is (at most) \(\mathbb{R}\)[43]. In contrast to single-objective optimization difficulties, multi-objective optimization problems may not always have an optimal solution that simultaneously minimizes all of the multi-objective functions. Diverse goals may frequently compete with one another, and the ideal conditions for one goal rarely result in the optimality of another (and can even enhance it). In seismic design optimization, the objective function used is usually defined to increase the seismic performance of structures and maximize their resistance to earthquake loads. Such an objective function can be based on criteria such as displacement, velocity, acceleration or energy dissipation rates in the structure. These functions, which are usually created by considering multiple objectives such as minimum cost, maximum safety, and structural integrity are used in multi-objective optimization processes to obtain Pareto-optimal solutions. For specific cases of energy dissipation devices, this objective function may need to be modified based on criteria such as energy dissipation efficiency, the effect of the device on structural performance, and cost-effectiveness analysis. For example, how effectively the devices dissipate and reduce the energy transferred to the structure during an earthquake will be an important component of this objective function. In such a case, the effectiveness of energy dissipation devices can be optimized according to the additional stiffness or damping capacity that the device provides to the structure. In addition, a balanced objective function should be established in terms of both safety and economic performance, taking into account the cost of the device and its effect on structural integrity. Various algorithms have been developed for multi-objective optimization problems. These include evolutionary algorithms such as genetic algorithms, particle swarm optimization (PSO), and evolutionary strategies. These algorithms are used to explore a large solution space while optimizing multiple objectives. Genetic algorithms are search methods based on natural selection and genetic processes and are widely used to explore the Pareto front in multi-objective optimization problems [44]. In solving multi-objective optimization problems, techniques such as the weighting method, ideal point convergence method, and \(\varepsilon\)-constraint method are used. The weighting method works by reducing all objectives to a single-objective function by assigning a certain weight to each objective function. In this way, the problem can be solved as a classical single-objective optimization problem [45]. [PERSON] and [PERSON] explained the multi-objective optimization techniques and their versions with benefits and drawbacks [46]. [PERSON] et al. examined an updated overview of the primary techniques that allow the application of multi-objective schemes for single-objective optimization [47]. [PERSON] et al. presented the primary ideas of multi-objective optimization along with a thorough analysis of the most widely cited studies in mechanical engineering over the past few years. Their analysis provides information on the most widely used multi-objective optimization techniques and algorithms in this field [48].