# Exploring Evolutionary Algorithms for Multi-Objective Optimization in Seismic Structural Design
## 2 Background
### Heuristics and Metaheuristics
The new solution \(S^{\prime}\) is accepted with the following condition:  
\[P(\Delta E)=exp\bigg{(}-\frac{\Delta E}{T}\bigg{)} \tag{7}\]  
Here, \(\Delta E\) represents the energy difference (i.e., the difference in the objective function), and \(T\) represents the \"temperature\" parameter. The new solution is accepted if there is an energy decrease \((\Delta E<0)\). However, even if there is an energy increase \((\Delta E>0)\), it can be accepted with an arbitrary probability. This probability varies with temperature and is more accepted at high temperatures and less accepted at low temperatures. This probability allows the algorithm to reach a global optimum without getting stuck in local minima [56]. Ant colony optimization is inspired by the foraging behavior of ants. This algorithm is particularly effective in combinatorial optimization problems. The mathematical model of ACO is characterized by pheromone updates. The pheromones that ants release along their path influence the decisions of subsequent ants and thus the optimal solution can be reached. In multi-objective optimization, ACO can be used to find solutions on the Pareto front [57]. Metaheuristic algorithms are well suited for exploring the Pareto front and exploring a large solution space in multi-objective optimization problems. These algorithms attempt to find optimal or Pareto-optimal solutions by balancing between often conflicting objectives. Evolutionary metaheuristic algorithms such as NSGA-II (Non-dominated Sorting Genetic Algorithm II) are widely used in solving multi-objective optimization problems and are an effective tool used to quickly discover the Pareto front [58]. Heuristic and metaheuristic algorithms are powerful tools widely used in multi-objective optimization problems. While heuristic algorithms provide fast solutions, metaheuristic algorithms offer a more comprehensive search strategy and are often effective in finding Pareto-optimal solutions. The mathematical foundations of these algorithms allow us to better understand the optimization process and find more efficient solutions to complex problems. The use of heuristic and metaheuristic algorithms is one of the current developments, while traditional approaches typically involve local search algorithms. It is important to note that the literature lacks consensus regarding the definitions of heuristics and metaheuristics; in fact, some authors use the terms interchangeably. Since most metaheuristic algorithms were created using some abstraction of nature, they are largely influenced by nature. Thus, we can create heuristic and/or metaheuristic algorithms that are inspired by nature and learn from them how to solve problems successfully. Since randomness exists everywhere, there is no compelling case against including it while creating algorithms. A lot of contemporary search algorithms make excellent use of randomization. Heuristic approaches, for instance, employ a trial-and-error methodology to discover answers to a variety of challenging issues. Many of the stochastic search techniques used today are evolutionary algorithms, or more recently, \"meta-heuristic\" techniques. Each of these algorithms is a component of the computational development. In the broad context of computer science and artificial intelligence, evolutionary computation is loosely categorized as a component of computational intelligence. Moreover, evolutionary algorithms and nature-inspired metaheuristic algorithms, particularly those based on swarm intelligence, are used increasingly frequently in modern approaches to solving challenging optimization issues [41]. Metaheuristic algorithms have found a significant place in the optimization problems of seismic energy dissipation devices, as evidenced by the research papers provided. These algorithms, which include particle swarm optimization (PSO), genetic algorithms (GA), and extreme machine learning (ELM), have been effectively combined with adaptive neuro-fuzzy systems to predict seismic loads with high accuracy [59].