## 1 Introduction
For instance, in CCS simulations, it is crucial to capture the dynamics of CO\({}_{2}\) dissolution, which significantly depends on the concentration of salts in the aquifer [24]. Building upon the foundation of accurate simulation models, the optimization of well placement becomes paramount to maximizing the sequestration potential of the aquifer in CCS endeavors [25; 26]. The primary objective of CCS projects is to maximize CO\({}_{2}\) storage while adhering to constraints and technical policies [27; 28]. In its most commonly employed form, the CCS plan requires that brine producers be closed off once significant CO\({}_{2}\) breakthrough occurs, whereas the injectors rate is reduced when the bottomhole pressure reaches the safety limit. Consequently, optimal well placement significantly influences the overall success of the sequestration project by delaying the breakthrough time. The objective function maximization in this context is defined as achieving the highest attainable CO\({}_{2}\) storage, considering the spatial distribution of the injection and brine withdrawal wells. This multi-dimensional function has an unknown functional form and its point values are expensive to compute since each one requires a fully implicit simulation to be run. Therefore, it needs to be treated as a black-box function. Well placement decisions cannot rely solely on static properties, since geological variables are mostly non-linearly correlated to production performance. This is demonstrated in Figure 1, where the objective function of oil production in the form of the expected net present value (NPV) is evaluated for the placement of a single oil producer in each cell. The complexity and non-linearity in CCS projects parallel those encountered in oil production, underscoring the importance of optimized well placement for maximizing storage efficiency while considering factors such as CO\({}_{2}\) dissolution dynamics and aquifer characteristics. In general, well placement optimization poses a formidable challenge due to the large number of the decision variables involved, the high non-linearity of the system response, the abundance of local optima, and the well placement constraints. Due to the discontinuities and the inherent non-smoothness of the objective, research has been mostly focused on derivative-free optimization methods such as Genetic Algorithms [29] and Particle Swarm Optimization [30] combined with various heuristics. [PERSON] et al. (2002) [31] developed and applied the Hybrid Genetic Algorithm (HGA) [32] to determine the optimal location and number of vertical wells, while [PERSON] et al. (2003) [33] extended this work to also include horizontal wells. In essence, HGA comprises Genetic Algorithm (GA), the polytope algorithm for selecting the fittest individuals and a kriging proxy to expedite the optimization process. The results showed that after a few simulation runs, the method was able to optimize the production's NPV compared with the base case. In another work, [PERSON] et al. (2009) ([PERSON] et al., 2019) designed a tool for well placement optimization using a GA with non-linear constraints. They applied the GENOCOP III algorithm ([PERSON] et al., 2019) which utilizes two separate populations where the evolution in one influences the evaluation of the other. The first population, named the \"search population\", consists of individuals that satisfy the linear constraints, whereas the second, called the \"reference population\", consists only of those that satisfy both linear and non-linear constraints. By using this procedure, the research team developed a tool that handled a total of eight decision variables per well (six in total that define the heel and toe coordinates of the well, one binary for producer or injector, and one defining active or inactive well). The results showed a significant increase in the NPV of the production plan in comparison with the base case proposed plans. [PERSON] et al. (2016) ([PERSON] et al., 2016) applied both GA and PSO to optimize well placement and well rates.