## 1 Introduction  
A challenging problem in engineering analytics has been the existence of many objectives. Multi-objective optimization attempts to find the optimal trade-offs that are most acceptable to the decision maker among all objective functions [1; 2; 3]. The Pareto front, i.e., a set of Pareto solutions, illustrates the trade-offs for which algorithms should secure solution diversity as well as make comparative evaluations among the potential solutions [4; 5; 6; 7; 8]. Evolutionary multi-objective optimization (EMO) algorithms, e.g., the non-dominated sorting genetic algorithm (NSGA; NSGA-II; NSGA-III), strength Pareto evolutionary algorithm (SPEA; SPEA-II), Pareto envelope-based selection algorithm (PESA; PESA-II), and multi-objective evolutionary algorithm based on decomposition (MOEA/D), have continuously improved fitness assignment and diversity control [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. NSGA is a well-known scheme designed to preserve non-dominated points in objective space that also has a wide solution-searching capability with a genetic algorithm. Its strength is that it can provide non-dominated trade-offs in the comparison of objective functions, while its weaknesses are the fact that it requires a large amount of computing power and its decreasing convergence with an increasing number of objective functions, i.e., 'the curse of dimensionality' [5; 6; 7; 8; 9; 10]. Geological uncertainty limits quantitative analyses of subsurface flow [11; 12; 13; 14]. The input uncertainties in geo-modeling are non-linearly interacted; some are heterogeneous (e.g., porosity, permeability, and lithology) while others are functional (e.g., relative permeability, solubility, and capillary pressure) or scenario-based (e.g., the depositional system) [13; 14; 15; 16; 17]. The flow responses are spatiotemporal. Sensitivity measures the relationship between the inputs and the responses and, thus, denotes some influential parameters that significantly affect the responses. The stochastic features between the inputs and the responses do not result in the emergence of a certain parameter as a significant factor but instead require multi-way parameter interactions. The distance-based generalized sensitivity analysis (DGSA) has been successfully used to evaluate the significance of scale-variant properties in heterogeneous geo-models [10; 15; 16; 17; 18; 19]. [PERSON] et al. [15] quantified the interaction of asymmetric parameters such as residual oil saturation, maximum water relative permeability, and training images. [PERSON] et al. [16] analyzed spatial uncertainty using kernel principal components and self-organizing maps. CO\({}_{2}\) sequestration into deep saline aquifers, e.g., around 1 km below ground level, is known to have enormous storage potential, but little is known about its geological characterization and project experiences compared to those of depleted oil or gas reservoirs. The significant uncertainties can be categorized into capacity, injectivity, and containment: the capacity determines the storable amount, the injectivity estimates the possible injection rates, and the containment evaluates the risks of leakage [20; 21; 22; 23; 24]. [PERSON] [20] explained the importance of the hydrodynamic and buoyancy forces needed for the CO\({}_{2}\) plume to propagate into the homogeneous saline formation. [PERSON] et al. [21] discussed the key factors related to the rock and fluid properties, reservoir conditions, and injection strategy as storage mechanisms (structural, residual, solubility, and mineral trapping) in saline aquifers; these include reservoir heterogeneity, depth, permeability, pressure, and temperature. Along with these geological properties, the injection pressure is one of the crucial operating parameters depending on the containment and the security. One reason for this is the well injectivity--defined as the CO\({}_{2}\) injection mass rate per unit pressure differential--which determines the total CO\({}_{2}\) amount injected into the geological formation.