## 1 Introduction
These tools are based on Mass Estimate Relationships (MERs), which are empirical models derived from parametric equations between thrust and engine mass [7]. Therefore, the accuracy of the model is proportional to the number of data points used. A review of MERs determined that there is no single set of relationships that is more accurate [8]. [PERSON] [9], therefore, recently developed a structural dry mass model for an LV, with the aim of moving away from empirical-based mass estimates. Optimization techniques initially used on LPRE cycles included non-gradient- and gradient-based methods such as Genetic Algorithm (GA) and Sequential Quadratic Programming (SQP) for both entire cycles as well as specific sub-systems [10; 11; 12]. [PERSON] et al. and [PERSON] et al. [13; 14] used GA-based techniques to optimize a single-stage and a four-stage LV, respectively. [PERSON] [PERSON] [15] utilized SQP to optimize two LPRE cycles with the objective of maximizing payloads. He concluded that algorithms such as Particle Swarm Optimization (PSO) should also be studied. [PERSON] et al. [16] modelled the optimal starting and regulating characteristics of an electric pump for LPRE using the GA technique. A fuzzy Multi-Objective GA (MOGA) technique has been applied to a GG cycle [17] as well as on a hybrid rocket [18] with the objectives of maximizing altitude and minimizing Gross Lift-Off Weight (GLOW). [PERSON] et al. [19] compiled a database of existing LPREs and examined conceptual multistage LVs based on those existing engines. A GA technique was used on these conceptual LVs to optimize the GLOW based on different trajectories. [PERSON] et al. [20] compared different techniques to optimize the LV ascent trajectory and concluded that GA and PSO techniques were the most feasible techniques to use. A surrogate model-based two-step method was used by [PERSON] et al. [21] to optimize a radial turbine in an Expander cycle LPRE. First, Response Surface Approximation was used to search the solution space to develop an approximate model. Secondly, GA was used to refine the search area and obtain a global optimum point. An alternative to this method is CFD, which is computationally intensive and time-consuming. [PERSON] et al. [22]also used a surrogate-based model to optimize the trajectory of an air-launched solid rocket. Neural Network (NN)-based models were applied by [PERSON] et al. [23] to LPRE problems such as estimating the fatigue life of reusable thrust chambers and estimating the maximum temperature in nozzle cooling channels. In both cases, NN models were created as large sets of training data were available: 120,000 data points to estimate fatigue life and 20,000 CFD simulations to calculate the maximum temperature. NN-based controllers are proposed by [PERSON] et al. [24] to ensure steady-state spacecraft formation when in orbit. Therefore, similarly to [25], surrogate and NN models are beneficial when problems are computationally intensive and already have numerous data sets available. For the purposes of this research, the numerical calculations are not computationally intensive; therefore, the benefits of such techniques are minimized and non-gradient- and gradient-based algorithms can be directly applied. When determining GLOW for an LV, according to the best of our investigations, researchers, apart from [19], used mass models based on MERs to provide estimates for the masses. While minimizing GLOW and maximizing payload have been used as Objective Functions (OFs), to the best of our knowledge, other OFs such as maximizing \(I_{sp}\) or Thrust-to-Weight ratio (\(T/W\)) have not been investigated. In addition, the optimization models mentioned previously require Thrust (\(F\)) and \(p_{c}\) as inputs. This results in running the optimizer numerous times at different user defined \(F\) and \(p_{c}\) values in order to obtain a Pareto front of optimal points.