## 2 Literature Review  
OPS can be considered as a search for a set of sequenced primitive operations that transform a plant system from an initial state to a pre-specified goal state through a series of intermediate states. These primitive operations must be carried out in such a way that no violations are made of any relevant process or mechanical, safety, and environmental constraints. Figure 1: Schematic representation of the drum boiler. Most attempts to solve OPS problems have relied on simplified process behavior models [12]. In contrast to this, simulation-based planning approaches make use of detailed dynamic behavior models of the process and a mathematical representation of quantitative constraints embedded within a rigorous dynamic optimization framework. Regarding drum boiler transient operations, a lot of work has been done regarding the optimization of steam generation in a drum boiler from a procedural point of view. [PERSON] and [PERSON] [9] developed a nonlinear physical model with a complexity that is suitable for dynamic optimization and OPS. The model is based on physical parameters for the plant and can be easily scaled to simulate any power plant drum boiler. [PERSON] et al. [15] developed a nonlinear dynamic model of a drum boiler based on [PERSON]'s physical model, using the Modelica language. Their model had three control inputs in terms of feedwater flow rate, heat supply, and steam outlet. They solved a dynamic optimization problem using a sequential quadratic programming (SQP) algorithm. Using this approach, the startup time could be reduced by 30%. [PERSON] et al. [16] proposed a quadratic programming optimization approach to determine the optimal values of steam pressure and steam temperature in a startup process. Their model considered hard constraints such as control bounds and stress levels for the drum and header. They concluded that their optimization model could minimize both fuel consumption and startup time. [PERSON] et al. [17] investigated the minimization of the startup time of a drum boiler. Their proposed startup strategy defined the initial and goal states in terms of steam mass flow rate and the internal pressure of the drum. The startup process was formulated as an optimal control problem that minimized a quadratic objective function under physical and operational constraints. The physical constraints were related to the structural integrity of thick-walled components due to higher thermal stresses. The optimization problem was solved by combining a framework developed on the JModelica environment and the interior-point optimizer algorithm (IPOPT). Their results were compared with the optimal start-up trajectories in [PERSON] et al. [18], and the optimized profiles reached desired states in a shorter time without violating the operational and physical constraints. [PERSON] et al. [19] reported the dynamic analysis of the steam and water system of the natural circulation boiler using the environment of MATLAB/Simulink. They proposed a boiler model based on the work of [PERSON] and [PERSON] with specific parameters to simulate the dynamic analysis of the steam water system. They solved the model using the ode45 algorithm, which is based on the fourth-order Runge-Kutta and Dormand-Prince methods. The boiler startup aimed at saving water and fuel. Nevertheless, these works have limited applicability since they were solutions to specific problems. For instance, in many cases, the simulation model is embedded within the optimization tool and it is not possible to scale them for more complex problems. Other works propose approaches using commercial tools for the coupling of a simulation-optimization system. The drawback is that these tools operate as black boxes, with limited information about the modeling assumptions. A third group of contributions, despite considering thermal stress evaluation, seek to minimize startup times regardless of how the plant must be operated to achieve a given goal state.