###### Abstract
Rate of penetration (ROP), mechanical specific energy (MSE), and vibrations are key performance indicators for optimizing the drilling process. It is fair to consider that these parameters are influenced mainly by two types of factors: (i) drilling mechanical parameters, e.g., weight on bit (WOB), rotation speed (RPM), flow rate (FLOW), and drilling fluid characteristics; and (ii) formation factors, i.e., rock type and strength, hardness, mineral composition, porosity, and further physical and mechanical geological formation properties [14]. ROP is a significant indicator for evaluating drilling speed [14] (but not effective penetration efficiency [15]) and can be defined as the speed at which a drill bit breaks through a formation and advances in depth, deepening the borehole [16], or as the volume of rock removed per unit area per unit time [17; 18]. MSE can be seen as a measure of the efficiency of the drilling process. [PERSON] [19] defined MSE as the energy necessary to remove a unit volume of rock [18; 20; 21] and is used as a reference for drilling optimization [22]. MSE has been widely applied to evaluate the rock-breaking drill-bit penetration efficiency and to monitor drill-bit cutter wear [23]. Ideally, MSE should be numerically close to the ultimate confined compressive strength (UCCS) of the formation [18; 24; 25]. However, the bottomhole MSE is typically affected by non-rock-breaking factors, such as drill-string friction, drill-bit cutter wear, vibrations, and stick-slip events [23]. During drilling, three types or modes of vibrations can occur in the drill string: axial, torsional, and lateral [26]. One of the most severe vibration-induced events that is harmful for the drillability is the stick-slip [27]. Stick-slip is an issue when drilling deep wells, especially in complex trajectory wells, such as highly-deviated wells [28]. This occurs when the BHA is momentarily caught by drill-bit/rock interaction friction torque (i.e., stick) and then suddenly released (i.e., slip) [28; 29; 30]. The sudden release of stored potential energy in the drill-strings (also including BHA and drill-bit) during the slip phase can vary the rotational speed of the BHA from zero to as much as six times the speed of the top rotary mechanism [30]. Stick-slip events commonly occur in up to 50% of the total drilling operation time [31; 32; 33]. These events are dependent on several factors, such as drill-bit/rock interaction, characteristics of the formation being drilled, wellbore trajectory tortuosity, and drilling fluid used, among others [32; 33]. Currently, engineers and researchers have been conducting studies on drilling optimization using multi-objective optimization, specifically based on ROP and MSE [34]. The goal is to find the ideal combination of the highest ROP and the lowest MSE [18; 21]. However, multi-objective research involving MSE concurrently with stick-slip vibration has still been overlooked during the drilling process, given that a significant portion of the energy provided at the surface is not satisfactorily utilized, and this energy is also converted into vibration. Mitigating the vibrations of the drill string is crucial for increasing ROP, reducing operational costs, preventing severe damage to the drill string and drill bit, improving drilling quality and safety, and enhancing controller performance [26]. To minimize the issue of torsional vibrations during the real-time drilling process, companies utilize flowcharts that serve as action plans to mitigate vibration. However, the flowchart is still quite limited as it only involves manipulating the parameters of RPM and WOB while neglecting FLOW, which is an essential parameter in the process. FLOW becomes crucial for mitigating drilling vibrations from a new point of view and methodology, especially when referring to torsional vibration and stick-slip. The fluid flow rate is fundamental for ensuring adequate lubrication of the BHA, which also prevents debris buildup across the drill bit.