###### Abstract
[24] conducted optimization-based work on the slotted vortex finder (SVF). Their study resulted in a 34.57% reduction in the Euler number and a 4.32% enhancement in the collection efficiency, followed by a reduction of nearly 5.53% in the cut-off diameter. In a similar study, [PERSON] et al. [25] optimized the length, height, and diameter of the dustbin, achieving superior performance over the baseline model. Furthermore, [PERSON] and [PERSON] [26] were able to attain better results compared to the reference geometry via optimization of the convergent-divergent outlet tube. [PERSON] and [PERSON] [27] carried out multi-objective optimization with an artificial neural network (ANN) as well as the genetic algorithm (GA), which resulted in considerably minimum pressure drop and maximum collection efficiency over different (eccentric) locations of the vortex finder centers. [PERSON] et al. [28] carried out multi-objective optimization using the Muschelknautz method of modeling (MM) to optimize the cyclone performance for a fixed total height condition. The study considered three optimization scenarios, and a noteworthy improvement in cyclone models was reported. To date, the Muschelknautz method of modeling (MM) [29; 30] has become one of the most widely used mathematical models. This is due to only a few simplifying assumptions, the incorporation of all the geometric entities, the consideration of the fluid contraction at the inlet, the mass loading effects of the solid particles on the cyclone performance, the impact on the frictional drag due to total inside area of the separator, etc. Because of this, the MM model has been extensively used in the current work. This model can predict the cut-off size and pressure losses with a high level of accuracy in nearly all cyclone designs [14]. Most of the studies undertaken so far did not include the cyclone main body diameter for optimization. This parameter significantly influences the pressure drop values and moderately affects the collection efficiency. With an increase in the cyclone diameter, there is an increase in the pressure drop, whereas the collection efficiency reduces by a small amount. In the latter, the efficiency of bigger particles largely increases, whereas for smaller particles, the efficiency mildly reduces, as reported by [PERSON] and [PERSON] [31]. Hence, the cyclone diameter is worth considering for optimization. [PERSON] et al. [28] accounted for this parameter in an optimization study, and the results showed significant improvement over the reference model--the authors focused on compact cyclone separators, for which they chose to fix the total height of the cyclone. It is also known that an increase in the cyclone length tremendously reduces the pressure losses, followed by a significant increase in the collection efficiency. [PERSON] et al. [32] reported a 34% reduction in pressure losses and a nearly 10% increase in collection efficiency for elongation in the length of the cylindrical segment from 1.5 to 5.5 times the cyclone diameter. On the other hand, increasing the cone length from 2.5 to 6.5 times the cyclone diameter resulted in an 11% increase in efficiency, whereas the pressure losses reduced by 29%. Based on the above discussion, it follows that both the cyclone's main body diameter and total height must also be included for optimization. However, most of the studies have neglected the main body diameter of the cyclones for optimization. Hence, in the present study, all the geometrical entities are considered for optimization to reduce both the pressure losses and cut-off particle size. For this, we make use of the expressions from the MM as objective functions subjected to optimization using Ga with the prescribed range for all the independent variables. Hence, the work has been planned in the following manner: Firstly, the flow system has been defined with detailed information on cyclone geometry. Then, we elaborate on the MM, followed by the description of the range by which each independent geometrical entity is permitted to vary.