###### Abstract  
The present study focuses on performing multi-objective optimization of the cyclone separator geometry to lower the pressure losses and enhance the collection efficiency. For this, six geometrical entities, such as the main body diameter of the cyclone, the vortex finder diameter and its insertion length, the cone tip diameter, and the height of the cylindrical and conical segment, have been accounted for optimization, and the Muschelknautz method of modeling has been used as an objective function for genetic algorithms. To date, this is one of the most popular mathematical models that accurately predicts the cyclone performance, such as the pressure drop and cut-off particle size. Three cases have been selected from the Pareto fronts, and the cyclone performance is calculated using advanced closure large-eddy simulation--the results are then compared to the baseline model to evaluate the relative improvement. It has been observed that in one of the models, with merely a 2% reduction in the collection efficiency and an increase of 12% in the cut-off particle size, more than a 43% reduction in pressure drop value was obtained (an energy-efficient model). In another model, a nearly 25% increment in the collection efficiency and a reduction of 42% in the cut-off particle size with a nearly 36% increase in pressure drop value were observed (a high-efficiency model). cyclone separators; genetic algorithms (GAs); large-eddy simulation (LES); Muschelknautz method of modeling (MM) 2  
Several approaches have been attempted to improve the cyclone performance by modifying the standard geometrical parameters using different methods. [PERSON] and [PERSON] [6] optimized the geometrical parameters for low power consumption with increased collection capabilities of the clinker-burning process. [PERSON] et al. [7] used a multi-objective optimization approach on cyclones arranged in series to improve efficiency. [PERSON] et al. [8] optimized the Strokes number through the surrogate-based optimization. [PERSON] and [PERSON] [9] optimized various geometrical parameters of the Satiramand cyclone design utilizing response surface methodology. [PERSON] and [PERSON] [10] made use of genetic algorithms and numerical simulations and optimized the cyclone geometry for better performance. The authors found that the optimized cyclone design had a higher efficiency and lower pressure drop compared to the original design. The study also showed that the genetic algorithm was an effective tool for optimizing the cyclone separators. An innovative method for advancing centrifugal treatment equipment involves integrating dusty flow filtration with centrifugal cleaning [11; 12; 13; 14]. Many researchers have extensively investigated these innovations, with particular emphasis on exploring new-generation multi-channel cyclones, as highlighted by [15; 16; 17]. [PERSON] and [PERSON] [18] applied multi-channel cyclones and observed that the purification efficiency from fine wood ash solid particles reached 83.6% after 150 h of operation. [PERSON] [19] examined common tendencies in the sticking process of particles of various sizes and proposed a model suitable for numerically simulating ultrafine particle interactions. The cyclone performance was reported to have significant variations by [PERSON] et al. [20], who examined the effect of providing a 4-10% eccentricity to the vortex finder. In a related study, the authors analyzed various shapes of the dipleg and found that the inverted cone dipleg exhibited superior separation capability compared to the standard model [21]. Similarly, [PERSON] et al. [22] also employed optimization techniques to improve the performance of the cyclone separators by optimizing geometry and inlet configuration, leading to increased particle collection efficiency and reduced pressure drop. [PERSON] and [PERSON] [23] conducted a study involving multi-objective optimization on the positioning and size of secondary inlets--they reported tremendous improvement compared to the reference model. [PERSON] et al.