## 1 Introduction  
The Monte Carlo method (MCM) is one of the most common computational algorithms based on the use of randomly distributed parameters with which it is possible to obtain the numerical solutions to a problem that, in general, can be either probabilistic or deterministic in nature [1]. This method has already been tested and implemented in different areas of experimental and applied sciences, such as physics [2], mathematics [3], engineering [4; 5], biology [6; 7], medicine [8] and others [1]. In physics- and mathematics-related problems, MCM is very useful if there is no way to obtain an exact analytical solution, particularly in the modeling of the optical response of photosynthetic pigment-protein complexes (PPC), when the inhomogeneous broadening of Q\({}_{y}\) electronic transition of chlorophylls (Chls) and bacteriochlorophylls has to be taken into account [9; 10]. Experimental and theoretical research on the optical properties of PPCs is an essential part of the study of photosynthesis as a fundamental process in nature [11]. PPCs are functional subunit proteins of the photosynthetic apparatus of higher plants and bacteria located in cell membranes [12]. Most of them serve as light-harvesting complexes that absorb light quanta, which are subsequently converted into excited states of the complexes [13; 14]. Excited states migrate along PPC until they are localized in the special complexes' reaction centers, where the charge separation takes place [15]. Generally speaking, all PPCs consist of pigment molecules bound to the protein matrix. Remarkably, the pigments are tightly fixed in their positions, forming a rigid spatial structure. The spatial structure of the pigments determines the coupling energies between excited states of molecules, thereby having a significant influence on the optical properties of PPC [16; 17]. Thus, in order to simulate the optical response of PPC most accurately, it is necessary to use a theory that will simultaneously account for both the spatial arrangement of the pigments, and the effect of the protein environment and electron-phonon interaction [18]. MCM has been used quite often to model the results of spectroscopy measurements made on PPC samples [17; 19; 20]. In this case, MCM allows taking into account the effect of slow modulations of an electronic transition which is caused by interactions with the corresponding nuclear degrees of freedom [10; 21; 22]. To do so, the diagonal elements of the Frenkel exciton Hamiltonian are modified by a Gaussian fluctuation parameter and the resulting spectrum is calculated by the averaging of this parameter over all realizations [23; 24; 25]. It is clear that the amount of computational work required for modeling the optical properties of PPC strongly depends on the number of pigments in PPC whose excited states are considered. For example, photosystem I monomeric and trimeric complexes contain about 100 and 300 pigments, and modeling the linear spectroscopy for such complexes is already a time-consuming exercise [17]. This is why we decided to employ the reaction center of photosystem II (PSIIRC) as a model for PPC. Firstly, it contains only eight porphyrin-like pigments (6 ChIs and 2 pheopbytins); secondly, there are many available experimental data measured at different temperatures, as well as theoretical studies on energy transfer and charge separation in PSIIRC. Application of any optimization algorithm for the fitting of PPC experimental data is a non-trivial task, since the exciton theory and the multimode Brownian oscillator model used for the spectra simulation have many input parameters and, most importantly, the dependence of simulated spectra on some parameters is nonlinear [9; 12; 21]. The use of evolutionary strategies as an optimization scheme, particularly a metaheuristic search procedure such as the genetic algorithm, can be considered successful for this kind of problem [26].