Recently, the use of multi-crystalline silicon solar cells (MCSSCs) has been increasing worldwide. This work proposes a novel MCSSC pattern for achieving a more accurate emulation of the electrical behavior of solar cells. Specifically, this pattern is dependent on the modification of the double diode model of MCSSCs. Importantly, the proposed pattern has an extra diode compared to the previously modified double-diode model (MDDM) described in the literature for considering the defect region of MCSSC to form a modified three diode model (MTDM). For estimating the parameters of the proposed MTDM, two metaheuristic algorithms called closed-loop particle swarm optimization (CLPSO) and elephant herd optimization (EHO) are developed, which have superior convergence rates. The competitive algorithms are executed on experimental data based on a MCSSC of area 7.7 cm2 from Q6-1380 and CS6P-240P solar modules under different irradiance and temperature levels for both MDDM and MTDM. Also, the proposed elephant herd optimization soft paradigm is extended for a high irradiance level at 1000 W/m2 on an R.T.C. France Solar cell. The proposed new optimization models are more efficient in dealing with the natural characteristics of the MCSSC. The simulation results show that the MTDM gives more accurate solutions as a model to the MCSSC compared with the results reported in the literature. From the viewpoint of soft computing paradigms, the EHO outperforms CLPSO in terms of the solution quality and convergence rates.