Controllable optical properties are important for optoelectronic applications. Recently, the two-dimensional MoSi2N4 monolayer was successfully synthesized by chemical vapor deposition, showing remarkable stability in the ambient condition. Motivated by this achievement, herein, we investigate the electronic and optical properties of MoSi2N4 monolayer under mechanical strain through the first-principle calculations. The considered monolayer is structurally and dynamically stable. It is a semiconductor with an indirect band gap of 1.92 eV so that the size of the band gap is easily tuned under biaxial strain. By increasing the tensile strain up to 6%, the effective mass of holes increases to 3.84 me whereas the effective mass of electrons reduces to 0.43 me. In other words, under the strain of 6%, one can have strongly localized holes together with free electrons simultaneously in MoSi2N4 monolayer, which could bring fascinating features like ferromagnetism and superconductivity. Under the strain from 10% to 18%, a Mexican hat dispersion is observed in the highest valence band in such a manner that its coefficient increases from 0.28 to 2.89 eVÅ, indicating the potential thermoelectric application of MoSi2N4 monolayer under strain. Under the strain of 8%, the light absorption coefficient is improved by almost 70%. More importantly, this monolayer tolerates biaxial strain up to 18% and stays mechanically and dynamically stable, making it very promising for flexible nanoelectronics. The controllable electronic and optical properties of MoSi2N4 monolayer may open up an important path for exploring next-generation optoelectronic applications.

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This paper proposes using the opposition-based learning (OBL) strategy in the shuffled differential evolution (SDE). In the SDE, population is divided into several memeplexes and each memeplex is improved by the differential evolution (DE) algorithm. The OBL by comparing the fitness of an individual to its opposite and retaining the fitter one in the population accelerates search process. The objective of this paper is to introduce new versions of the DE which, on one hand, use the partitioning and shuffling concepts of SDE to compensate for the limited amount of search moves of the original DE and, on the other hand, employ the OBL to accelerate the DE without making premature convergence. Four versions of DE algorithm are proposed based on the OBL and SDE strategies. All algorithms similarly use the opposition-based population initialization to achieve fitter initial individuals and their difference is in applying opposition-based generation jumping. Experiments on 25 benchmark functions designed for the special session on real-parameter optimization of CEC2005 and non-parametric analysis of obtained results demonstrate that the performances of the proposed algorithms are better than the SDE. The fourth version of proposed algorithm has a significant difference compared to the SDE in terms of all considered aspects. The emphasis of comparison results is to obtain some successful performances on unsolved functions for the first time, which so far have not been reported any successful runs on them. In a later part of the comparative experiments, performance comparisons of the proposed algorithm with some modern DE algorithms reported in the literature confirm a significantly better performance of our proposed algorithm, especially on high-dimensional functions.

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