The minimum energy path (MEP) and transition state are two key parameters in the investigation of the mechanisms of chemical reactions and structural phase transformations. However, determination of transition paths in solids is challenging. Here, we present an evolutionary method to search for the lowest energy path and the transition state for pressure-induced structural transformations in solids without any user input or prior knowledge of possible paths. Instead, the initial paths are chosen stochastically by connecting randomly selected atoms from the initial to final structure. The MEP of these trials paths were computed and ranked in order of their energies. The matrix particle swarm optimization algorithm is then used to generate improved transition paths. The procedure is repeated until the lowest energy MEP is found. This method is validated by reproducing results of several known systems. The new method also successfully located the MEP for the direct low-temperature pressure induced transformation of face centered-cubic (FCC) silicon to the simple hexagonal(sh) phase and FCC lithium to a complex body centered-cubic cI16 high-pressure phase. The proposed method provides a convenient, robust, and reliable approach to identify the MEP of phase transformations. The method is general and applicable to a variety of problems requiring the location of the transition state.

最小能量路径（MEP）和过渡态是化学反应和结构相变机理研究中的两个关键参数。但是，确定固体中的过渡路径具有挑战性。在这里，我们提出了一种进化方法来搜索最低能量路径和固体中压力诱导的结构转变的过渡状态，而无需任何用户输入或可能路径的先验知识。相反，通过将随机选择的原子从初始结构连接到最终结构，可以随机选择初始路径。计算这些试验路径的MEP，并按其能量顺序对其进行排名。然后使用矩阵粒子群优化算法来生成改进的过渡路径。重复该过程，直到找到最低能量的MEP。通过重现几个已知系统的结果验证了此方法。该新方法还成功地找到了MEP，可将低温直接诱导的面心立方（FCC）硅转变为简单的六方（sh）相，将FCC锂转变为复杂的体心立方cI16高压相。所提出的方法提供了一种方便，可靠且可靠的方法来识别相变的MEP。该方法是通用的并且适用于需要过渡状态的位置的各种问题。该新方法还成功地找到了MEP，可将低温直接诱导的面心立方（FCC）硅转变为简单的六方（sh）相，将FCC锂转变为复杂的体心立方cI16高压相。所提出的方法提供了一种方便，可靠，可靠的方法来识别相变的MEP。该方法是通用的并且适用于需要过渡状态的位置的各种问题。该新方法还成功地找到了MEP，可将低温直接诱导的面心立方（FCC）硅转变为简单的六方（sh）相，将FCC锂转变为复杂的体心立方cI16高压相。所提出的方法提供了一种方便，可靠且可靠的方法来识别相变的MEP。该方法是通用的并且适用于需要过渡状态的位置的各种问题。