The Manta Ray Foraging Optimization algorithm (MRFO) has proven to be a powerful heuristic strategy in the optimal solution of a large number of engineering problems. In this paper, an improvement of MRFO with Levy Flight is suggested for the training of extreme learning machines (ELMs) whose basic model is a Single Layer Feedforward Network (SLFN). The proposed methodology that we called Evolutionary EELM-MRFO-LF for short is implemented to the prediction of unrelaxed and relaxed formation energy compounds relative to ground state crystal structure of pure components in binary systems. EELM-MRFO-LF follows the learning procedure of traditional Evolutionary ELMs in which first MRFO with LF is used to select the input weights and Moore-Penrose (MP) generalized inverse is applied to analytically determine the output weights. Levy Flight trajectory is implemented for increasing the diversity of the population of ELMs against premature convergence and the ability of avoiding getting trapped in a local optima. The performance of the suggested EELM-MRFO-LF is compared with other well-known nature-inspired algorithms under similar conditions.

翻译：蝠鲼觅食优化算法（MRFO）已被证明是解决大量工程问题最优解的有效启发式策略。本文提出一种结合Levy飞行的改进MRFO算法，用于训练以单层前馈网络（SLFN）为基本模型的极限学习机（ELM）。该方法简称EELM-MRFO-LF，应用于预测二元系中纯组分基态晶体结构相关的未弛豫和弛豫形成能化合物。EELM-MRFO-LF遵循传统进化ELM的学习流程：首先利用带LF的MRFO选择输入权重，然后应用Moore-Penrose（MP）广义逆解析确定输出权重。采用Levy飞行轨迹以增加ELM种群的多样性，防止早熟收敛并提升避免陷入局部最优的能力。在相同条件下，将所提出的EELM-MRFO-LF性能与其他知名自然启发算法进行了比较。