This book presents theory and applications of recently introduced butterfly optimization algorithm (BOA). It also highlights hybridization process in the basic structure of BOA with in-depth analysis of complexity. This book also describes the constraint handling process. The newly introduced variant is implemented and validated on a set of linear and nonlinear real works problems of engineering and pulp and paper industry. The simulated results are compared with most of the basic algorithms. Comparative and nonparametric statistical result analysis illustrates the efficacy of the algorithm.