Butterfly Optimization Algorithm (BOA) is a recently developed metaheuristic search algorithm that mimics the food-search process of the butterflies in nature. The studies reveal that BOA shows significant performance on the non-constrained and unbiased mathematical functions, but in the cases of shifted and rotated functions and/or constrained optimization problems, its search capacity is considerably restricted. To address this shortcoming, the present study deals with developing a new fuzzy decision-making strategy and introducing a new auxiliary concept called "virtual butterfly'' to enhance the search capability of the standard BOA. The developed fuzzy strategy permanently monitors the optimization process and tries to adjust each butterfly's search behavior based on the governing conditions of the current problem. Also, the virtual butterfly concept involving the information of the whole colony tries to provide alternative promising search directions for the other butterflies. The new reinforced method is named Fuzzy Butterfly Optimization Algorithm (FBOA). To evaluate the search performance of the proposed FBOA, it is tested on solving a suit of constrained and non-constrained optimization problems and the achieved outcomes are compared with those given by some other well-established techniques including its parent method (i.e. BOA). The results show that the implemented improvements significantly increase the search capability of the regular BOA, especially in the case of constrained engineering problems. (C) 2021 Elsevier B.V. All rights reserved.