Effective Butterfly Optimizer(EBO) is a self-adaptive Butterfly Optimizer which incorporates a crossover operator in Perching and Patrolling to increase the diversity of the population. This paper proposes a new retreat phase called Covariance Matrix Adapted Retreat Phase (CMAR), which uses covariance matrix to generate a new solution and thus improves the local search capability of EBO. This version of EBO is called EBOwithCMAR. We evaluated the performance of EBOwithCMAR on CEC-2017 benchmark problems and compared with the results of winners of a special session of CEC-2016 for bound-constrained problems. The experimental results show that EBOwithCMAR is competitive with the compared algorithms.

Determination of the global optimum of complex non-convex optimization problems of the real-world applications has remained a challenging task. Many researchers have been developing various types of effective direct search-based methods to tackle these problems. In this paper, we introduce a new variant of the recently developed Spherical Search (SS) algorithm, which contains a powerful and effective self-adaptation structure to enhance the performance. To analyze the performance, proposed algorithm is tested on the 57 test problems collected from different real-world applications. The obtained results statistically confirm the efficacy and efficiency of the proposed algorithm.