LMBO-DE: a linearized monarch butterfly optimization algorithm improved with differential evolution

Abstract

Monarch butterfly optimization (MBO) is a recently developed evolutionary algorithm which has been used in many optimization problems. Migration and adjusting operators of MBO have a significant effect on the performance of it. These two operators change candidate variables of each individual independently. So, they are rotationally variant and this is one of the limitations of MBO which can degrade its performance on non-separable problems. There are interactions among variables in non-separable problems and MBO’s operators have not any consideration to it. In this paper, we propose a linearized version of MBO to overcome the above-mentioned limitation of MBO. In other words, migration and adjusting operators of MBO are linearized. Moreover, DE’s mutation operator is integrated in our proposed algorithm to improve exploration of MBO. Our proposed algorithm which is a linearized and hybrid version of MBO (LMBO-DE) is validated by 18 benchmark functions in different dimensionality and is compared with original MBO, one of recently MBO’s improvements, and three other evolutionary algorithms (jDE, JADE, and CLPSO). Experimental results show that our proposed algorithm significantly outperforms the original MBO and its improvement in terms of solution quality and convergence rate. In comparison with the other three algorithms, LMBO-DE can find more accurate solutions.