Improving monarch butterfly optimization through simulated annealing strategy

Dongfang Yang,Xin Tian,Xitong Wang,Yonggang Zhang

doi:10.1007/s12652-020-01702-y

Abstract

AbstractCurrently, a novel of meta-heuristic algorithm called monarch butterfly optimization (MBO) is presented for solving machine learning and continuous optimization problems. It has been proved experimentally that MBO is superior to artificial bee colony algorithm (ABC), ant colony optimization algorithm (ACO), Biogeography-based optimization (BBO), differential evolution algorithm (DE) and simple genetic algorithm (SGA) algorithms on most test functions. This paper presents a new version of MBO with simulated annealing (SA) strategy called SAMBO. The SA strategy is put in the migration operator and butterfly adjusting operator. So the newly proposed algorithm has two features: One is that the algorithm accepts all the butterfly individuals whose fitness are better than their parents. The other is that the algorithm randomly selects some individuals which are worse than their parents to disturbance the convergence of algorithm. In this way, the SAMBO algorithm can escape from local optima. Finally, the experiments are carried on 14 continuous nonlinear functions, and results show that SAMBO method exceeds the MBO algorithm on most test functions.

Highlights

More and more nature-inspired algorithms (Yang 2014) have been proposed and generally applied in numerous applications, such as path planning (Wang et al 2012), machine learning (Zhou 2016), knapsack problem (Feng et al 2015), fault diagnosis (Duan and Luo 2015; Gao et al 2008) and directing orbits of chaotic system (Cui et al 2013)
It’s worth noting that monarch butterfly optimization (MBO) and probability-based incremental learning (PBIL) have a terrible performance on the mean value of F11
This paper primarily demonstrates that the MBO has been improved, so we just provide the convergence curves of MBO and SAMBO on F02, F04, F05, F08 and F10

Summary

Introduction

More and more nature-inspired algorithms (Yang 2014) have been proposed and generally applied in numerous applications, such as path planning (Wang et al 2012), machine learning (Zhou 2016), knapsack problem (Feng et al 2015), fault diagnosis (Duan and Luo 2015; Gao et al 2008) and directing orbits of chaotic system (Cui et al 2013). Among all kinds of natural-inspired algorithms, clustering algorithms and evolutionary algorithms are the most representative ones. Analysis of nature-inspired algorithms from the exploration and search space shows that they both have two major. SI was originally inspired by the collective behavior of social insects. It was first formally proposed by Dorigo et al in his book “Swarm Intelligence: From Natural to Artificial Systems” in 1999. The following particle swarm optimization (PSO) (Zhao 2010; Kennedy and Eberhart 2002; Mirjalili et al 2014), animal migration optimization (AMO) (Li et al 2014), artificial fish swarm algorithm (Zainal et al. Vol.:(0123456789)

Methods

Results

Conclusion