A Hybrid Butterfly Optimization Algorithm for Numerical Optimization Problems.

Huan Zhou,An-Di Tang,Lei Xie,Hao-Yu Cheng,Zheng-Lei Wei,Xin Zhao,Ahmed Mostafa Khalil

doi:10.1155/2021/7981670

Abstract

The butterfly optimization algorithm (BOA) is a swarm-based metaheuristic algorithm inspired by the foraging behaviour and information sharing of butterflies. BOA has been applied to various fields of optimization problems due to its performance. However, BOA also suffers from drawbacks such as diminished population diversity and the tendency to get trapped in local optimum. In this paper, a hybrid butterfly optimization algorithm based on a Gaussian distribution estimation strategy, called GDEBOA, is proposed. A Gaussian distribution estimation strategy is used to sample dominant population information and thus modify the evolutionary direction of butterfly populations, improving the exploitation and exploration capabilities of the algorithm. To evaluate the superiority of the proposed algorithm, GDEBOA was compared with six state-of-the-art algorithms in CEC2017. In addition, GDEBOA was employed to solve the UAV path planning problem. The simulation results show that GDEBOA is highly competitive.

Highlights

Optimization problems exist in all aspects of our society, including business, engineering, and science
The application of GDEBOA to UAV route planning is discussed in detail. e UAV route planning problem aims to minimize the cost of carrying out the mission, which can be considered as a multi-constraint optimization problem. e route planning model is described in detail
We propose a variant of butterfly optimization algorithm (BOA) using a distribution estimation strategy, called GDEBOA, to solve the global optimization problem. e performance of BOA is enhanced by using the distribution estimation strategy to sample the evolutionary information of the dominant population and to guide the direction of individual evolution

Summary

Introduction

Optimization problems exist in all aspects of our society, including business, engineering, and science. With the popularity of GA and GA variants, more and more evolutionary-based algorithms are continuously being proposed, including differential evolution (DE) [15], genetic programming (GP) [16], evolutionary strategies (ES) [17], and evolutionary programming (EP) [18]. Houssein et al [42] proposed a variant of the slime mould algorithm with hybrid adaptive guided differential evolution in order to overcome the disadvantages of unbalanced exploitation and exploration. Inspired by these hybrid variants, this paper proposes a BOA variant with hybrid distribution estimation strategy, GDEBOA. BOA solves the optimization problem through global and local search with the following mathematical model. BOA constantly executes two search strategies during the search process. erefore, a switching probability p is introduced to control the switching of the two strategies. e pseudocode for BOA is given in Algorithm 1

Proposed GDEBOA

Numerical Experiment and Analysis

UAV Route Planning

Conclusions