PPubMed24 Dec 2021Cited 20×

A Hybrid Butterfly Optimization Algorithm for Numerical Optimization Problems

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

Abstract

'Lei Xie'] 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.

A figure from A Hybrid Butterfly Optimization Algorithm for Numerical Optimization Problems — fig. from the paper

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The proposed GDEBOA hybrid algorithm outperforms six state‑of‑the‑art metaheuristics on CEC2017 benchmarks and UAV path‑planning, offering better exploration‑exploitation balance and higher success rates.

What’s new

i.Introduce GDEBOA, a hybrid butterfly optimization algorithm using Gaussian distribution estimation.
ii.Demonstrate that Gaussian estimation enhances population diversity and balances exploration and exploitation.
iii.Validate GDEBOA on the CEC2017 28‑function benchmark and on UAV route‑planning, achieving superior performance.
iv.Provide statistical analysis (Wilcoxon, Friedman tests) confirming the algorithm’s advantage over six peer methods.

How they did it

The authors integrate a Gaussian distribution estimation strategy into the standard butterfly optimization algorithm to guide population updates. They evaluate the resulting GDEBOA on the IEEE CEC2017 single‑objective test suite (28 functions) with 51 independent runs per algorithm, and on a UAV path‑planning problem using MATLAB simulations (30 runs, population size 50, 300 iterations). Results are compared against six recent metaheuristics using mean, standard deviation, rank, and success‑rate metrics.

What they found

GDEBOA achieved rank 1 on the majority of CEC2017 functions, often with the lowest mean error (e.g., F1 mean 7.70E‑06, rank 1).
In UAV path‑planning, GDEBOA attained a mean cost of 2.22E+02, standard deviation 5.41E+00, and 100 % success rate, outperforming BOA, MRFO, and SMA.

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