[2023-Vol.20-Issue 2]Non-dominated Sorting Advanced Butterfly Optimization Algorithm for Multi-objective Problems
Post: 2023-03-07 13:27  View:561

Journal of Bionic Engineering (2023) 20:819–843

Non-dominated Sorting Advanced Butterfly Optimization Algorithm for Multi?objective Problems

Sushmita Sharma1 · Nima Khodadadi2 · Apu Kumar Saha1 · Farhad Soleimanian Gharehchopogh3 ·

Seyedali Mirjalili4,5

1 Department of Mathematics, National Institute of Technology Agartala, Tripura 799046, India

2 Department of Civil and Environment Engineering, Florida International University Miami, Miami, FL 33199, USA

3 Department of Computer Engineering, Urmia Branch, Islamic Azad University, Urmia 5914633817, Iran

4 Centre for Artificial Intelligence Research and Optimization,Torrens University, Fortitude Valley, QLD 4006, Australia

5 Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea

Abstract This paper uses the Butterfly Optimization Algorithm (BOA) with dominated sorting and crowding distance mechanisms to solve multi-objective optimization problems. There is also an improvement to the original version of BOA to alleviate its drawbacks before extending it into a multi-objective version. Due to better coverage and a well-distributed Pareto front, non-dominant rankings are applied to the modified BOA using the crowding distance strategy. Seven benchmark functions and eight real-world problems have been used to test the performance of multi-objective non-dominated advanced BOA (MONSBOA), including unconstrained, constrained, and real-world design multiple-objective, highly nonlinear constraint problems. Various performance metrics, such as Generational Distance (GD), Inverted Generational Distance (IGD), Maximum Spread (MS), and Spacing (S), have been used for performance comparison. It is demonstrated that the new MONSBOA algorithm is better than the compared algorithms in more than 80% occasions in solving problems with a variety of linear, nonlinear, continuous, and discrete characteristics based on the Pareto front when compared quantitatively. From all the analysis, it may be concluded that the suggested MONSBOA is capable of producing high-quality Pareto fronts with very competitive results with rapid convergence.

Keywords Multi-objective problems · Butterfly optimization algorithm · Non-dominated sorting · Crowding distance


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