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

Sushmita Sharma, Nima Khodadadi, Apu Kumar Saha, Farhad Soleimanian Gharehchopogh, Seyedali Mirjalili

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


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.

Original languageEnglish
JournalJournal of Bionic Engineering
Publication statusPublished - 2023


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


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