Next Article in Journal
Gray Wolf Optimization Algorithm for Multi-Constraints Second-Order Stochastic Dominance Portfolio Optimization
Next Article in Special Issue
Probabilistic Interval-Valued Hesitant Fuzzy Information Aggregation Operators and Their Application to Multi-Attribute Decision Making
Previous Article in Journal
Estimating Functional Connectivity Symmetry between Oxy- and Deoxy-Haemoglobin: Implications for fNIRS Connectivity Analysis
Previous Article in Special Issue
The Supplier Selection of the Marine Rescue Equipment Based on the Analytic Hierarchy Process (AHP)-Limited Diversity Factors Method
Article Menu

Export Article

Open AccessArticle

Improving Monarch Butterfly Optimization Algorithm with Self-Adaptive Population

Department of Information Science and Technology, Huizhou University, Huizhou 516007, China
Educational Technology Center, Huizhou University, Huizhou 516007, China
Author to whom correspondence should be addressed.
Algorithms 2018, 11(5), 71;
Received: 21 March 2018 / Revised: 27 April 2018 / Accepted: 27 April 2018 / Published: 14 May 2018
(This article belongs to the Special Issue Algorithms for Decision Making)
PDF [382 KB, uploaded 14 May 2018]


Inspired by the migration behavior of monarch butterflies in nature, Wang et al. proposed a novel, promising, intelligent swarm-based algorithm, monarch butterfly optimization (MBO), for tackling global optimization problems. In the basic MBO algorithm, the butterflies in land 1 (subpopulation 1) and land 2 (subpopulation 2) are calculated according to the parameter p, which is unchanged during the entire optimization process. In our present work, a self-adaptive strategy is introduced to dynamically adjust the butterflies in land 1 and 2. Accordingly, the population size in subpopulation 1 and 2 are dynamically changed as the algorithm evolves in a linear way. After introducing the concept of a self-adaptive strategy, an improved MBO algorithm, called monarch butterfly optimization with self-adaptive population (SPMBO), is put forward. In SPMBO, only generated individuals who are better than before can be accepted as new individuals for the next generations in the migration operation. Finally, the proposed SPMBO algorithm is benchmarked by thirteen standard test functions with dimensions of 30 and 60. The experimental results indicate that the search ability of the proposed SPMBO approach significantly outperforms the basic MBO algorithm on most test functions. This also implies the self-adaptive strategy is an effective way to improve the performance of the basic MBO algorithm. View Full-Text
Keywords: monarch butterfly optimization; migration operator; butterfly adjusting operator; greedy strategy; benchmark problems monarch butterfly optimization; migration operator; butterfly adjusting operator; greedy strategy; benchmark problems

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Hu, H.; Cai, Z.; Hu, S.; Cai, Y.; Chen, J.; Huang, S. Improving Monarch Butterfly Optimization Algorithm with Self-Adaptive Population. Algorithms 2018, 11, 71.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Algorithms EISSN 1999-4893 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top