Monarch Butterfly Optimization Algorithm Research Articles

Hybridizing artificial bee colony with monarch butterfly optimization for numerical optimization problems

The aim of the study was to propose a new metaheuristic algorithm that combines parts of the well-known artificial bee colony (ABC) optimization with elements from the recent monarch butterfly optimization (MBO) algorithm. The idea is to improve the balance between the characteristics of exploration and exploitation in those algorithms in order to address the issues of trapping in local optimal solution, slow convergence, and low accuracy in numerical optimization problems. This article introduces a new hybrid approach by modifying the butterfly adjusting operator in MBO algorithm and uses that as a mutation operator to replace employee phase of the ABC algorithm. The new algorithm is called Hybrid ABC/MBO (HAM). The HAM algorithm is basically employed to boost the exploration versus exploitation balance of the original algorithms, by increasing the diversity of the ABC search process using a modified operator from MBO algorithm. The resultant design contains three components: The first and third component implements global search, while the second one performs local search. The proposed algorithm was evaluated using 13 benchmark functions and compared with the performance of nine metaheuristic methods from swarm intelligence and evolutionary computing: ABC, MBO, ACO, PSO, GA, DE, ES, PBIL, and STUDGA. The experimental results show that the HAM algorithm is clearly superior to the standard ABC and MBO algorithms, as well as to other well-known algorithms, in terms of achieving the best optimal value and convergence speed. The proposed HAM algorithm is a promising metaheuristic technique to be added to the repertory of optimization techniques at the disposal of researchers. The next step is to look into application fields for HAM.

Solving 0–1 knapsack problems by chaotic monarch butterfly optimization algorithm with Gaussian mutation

Recently, inspired by the migration behavior of monarch butterflies in nature, a metaheuristic optimization algorithm, called monarch butterfly optimization (MBO), was proposed. In the present study, a novel chaotic MBO algorithm (CMBO) is proposed, in which chaos theory is introduced in order to enhance its global optimization ability. Here, 12 one-dimensional classical chaotic maps are used to tune two main migration processes of monarch butterflies. Meanwhile, applying Gaussian mutation operator to some worst individuals can effectively prevent premature convergence of the optimization process. The performance of CMBO is verified and analyzed by three groups of large-scale 0–1 knapsack problems instances. The results show that the introduction of appropriate chaotic map and Gaussian perturbation can significantly improve the solution quality together with the overall performance of the proposed CMBO algorithm. The proposed CMBO can outperform the standard MBO and other eight state-of-the-art canonical algorithms.

A new monarch butterfly optimization with an improved crossover operator

Recently, by examining and simulating the migration behavior of monarch butterflies in nature, Wang et al. proposed a new swarm intelligence-based metaheuristic algorithm, called monarch butterfly optimization (MBO), for addressing various global optimization tasks. The effectiveness of MBO was verified by benchmark evaluation on an array of unimodal and multimodal test functions in comparison with the five state-of-the-art metaheuristic algorithms on most benchmarks. However, MBO failed to come up with satisfactory performance (Std values and mean fitness) on some benchmarks. In order to overcome this, a new version of MBO algorithm, incorporating crossover operator is presented in this paper. A variant of the original MBO, the proposed one is essentially a self-adaptive crossover (SAC) operator. A kind of greedy strategy is also utilized. It ensures that only the better monarch butterfly individuals, satisfying a certain criterion, are allowed to pass to the next generation, instead of all the updated monarch butterfly individuals, as was done in the basic MBO. In other words, the proposed methodology is essentially a new version of the original MBO, supplemented with Greedy strategy and self-adaptive Crossover operator (GCMBO). In GCMBO, the SAC operator can significantly improve the diversity of population during the later run phase of the search. In butterfly adjusting operator, the greedy strategy is used to select only those monarch butterfly individuals, possessing improved fitness and hence can aid towards accelerating convergence. Finally, the proposed GCMBO method is benchmarked by twenty-five standard unimodal and multimodal test functions. The results clearly demonstrate the capability of GCMBO in significantly outperforming the basic MBO method for almost all the test cases. The MATLAB code used in the paper can be found in the website: http://www.mathworks.com/matlabcentral/fileexchange/55339-gcmbo .

Monarch butterfly optimization

In nature, the eastern North American monarch population is known for its southward migration during the late summer/autumn from the northern USA and southern Canada to Mexico, covering thousands of miles. By simplifying and idealizing the migration of monarch butterflies, a new kind of nature-inspired metaheuristic algorithm, called monarch butterfly optimization (MBO), a first of its kind, is proposed in this paper. In MBO, all the monarch butterfly individuals are located in two distinct lands, viz. southern Canada and the northern USA (Land 1) and Mexico (Land 2). Accordingly, the positions of the monarch butterflies are updated in two ways. Firstly, the offsprings are generated (position updating) by migration operator, which can be adjusted by the migration ratio. It is followed by tuning the positions for other butterflies by means of butterfly adjusting operator. In order to keep the population unchanged and minimize fitness evaluations, the sum of the newly generated butterflies in these two ways remains equal to the original population. In order to demonstrate the superior performance of the MBO algorithm, a comparative study with five other metaheuristic algorithms through thirty-eight benchmark problems is carried out. The results clearly exhibit the capability of the MBO method toward finding the enhanced function values on most of the benchmark problems with respect to the other five algorithms. Note that the source codes of the proposed MBO algorithm are publicly available at GitHub ( https://github.com/ggw0122/Monarch-Butterfly-Optimization , C++/MATLAB) and MATLAB Central ( http://www.mathworks.com/matlabcentral/fileexchange/50828-monarch-butterfly-optimization , MATLAB).