An Enhanced Monarch Butterfly Optimization with Self-adaptive Butterfly Adjusting and Crossover Operators

Inspired by the phenomenon of migration of monarch butterflies, Wang et al. developed a novel promising swarm intelligence algorithm, called monarch butterfly optimization (MBO), for addressing unconstrained low-dimensional optimization problems. In this paper, we firstly extend the application area of the basic MBO to solve the constrained optimization problems. At the same time, the crossover operator originally used in evolutionary algorithms (EAs) is incorporated into the butterfly adjusting operator in order to strengthen the exploitation of the basic MBO algorithm. Furthermore, the crossover rate is self-adaptively adjusted according to the fitness of the corresponding individual instead of the fixed crossover rate used in EAs. For migration operator, only individuals having better fitness are accepted and passed to the next generation instead of accepting all the individuals in the basic MBO algorithm. After incorporated all the modifications into the basic MBO algorithm, an improved MBO algorithm with self-adaptive crossover namely SACMBO, is proposed for unstrained and constrained optimization problems. Finally, the proposed SACMBO algorithm is further used to solve 22 unstrained optimization problems (with dimension of 100, 300, 500, 1000, and 1500) and 28 constrained real-parameter optimization functions from CEC 2017 competition (with dimension of 50 and 100), respectively. The experimental results indicate that the proposed SACMBO algorithm outperforms the basic MBO and other five state-of-the-art metaheuristic algorithms.

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).

Monarch butterfly optimization is inspired by the migration of monarch butterflies in nature: monarch butterflies in eastern North America migrate southward from northern United States and southern Canada to Mexico every summer/autumn. It is a new swarm intelligence metaheuristic algorithm, which is called monarch butterfly optimization (MBO). In MBO, the monarch butterfly population is ideally divided into two populations, one is located in southern Canada and northern United States (land 1), and the other is located in Mexico (land 2). We update the individuals in the population through migration and butterfly shape adjustment. To maintain the diversity of the population and minimize the fitness value, the total number of butterflies generated by the operation should be equal to the original population. In the experiment, MBO is compared with five metaheuristic algorithms through 38 test functions, especially applied to solve a large-scale 0-1 knapsack (KP) problem. Three groups of 15 large-scale 0-1 KP cases from 800 to 2000 dimensions are used to test. It is proved that MBO has strong advantages in solving global numerical optimization and engineering problems, which provides a reference for further discussion of MBO in the future.

As a significant subset of the family of discrete optimization problems, the 0-1 knapsack problem (0-1 KP) has received considerable attention among the relevant researchers. The monarch butterfly optimization (MBO) is a recent metaheuristic algorithm inspired by the migration behavior of monarch butterflies. The original MBO is proposed to solve continuous optimization problems. This paper presents a novel monarch butterfly optimization with a global position updating operator (GMBO), which can address 0-1 KP known as an NP-complete problem. The global position updating operator is incorporated to help all the monarch butterflies rapidly move towards the global best position. Moreover, a dichotomy encoding scheme is adopted to represent monarch butterflies for solving 0-1 KP. In addition, a specific two-stage repair operator is used to repair the infeasible solutions and further optimize the feasible solutions. Finally, Orthogonal Design (OD) is employed in order to find the most suitable parameters. Two sets of low-dimensional 0-1 KP instances and three kinds of 15 high-dimensional 0-1 KP instances are used to verify the ability of the proposed GMBO. An extensive comparative study of GMBO with five classical and two state-of-the-art algorithms is carried out. The experimental results clearly indicate that GMBO can achieve better solutions on almost all the 0-1 KP instances and significantly outperforms the rest.

In the dynamic development of technology, the Internet of Things (IoT) stands as a driving force of innovation and opening new frontiers. Data collection and processing in IoT systems provide services to decision making in various fields including home automation, disaster management, healthcare, and so on. In such services, the IoT has certain limitations to perform the required tasks and it can cause extreme consequences in the network. One of the main challenge in IoT is to ensure maximum coverage by optimally placing the sensors. To address the coverage problem, a meta-heuristic algorithm Monarch Butterfly Optimization with greedy strategy and self-adaptive crossover operator (GCMBO) is proposed for Optimal Sensor Placement (OSP) in 3D monitoring region. The performance of proposed algorithm is evaluated by a series of simulation and it provide efficient results when compared to other similar existing optimization algorithms. Additionally, a statistical analysis (ANOVA and LSD post-hoc) is exhibited from the comparative results.

The aim of this paper is to denoise the high noise density image proficiently with minimal computation cost using various techniques. This paper proposes an approach for image denoising based on Discrete Wavelet Transform (DWT) in association with Monarch Butterfly Optimization (MBO) technique. Along with Gaussian noise, salt & pepper and speckle noise are added to the image and DWT is applied on the noisy image. The Haar wavelet is used to segregate the sub bands and threshold operation is carried out in three bands. The wavelet coefficient optimization process is performed for optimizing the coefficient value with the assistance of MBO technique. In this wavelet-optimized parameter, the inverse DWT (IDWT) is applied. The proposed method decreases the noise from images more efficiently. The result exhibits that MBO technique is better than the existing and other traditional techniques as it minimize the mean square error (MSE). This process is validated with PSNR value and implemented in MATLAB.

This paper proposes an effective feature selection method based on monarch butterfly optimization and Fisher criterion. Fisher criterion is applied to evaluate the feature subsets, based on which the optimal feature subsets are searched by using monarch butterfly optimization algorithm. To combine these two components, a method is developed to binarize continuous solution vectors for deciding the feature selection. We conduct experiments on widely used UCI (University of California, Irvine) classification datasets to study the design of our algorithm and compare it with other state-of-the-art counterparts. The experimental results show that the proposed method is reasonable and effective, which achieves the best result of feature selection among the compared methods and has satisfactory efficiency.

Picking a subset of possible features is a vital step in the data-mining procedure. The decisive goal of feature-selection is to determine the optimal number of superior characteristics to make best use of the presentation of the learning algorithm. However, this problem becomes increasingly challenging to resolve as the number of features in a data set increase. Therefore, to identify the optimal feature combinations, contemporary optimization techniques are used. Numerous optimization problems have been successfully resolved using the innovative metaheuristic known as the marine predators algorithm (MPA). Support vector machines (SVMs) are a crucial technique that is expertly applied to classification issues. In this work, the issue of feature picking in large dimensional data sets is solved by adjusting the MPA using the SVM as a classifier. In order to address the problem of feature selection in large dimensional data sets, the current study suggests MPA + SVM. Ten high-dimensional data sets got from the Arizona State University (ASU) source were employed to prove the usefulness of the planned method; the outcomes are likened with those of the additional six cutting-edge picking features algorithms. We compared the following algorithms: atom search optimization (ASO), satin bowerbird optimizer (SBO), emperor penguin optimizer (EPO), equilibrium optimizer (EO), monarch butterfly optimization (MBO), and sine cosine algorithm (SCA). The consequences confirm that the planned MPA+SVM approach outperformed several metaheuristic algorithms and presented a remarkable capability to pick the utmost weighty and optimum features. MPA + SVM yields the lowermost averaged error rates, minimal classification standard deviation (STD) values, and FS rates across all data sets.

Improved random selection strategy, self-adaptive crossover and mutation operators, population co-evolution algorithm are adopted in this paper to set up a new genetic algorithm(GA), guaranteeing the universality of population, the thoroughness of solution and the execution efficiency of algorithm in solving multi-process, process crossover, work-piece flow and other condition based scheduling problem of flexible manufacturing system(FMS). The problem of GA in solving FMS scheduling is summarized in this paper, reasons and countermeasures for GA's pre-maturing are studied, longitudinal and transverse comprehensive state-based correlative self-adaptive crossover and mutation operators are raised according to the analysis on GA to avoid local optimization and pre-maturity, the co-evolutionary GA is designed to solve the scheduling model for FMS, and the algorithm is validated for the scheduling of box-type parts for precise machine tools.

Parallel processing has been employed many years in high-performance computing. Parallel processing is mostly used because it provides concurrency, maximizes load balancing, and minimizes system idle time and execution time which depend on various computer architecture. Task scheduling is a parallel processing technique which allocates the tasks to various processors. Mapping of heterogeneous tasks to a heterogeneous processor or core dynamically in a distributed environment is one of the active area of research in the field of parallel computing system. Here in this paper, monarch butterfly optimization (MBO) [1], a nature-inspired metaheuristic algorithm is implemented for a task scheduling problem. A monarch, a North American butterfly is best known for its migratory behavior in the summer season. There are mainly two processes to get the best solution. First, using a migration operator, a new generation is created. Second, they update their position by using a butterfly adjusting operator. The fitness value is evaluated and updated the population with a higher fitness value to satisfy the objective of the problem. Minimizing the cost and time of the scheduling strategy is the main objective of the proposed work.

Electric Vehicle-to-Grid (V2G) arrangements stand at the center of bidirectional energy exchange in modern smart grids and are, however, challenged by real-time decision-making, load balancing, and the security of transaction validation. This paper has proposed an energy-efficient optimization framework based on a Bio-Inspired Deep Learning Controller using a Monarch Butterfly Optimization (MBO) algorithm with Gated Recurrent Unit (GRU) network for optimizing charging and discharging schedules across EV fleets. GRU networks forecast short-term grid demand and EV battery availability while MBO tunes the controller weights dynamically to adapt to scheduling under varying conditions. Furthermore, in order to maintain the trust over the transaction in a tamper-resistant fashion, a blockchain layer is embedded with the use of smart contracts to keep a track of authentication, pricing, and energy transfer log records for V2G. The proposed system shows charging cost reduction of 19.6%, peak load shaving efficiency of 23.2%, and forecast accuracy of 96.4%, in all mobility scenarios evaluated. The architecture also contributes to improving grid regulation response time by 28% and reducing EV queuing delay by 31%. Simulated by using MATLAB/Simulink, TensorFlow, and Ethereum-based blockchain, the architecture renders a scalable and secure framework for V2G coordination. It is noted that the findings are based on simulation, and co-simulation experiments, and the actual conditions of deployment like latency in communications, non-idealities of the hardware and regulatory factors are not factored into the analysis. Furthermore, the model facilitates real-time adaptation, strengthens grid resilience, and guides EV operation according to concurrent market conditions for energy.

A new method for optimal parameters identification of a PEMFC using an improved version of Monarch Butterfly Optimization Algorithm

Evolutionary algorithms (EAs), as global search methods, are proved to be more robust than their counterpart local heuristics for detecting protein complexes in protein-protein interaction (PPI) networks. Typically, the source of robustness of these EAs comes from their components and parameters. These components are solution representation, selection, crossover, and mutation. Unfortunately, almost all EA based complex detection methods suggested in the literature were designed with only canonical or traditional components. Further, topological structure of the protein network is the main information that is used in the design of almost all such components. The main contribution of this paper is to formulate a more robust EA with more biological consistency. For this purpose, a new crossover operator is suggested where biological information in terms of both gene semantic similarity and protein functional similarity is fed into its design. To reflect the heuristic roles of both semantic and functional similarities, this paper introduces two gene ontology (GO) aware crossover operators. These are direct annotation-aware and inherited annotation-aware crossover operators. The first strategy is handled with the direct gene ontology annotation of the proteins, while the second strategy is handled with the directed acyclic graph (DAG) of each gene ontology term in the gene product. To conduct our experiments, the proposed EAs with GO-aware crossover operators are compared against the state-of-the-art heuristic, canonical EAs with the traditional crossover operator, and GO-based EAs. Simulation results are evaluated in terms of recall, precision, and F measure at both complex level and protein level. The results prove that the new EA design encourages a more reliable treatment of exploration and exploitation and, thus, improves the detection ability for more accurate protein complex structures.

This chapter presents an evolutionary approach for solving the traveling salesman problem (TSP) and the TSP with backhauls (TSPB). We propose two evolutionary algorithms for solving the difficult TSPs. Our focus is on developing evolutionary operators based on conventional heuristics. We rely on a set of detailed computational experiments and statistical tests for developing an effective algorithm.The chapter starts with a careful survey of the algorithms for the TSP and the TSPB, with a special emphasis on crossover and mutation operators and applications on benchmark test instances. The second part addresses our first evolutionary algorithm. We explore the use of two tour construction heuristics, nearest neighbor and greedy, in developing new crossover operators.We focus on preserving the edges in the union graph constructed by edges of the parent tours.We let the heuristics exploit the building blocks found in this graph. This way, new solutions can inherit good blocks from both parents. We also combine the two crossover operators together in generating offspring to explore the potential gain due to synergy. In addition, we make use of 2-edge exchange moves as the mutation operator to incorporate more problem specific information in the evolution process. Our reproduction strategy is based on the generational approach. Experimental results indicate that our operators are promising in terms of both solution quality and computation time.In the third part of the chapter, we present the second evolutionary algorithm developed. This part can be thought of as an enhancement of the first algorithm. A common practice with such algorithms is to generate one child or two children from two parents. In the second implementation, we investigate the preservation of good edges available in more than two parents and generate multiple children.We use the steady-state evolution as a reproduction strategy this time and test the replacement of the worst parent or the worst population member to find the better replacement strategy. Our two mutation operators try to eliminate the longest and randomly selected edges and a third operator makes use of the cheapest insertion heuristic. The algorithm is finalized after conducting a set of experiments for best parameter settings and testing on larger TSPLIB instances. The second evolutionary algorithm is also implemented for solving randomly generated instances of the TSPB. Our experiments reveal that the algorithm is significantly better than the competitors in the literature. The last part concludes the chapter.KeywordsNetworks-GraphsTraveling Salesman ProblemsEvolutionary AlgorithmsCrossover OperatorMutation OperatorHeuristics

A multi-objective evolutionary algorithm with interval based initialization and self-adaptive crossover operator for large-scale feature selection in classification