A Novel Monarch Butterfly Optimization with Global Position Updating Operator for Large-Scale 0-1 Knapsack Problems

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.

After studying the behavior of monarch butterflies in nature, Wang et al. proposed a new promising swarm intelligence algorithm, called monarch butterfly optimization (MBO), for addressing unconstrained optimization tasks. In the basic MBO algorithm, the fixed butterfly adjusting rate is used to carry out the butterfly adjusting operator. In this paper, the self-adaptive strategy is introduced to adjust the butterfly adjusting rate. In addition, the crossover operator that is generally used in evolutionary algorithms (EAs) is used to further improve the quality of butterfly individuals. The two optimization strategies, self-adaptive and crossover operator, are combined, and then self-adaptive crossover operator is proposed. After incorporating the above strategies into the basic MBO algorithm, a new version of MBO algorithm, called Self-adaptive Monarch Butterfly Optimization (SaMBO), is put forward. Also, few studies of constrained optimization has been done for MBO research. In this paper, in order to verify the performance of our proposed SaMBO algorithm, the proposed SaMBO algorithm is further benchmarked by 21 CEC 2017 constrained optimization problems. The experimental results indicate that the proposed SaMBO 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).

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.

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.

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

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.

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.

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.

This paper presents two improved versions of the monarch butterfly optimization algorithm adopted for solving multi-objective optimization problems. Monarch butterfly optimization is a relatively new swarm intelligence metaheuristic that proved to be robust and efficient method when dealing with NP hard problems. However, in the original monarch butterfly approach some deficiencies were noticed and we addressed these deficiencies by developing one modified, and one hybridized version of the original monarch butterfly algorithm. In the experimental section of this paper we show comparative analysis between the original, and improved versions of monarch butterfly algorithm. According to experimental results, hybridized monarch butterfly approach outperformed all other metaheuristics included in comparative analysis.

Comparative Study of Several Intelligent Algorithms for Knapsack Problem

New method of multi-extremal optimization has been developed - a network programming method, which is based on the possibility to represent a complex function as a superposition of simpler functions. The paper deals with network (dichotomous) programming method and its application for solving multi-extremal and discrete optimization problems in Project Management. The main goal of the paper is to develop a new approach to solving knapsack problem and to solve a number of optimization problems of project building management. The optimal structure of the dichotomous representation is determined. On the basis dichotomous programming method new algorithm to solve a optimization problem is proposed

Knapsack problems are among the most common problems in literature tackled with evolutionary algorithms (EA). Their major advantage lies in the fact that they are relatively simple to implement while they allow generalizations for a wide range of real world problems. The multi-dimensional knapsack problem (MKP), which belongs to the class of NP-complete combinatorial optimization problems, is one of the variations of the knapsack problem. The MKP has a wide range of real world applications such as cargo loading, selecting projects to fund, budget management, cutting stock, etc. The MKP has been studied quite extensively in the EA community. Due to the constrained nature of the problem, constraint handling techniques gain great importance in the performance of the proposed EA approaches. In this study, the applicability of a generational EA that uses a penalty-based constraint handling technique and a gene locus based, asymmetric, adaptive mutation scheme is explored for the MKP. The effects of the parameters of the explored approach is determined through tests. Further experiments, using large MKP instances from commonly used benchmarks available through the Internet are performed. Comparison tables are given for the performance of the explored approach and other good performing EAs found in literature for the MKP. Results show that performance improves greatly when compared with other penalty-based techniques, but the explored approach is still not the best performer among all. However, unlike the explored technique, the EAs using the other constraint handling techniques require a great amount of extra computational effort and need heuristic information specific to the optimization problem. Based on these observations, and the fact that the performance difference between the explored scheme and the better performers is not too high, research on improving the explored approach is still in progress.