Energy-Saving Distributed Flexible Job Shop Scheduling Optimization with Dual Resource Constraints Based on Integrated Q-Learning Multi-Objective Grey Wolf Optimizer

The distributed flexible job shop scheduling problem(DFJSP)has attracted great attention with the growth of the global manufacturing industry.General DFJSP research only considers machine constraints and ignores worker constraints.As one critical factor of production,effective utilization of worker resources can increase productivity.Meanwhile,energy consumption is a growing concern due to the increasingly serious environmental issues.Therefore,the distributed flexible job shop scheduling problem with dual resource constraints(DFJSP-DRC)for minimizing makespan and total energy consumption is studied in this paper.To solve the problem,we present a multi-objective mathematical model for DFJSP-DRC and propose a Q-learning-based multi-objective grey wolf optimizer(Q-MOGWO).In Q-MOGWO,high-quality initial solutions are generated by a hybrid initialization strategy,and an improved active decoding strategy is designed to obtain the scheduling schemes.To further enhance the local search capability and expand the solution space,two wolf predation strategies and three critical factory neighborhood structures based on Q-learning are proposed.These strategies and structures enable Q-MOGWO to explore the solution space more efficiently and thus find better Pareto solutions.The effectiveness of Q-MOGWO in addressing DFJSP-DRC is verified through comparison with four algorithms using 45 instances.The results reveal that Q-MOGWO outperforms comparison algorithms in terms of solution quality.

Enhancing Hyper-Spectral Image Classification with Reinforcement Learning and Advanced Multi-Objective Binary Grey Wolf Optimization

Hyperspectral(HS)image classification plays a crucial role in numerous areas including remote sensing(RS),agriculture,and the monitoring of the environment.Optimal band selection in HS images is crucial for improving the efficiency and accuracy of image classification.This process involves selecting the most informative spectral bands,which leads to a reduction in data volume.Focusing on these key bands also enhances the accuracy of classification algorithms,as redundant or irrelevant bands,which can introduce noise and lower model performance,are excluded.In this paper,we propose an approach for HS image classification using deep Q learning(DQL)and a novel multi-objective binary grey wolf optimizer(MOBGWO).We investigate the MOBGWO for optimal band selection to further enhance the accuracy of HS image classification.In the suggested MOBGWO,a new sigmoid function is introduced as a transfer function to modify the wolves’position.The primary objective of this classification is to reduce the number of bands while maximizing classification accuracy.To evaluate the effectiveness of our approach,we conducted experiments on publicly available HS image datasets,including Pavia University,Washington Mall,and Indian Pines datasets.We compared the performance of our proposed method with several state-of-the-art deep learning(DL)and machine learning(ML)algorithms,including long short-term memory(LSTM),deep neural network(DNN),recurrent neural network(RNN),support vector machine(SVM),and random forest(RF).Our experimental results demonstrate that the Hybrid MOBGWO-DQL significantly improves classification accuracy compared to traditional optimization and DL techniques.MOBGWO-DQL shows greater accuracy in classifying most categories in both datasets used.For the Indian Pine dataset,the MOBGWO-DQL architecture achieved a kappa coefficient(KC)of 97.68%and an overall accuracy(OA)of 94.32%.This was accompanied by the lowest root mean square error(RMSE)of 0.94,indicating very precise predictions with minimal error.In the case of the Pavia University dataset,the MOBGWO-DQL model demonstrated outstanding performance with the highest KC of 98.72%and an impressive OA of 96.01%.It also recorded the lowest RMSE at 0.63,reinforcing its accuracy in predictions.The results clearly demonstrate that the proposed MOBGWO-DQL architecture not only reaches a highly accurate model more quickly but also maintains superior performance throughout the training process.

Enhanced Multi-Objective Grey Wolf Optimizer with Lévy Flight and Mutation Operators for Feature Selection

The process of selecting features or reducing dimensionality can be viewed as a multi-objective minimization problem in which both the number of features and error rate must be minimized.While it is a multi-objective problem,current methods tend to treat feature selection as a single-objective optimization task.This paper presents enhanced multi-objective grey wolf optimizer with Lévy flight and mutation phase(LMuMOGWO)for tackling feature selection problems.The proposed approach integrates two effective operators into the existing Multi-objective Grey Wolf optimizer(MOGWO):a Lévy flight and a mutation operator.The Lévy flight,a type of random walk with jump size determined by the Lévy distribution,enhances the global search capability of MOGWO,with the objective of maximizing classification accuracy while minimizing the number of selected features.The mutation operator is integrated to add more informative features that can assist in enhancing classification accuracy.As feature selection is a binary problem,the continuous search space is converted into a binary space using the sigmoid function.To evaluate the classification performance of the selected feature subset,the proposed approach employs a wrapper-based Artificial Neural Network(ANN).The effectiveness of the LMuMOGWO is validated on 12 conventional UCI benchmark datasets and compared with two existing variants of MOGWO,BMOGWO-S(based sigmoid),BMOGWO-V(based tanh)as well as Non-dominated Sorting Genetic Algorithm II(NSGA-II)and Multi-objective Particle Swarm Optimization(BMOPSO).The results demonstrate that the proposed LMuMOGWO approach is capable of successfully evolving and improving a set of randomly generated solutions for a given optimization problem.Moreover,the proposed approach outperforms existing approaches in most cases in terms of classification error rate,feature reduction,and computational cost.

Multi-Objective Grey Wolf Optimization Algorithm for Solving Real-World BLDC Motor Design Problem

The first step in the design phase of the Brushless Direct Current(BLDC)motor is the formulation of the mathematical framework and is often used due to its analytical structure.Therefore,the BLDC motor design problem is considered to be an optimization problem.In this paper,the analytical model of the BLDC motor is presented,and it is considered to be a basis for emphasizing the optimization methods.The analytical model used for the experimentation has 78 non-linear equations,two objective functions,five design variables,and six non-linear constraints,so the BLDC motor design problem is considered as highly non-linear in electromagnetic optimization.Multi-objective optimization becomes the forefront of the current research to obtain the global best solution using metaheuristic techniques.The bio-inspired multi-objective grey wolf optimizer(MOGWO)is presented in this paper,and it is formulated based on Pareto optimality,dominance,and archiving external.The performance of theMOGWO is verified on standard multi-objective unconstraint benchmark functions and applied to the BLDC motor design problem.The results proved that the proposedMOGWO algorithm could handle nonlinear constraints in electromagnetic optimization problems.The performance comparison in terms of Generational Distance,inversion GD,Hypervolume-matrix,scattered-matrix,and coverage metrics proves that the MOGWO algorithm can provide the best solution compared to other selected algorithms.The source code of this paper is backed up with extra online support at https://premkumarmanoharan.wixsite.com/mysite and https://www.mathworks.com/matlabcentral/fileexchange/75259-multiobjective-non-sorted-grey-wolf-mogwo-nsgwo.

Competitive binary multi-objective grey wolf optimizer for fast compact antenna topology optimization

We propose a competitive binary multi-objective grey wolf optimizer(CBMOGWO)to reduce the heavy computational burden of conventional multi-objective antenna topology optimization problems.This method introduces a population competition mechanism to reduce the burden of electromagnetic(EM)simulation and achieve appropriate fitness values.Furthermore,we introduce a function of cosine oscillation to improve the linear convergence factor of the original binary multi-objective grey wolf optimizer(BMOGWO)to achieve a good balance between exploration and exploitation.Then,the optimization performance of CBMOGWO is verified on 12 standard multi-objective test problems(MOTPs)and four multi-objective knapsack problems(MOKPs)by comparison with the original BMOGWO and the traditional binary multi-objective particle swarm optimization(BMOPSO).Finally,the effectiveness of our method in reducing the computational cost is validated by an example of a compact high-isolation dual-band multiple-input multiple-output(MIMO)antenna with high-dimensional mixed design variables and multiple objectives.The experimental results show that CBMOGWO reduces nearly half of the computational cost compared with traditional methods,which indicates that our method is highly efficient for complex antenna topology optimization problems.It provides new ideas for exploring new and unexpected antenna structures based on multi-objective evolutionary algorithms(MOEAs)in a flexible and efficient manner.