The Improved Distribution Estimation Algorithm Solves The Low-carbon Flow Shop Scheduling Problem

With the development of science and technology and the progress of society,intelligent manufacturing has gradually become the development trend of production and manufacturing.Intelligent manufacturing requires companies to play an important role in green development,resource allocation,data analysis and scheduling decisions.The optimal scheduling has the characteristics of NP hard,multi-local optimality,uncertainty,multi-objective,multi-constraint and nonlinear.Estimation of Distribution Algorithm(EDA)is a novel stochastic optimization algorithm based on probability and statistics in the field of evolutionary computing.While intelligent manufacturing brings economic benefits,it also brings great environmental pressures and energy-saving pressures,such as the greenhouse effect caused by carbon dioxide emissions,and a large amount of energy consumption.Therefore,it is of great significance to use EDA and its improved algorithm to solve the low-carbon flow shop scheduling problem.In this paper,EDA and its improved algorithm are applied to solve two kinds of important shop scheduling problems.The main tasks as follows:(1)In this paper,an Estimation of Distribution Algorithm Based on Bayesian Statistical Inference(BSIEDA)is proposed to solve the Low Carbon Flow-shop Scheduling Problem(FSP_LC).The criterion is to minimize the maximum completion time and carbon emissions.First,the population initialization strategy is designed;then,the Bayesian Network Probability Model(BNPM)is added;Finally,an Insert neighborhood structure is designed to improve the local search ability of the algorithm.The simulation experiment and algorithm comparison verify the effectiveness of the proposed algorithm.(2)For the research of low-carbon flow shop scheduling problem,based on the problem model of(1),the distributed flow shop scheduling is introduced.In the context of globalization,with the increasing popularity of production cooperation and corporate mergers between companies,distributed manufacturing has become a common production model.For the Low Carbon Distributed Flow-shop Scheduling Problem(DFSP_LC),an Improved Estimation of Distribution Algorithm Based on Bayesian Statistical Inference(IBSIEDA)is proposed.Firstly,the Latest Completion Factory rule for the problem are proposed.Then,the reverse decoding rule(Reverse LCF,RLCF)based on the problem solution is designed.This rule can map the subsequence to a unique new solution,thus preserving the high-quality solution's structural information.Finally,the neighborhood structure with mutation operation is designed to realize the local search of three different insert operator,i.e.,solution-based insert,inter-factory insert,and intra-factory.The simulation experiment and algorithm comparison verify the effectiveness of the proposed algorithm.(3)For the low-carbon distributed flow shop scheduling problem,based on the algorithm model of(2),further research on IBSDIDA is carried out,and Fourdimensional Matrix Based on Ordered Relationship(OFDM)is added.An Enhanced Estimation of Distribution Algorithm Based on Ordered Relationship(OEEDA)is proposed.In the first stage of OEEDA,IBSIEDA is utilized to perform the global search in the problem's solution space for a certain period of time,with the purpose of fining good solutions and storing them in the non-dominated set.In the second stage of OEEDA,OFDM is proposed to effectively learn and accumulate the excellent solutions' information of ordered relationship,i.e.,the information of job blocks and their corresponding positions.Then,a sampling scheme that fixes some blocks in the solution is designed to guide the global search direction more clearly.At the same time,the block structure-based search structure and various insert search methods are designed,which makes the algorithm achieve a good balance between global and local search.The simulation experiment and algorithm comparison verify the effectiveness of the proposed algorithm.