A Hybrid Cross-entropy Algorithm Solves Complex Scheduling Problems In Fuzzy Distributed Pipelines

Production scheduling,which directly affects the efficiency and competitiveness of enterprises,is an important link in the manufacturing system.The research and application of efficient optimization technologies and scheduling methods are the key to achieve energy saving,consumption reduction,emission reduction,cost reduction and improvement of the optimality of the production system.The distributed permutation flow-shop scheduling problem(DPFSP)and its derivative problems are based on the background of distributed manufacturing such as cooperative production between different companies or collaborative production between different factories.DPFSP studies the distribution of workpieces between factories and the processing sequence in each factory to achieve the optimal of scheduling indicators.However,since most of the actual production processes have uncertain factors,the use of fuzzy numbers in the fuzzy theory to represent the uncertain processing time will help to describe the actual production process more objectively and provide guidance for the production process.Therefore,studying the fuzzy distributed permutation flowshop complex scheduling problem and the corresponding algorithm has high theoretical and practical value.This paper studies the fuzzy distributed flow-shop complex scheduling problem and the intelligent algorithm to solve the problem.The main contents are as follows:(1)On the basis of the classic problem,that is DPFSP,the model of the distributed permutation flow-shop scheduling problem with fuzzy processing time(DPFSP?FPT)is established via considering the uncertainty of processing time which widely exists in the real-world production process.DPFSP?FPT uses fuzzy number to represent each job's processing time and its optimization objective is the fuzzy maximum completion time.Then,an improved cross-entropy(ICE)algorithm is proposed for solving the DPFSP?FPT.To improve the performance of the cross-entropy algorithm,the ICE algorithm introduces local search and perturbation operations.Finally,Simulations and comparisons demonstrate the effectiveness of the proposed algorithm.(2)On the basis of(1),the model of the distributed permutation flow-shop low-carbon scheduling problem with fuzzy processing time(DPFLSP?FPT)is established via considering the requirements of energy saving and emission reduction in actual production.DPFLSP?FPT uses fuzzy number to represent each job's processing time and its optimization objectives are the fuzzy maximum completion time and the fuzzy total energy consumption.Then,a hyper-heuristic cross-entropy(HHCE)algorithm is proposed for solving the DPFLSP?FPT.Firstly,HHCE algorithm adopts a novel ranking rule of triangular fuzzy number to reasonably calculate the objective function values of individuals,which is helpful in finding the promsing regions more accurately during the search process.Secondly,in the upper layer,HHCE algorithm utilizes an evaluation method based on the contribution rate to estimate the permutations constructed by eight special neighbor operations,and also uses the cross-entropy algorithm to learn the information of better permutations and generate new permutations.Then,for searching more different regions in solution space,HHCE algorithm uses each permutation generated in the upper layer as a heuristic to perform a series of neighbor operations on the corresponding individuals in the lower layer.Thirdly,in order to enhence its ability of obtaining the non-dominated individuals or solutions with low energy consumption,HHCE algorithm utilizes an energy-saving strategy based on non-critical path to perform local search on better individuals of each generation.Finally,Simulations and comparisons demonstrate the effectiveness of the proposed algorithm.(3)On the basis of(2),the model of the fuzzy distributed assembly permutation flow-shop low-carbon scheduling problem(FDAPFLSP)is established via considering product assembly after production is completed.FDAPFLSP uses fuzzy numbers to represent each job's processing time and each product's assembly time and its criteria are the minimization of both the fuzzy maximum completion time and the fuzzy total energy consumption.Then,a hybrid cross-entropy algorithm(HCEA)is proposed for solving the FDAPFLSP.Firstly,a practical ranking correction rule of triangular fuzzy number is designed via analyzing the characteristics of the commonly used ranking rules of triangular fuzzy number and considering the basic constraints of the production scheduling problem.Secondly,HCEA adopts variable neighborhood local search with adaptive selection probability,which can efficiently search different regions in solution space and further enhance the performance of the algorithm.Finally,Simulations and comparisons demonstrate the effectiveness of the proposed algorithm.