Cross-entropy Evolutionary Algorithm To Solve The Balancing Problem Of Complex U-shaped Assembly Line

Assembly is generally the final sta ge of product production and occupies an important position in the manufacturing industry.Assembly line i s the main way to achieve product assembly.With the rapid development of today's advanced manufacturing and artificial intelligence technology,assem bly line systems are also gradually developing towards intelligence,integration and greenness.The assembly line balancing problem(ALBP)mainly studies how to reasonably allocate a series of tasks with precedence constraints and independent working-time to different stations of the assembly line to improve the efficiency of the assembly line system.It is a n important NP-hard combinatorial optimization problem which is studied in the manufacturing field for a long time.Compared with the tr aditional straight layout assembly line,the U-shaped assembly line has adv antages in efficiency,flexibility and space utilization.As an important part of lean production,it is widely used in various manufacturing companies.Therefore,the U-shaped assembly line balance problem(UALBP)has become a hot issue in ALBP research in recent years.Cross-entropy(CE)method is a stochastic optimization method based on the principle of cross entropy,which associating the optimization problems with their associated probability estimation problems.Evolutionary algorithms based on Cross-entropy method generally generate a new population by updating and sampling the probability model of parameters corresponding to rare events in order to guide the search direction to approximate the optimal or suboptimal solution of the problem.In recent years,the evolutionary algorithm based on the CE method has been successfully used in many combinatorial optimization problems.Therefore,in this paper,three types of complex U-shaped assem bly line balancing problems based on actual production scenarios are studied using the evolutionary algorithm based on the CE method.main tasks as follows:(1)Aiming at the mixed-model U-shaped assembly line balancing problem(MMUALBP)with the maximum comprehensive index of line efficiency and variation of workload,a hybrid cross-entropy algorithm(HCEA)is proposed.First,in the coding stage of algorithm,an efficient task selection factor based coding(TSFBC)is adopted for the task allocation problem of UALBP.Then,at the global stage of the algorithm,an evolutionary search strategy based on the cross-entropy method is used to guide the search direction by updating and sampling the parameters of the corresponding probability model to generate a new po pulation.Secondly,in the local search stage,a variable neighborhood strategy(VNS)based on three types of neighborhood operations is used to improve the algorithm's ability to jump out of local optimum.Finally,the effectiveness of the a lgorithm is verified through simulation experiments under several scale s of calculation examples.(2)Aiming at the U-shaped robotic assembly line balancing problem(U RALBP)with the minimum energy consumption index,an enhanced cross-entropy algorithm(ECEA)is proposed to solve it.First,in the global phase of algorithm,the sub-sequence of task assignment and robot assignment are generated by sampling the cross-entropy probability model.Then the local search based on the simulated annealing(SA)mechanism is adopted to improve the defect of the premature convergence.Finally,contrast simulation experiments verify the effectiveness of the algorithm.(3)Aiming at the Man-Robot Cooperation U-shaped Assembly Line Balancing Problem(MRCUALBP)with the minimum index of cost and the maximum comprehensive index of line efficiency and variation of workl oad,a Co-evolutionary Algorithm based on Cross-entropy(CE)method and genetic algorithm(GA)(CE-GA Co-evolutionary,CE-GACEA)is proposed.Firstly,the mathema tical model of MRCUALBP is proposed.Then,in the global phase of algorithm,the sub-spaces of solution determined by the sub-sequence of the task? robot and assistant assignment are searched by GA and CE to enrich the direction of algorithm optimization.Secondly,the merge-split mechanism of population is adopted in the local search stage of the algorithm to balance the global and local search of t he algorithm.Finally,contrast simulation experiments verify that the algorithm is an effective algorithm to solve this problem.