Abstract: To obtain high-quality solutions and good performance solution sets during the optimization of many-objective Permutation Flow-shop Scheduling Problems(PFSP),a positive projection grey target model with comprehensive objective weight was proposed based on grey target theory,which could overcome the shortcoming of obtaining information in the optimization process.A PFSP mathematical model with four-objective and a grey target model in the field of multi-objective optimization were defined,then target distance was calculated to judge the pros and cons of Pareto front and to extract the uncertainty information among the objective function values.To solve the different target distances of Pareto front in same section plane and to get more information in the solution space,a Positive Projection Grey Target(PPGT)model was proposed.Further,to acquire the information of the volatility and the correlation among the objective function values,a novel comprehensive objective weight method based on CRITIC method and entropy weight method was introduced into PPGT model.The modified PPGT model was integrated into the genetic algorithm to solve the multi-objective PFSP.The effectiveness of the proposed method was verified by three sets of experiments and four comparison algorithms.

Key words: multi-objective optimization, permutation flow-shop scheduling, CRITIC method, entropy weight method, positive projection grey target, projective target distance, genetic algorithms

摘要： 为获得高维多目标置换流水车间调度问题的高质量解、良好性能解集,基于灰靶理论提出综合客观权重正向投影灰靶模型,解决多目标置换流水车间调度优化过程中信息获取不足的问题。首先,定义包含四目标调度问题的数学模型,同时在多目标优化领域中定义灰靶模型,用靶心距评判Pareto前端的优劣,提取目标函数值间的不确定性信息。为克服同一剖切面上不同Pareto前端的靶心距不同的问题,且更全面获取解空间信息,提出正向投影灰靶模型。进一步,在所提模型中引入由CRITIC法和熵权法组合的综合客观权重,提取目标函数值间的波动性和相关性信息,建立综合客观权重正向投影灰靶模型。将模型与遗传算法结合,提出基于正向投影灰靶模型的多目标进化算法求解高维多目标置换流水车间调度问题。通过3组实验,4种比较算法,验证了所提方法的有效性。

关键词: 多目标优化, 置换流水车间调度, CRITIC法, 熵权法, 正向投影灰靶, 投影靶心距, 遗传算法