Abstract: Cutting tools are important resources for machining,and the number of them determines the number of sublots that can be machined simultaneously.To solve this parallel machine equally lot-sizing and scheduling problem under the limited number of sublots,special constraints such as tool number and tool replacement were formulated.Correspondingly,a bi-objective mathematical programming model was constructed to minimize the maximum completion time and maximal deviation of jobs’ delivery time so as to promote the production productivity and ensure the punctuality and synchronization in delivery of all jobs in an order.A bi-objective whale swarm algorithm incorporating fast non-dominated sorting was proposed to solve this problem.Specifically,a fixed-length encoding allowing variations of the number of sublots was designed by introducing virtual placeholders;a multi-point preservative crossover strategy was incorporated into the design of individual movement rules so as to cross the sub-lot assignment vector,keep the sub-lot sequence unchanged and enhance the diversity of solutions;a non-inferior individual preservation strategy was embedded into the neighborhood search to guide the algorithm to jump out of the local optimum.Experimental results showed that the convergence and diversity of the proposed algorithm were significantly better than those of the comparison algorithms,which was beneficial to simultaneously achieving two production goals,punctuality and effectiveness.

Key words: cuttling tools, limited number of sublots, parallel machine scheduling, lot-sizing and scheduling, whale swarm algorithm, machining

摘要： 刀具是机械加工的重要资源,刀具数量决定了能同时加工的工件批次上限。针对此类批次受限的并行机等量分批调度问题,建立了刀具数量和刀具更换等特有约束,构建了双目标数学规划模型,以完工时间和交付时间偏差最大值的最小化为目标,力求提高生产效率、保证同一订单内工件准时且同步交付。提出融入快速非支配排序的双目标鲸鱼群算法,通过引入虚拟占位符,设计出允许批次数变化的定长编码;将多点保留交叉策略融入到个体移动规则设计中,以便跨越子批赋值向量、保持子批序列不变、增强解的多样性;将非劣个体保留策略嵌入到邻域搜索中,指导算法跳出局部最优。实验结果表明,所提算法的收敛性与多样性显著优于对比算法,有利于同时达到准时、高效的生产目标。

关键词: 刀具, 批次受限, 并行机调度, 分批调度, 鲸鱼群算法, 加工