资源约束下产品开发任务调度的多目标优化

鉴于产品开发任务调度过程中存在资源约束问题和学习与遗忘效应，需要对多个目标进行优化决策，通过定义资源平均利用率并提出学习遗忘效应矩阵，结合耦合设计的多阶段迭代模型，以各阶段资源利用率为约束条件，建立资源约束下考虑学习与遗忘效应的任务调度时间与成本的多目标优化数学模型。采用带精英策略的非支配排序遗传算法求解得出Pareto最优解集，并采用改进的多目标理想点法对该解集进行选优，得到最优任务调度方案。以某电动汽车的开发过程为例，验证了该优化模型能够减小产品开发时间，降低产品开发成本，提高总资源利用率。

Multi-objective optimization of product development task scheduling under resource constraints

In the process of product development task scheduling,there are resource constraints and learning and forgetting effects,which usually require optimization decisions for multiple objectives.By defining the average resource utilization rate,a learning forgetting effect matrix was proposed.By combining with the multi-stage iterative model of coupling design and taking the resource utilization rate of each stage as a constraint,a multi-objective optimization mathematical model of task scheduling time and cost with learning and forgetting effects under resource constraints was established.The Pareto optimal solution set was solved with the improved NSGA-Ⅱgenetic algorithm,and the solution set was optimized by the improved multi-objective ideal point method to obtain the optimal task scheduling scheme.Taking the development process of an electric vehicle as an example,it verified that the optimization model could reduce product development time,reduce product development costs and increase the overall resource utilization rate.