多项目环境下time-cost置换问题建模与求解

针对多项目环境下的time-cost置换问题，以活动资源为决策变量，建立了以各项目总延迟最小与总成本最小的双目标time-cost置换模型。在总结前人对于多目标优化求解方法的基础上，针对多项目的特点，提出了基于NSGA-II非劣排序的局部直接搜索改进遗传算法，并考虑资源为连续与离散两种情况进行求解。与NSGA-II相比，算法可以较快地收敛到最优解，并且具有较好的离散变量搜索能力，与ZDT系列测试函数的比较也体现了算法的优越性。

Model and resolution approach for problem of multi-project time-cost trade-off

For the time-cost trade-off problem with multi-project condition,this paper develops a bi-objective model that the decision variables are the allocated resource quantities,and the objective functions are the projects delay（to be minimized） and the project costs（min）.After summarizing other researchers’multi-objective evolution algorithms and considering the characteristics of multi-project,this paper puts forward a local direct search technology based on Nondominated Sorting Genetic Algorithm II（NSGA-II）.It adopts discrete-continuous decision variables to settle the problem.Compared with NSGA-II,the approved algorithm can find the optimal solutions rapidly,moreover,for discrete variables,the algorithm can also run better.Finally,it compares the improved algorithm to ZDT test problems,the algorithm is superior similarly.