Abstract: To solve a kind of task assignment problem of large-scale engineering project under multiple work calendars,a multi-objective optimization method was proposed.A multi-objective task assignment optimization model under multiple work calendars was established with the objective to minimize project cost and project duration.A time reckoning method based on multiple work calendars was proposed as a critical technology to solve the researched problem.A fast elitist Non-dominated Sorting Genetic Algorithm (NSGA-Ⅱ) was designed to solve the optimization model,in which an integer coding method based on contractor number was used to encode the chromosome,a two-point crossover method was used in crossover operation,and a single-point mutation method was used in mutation operation.The refusal strategy was used in the population initialization to ensure feasibility of the chromosomes,and a repair strategy was used in mutation operation to ensure feasibility of the offspring chromosomes.Project cost was obtained by summing up task cost got according to task cost array and contractor number array.Task time was obtained according to task time array and contractor number array.The earliest start time and finish time of each task were obtained based on critical path method by forward reckoning function FC.Project duration was got according to earliest start time and finish time of each task.At the end of evolution,a Pareto solution set was output to worksheet “Pareto solution set”.When the decision maker double-clicks on a Pareto solution,a scheduling matrix could be obtained by forward reckoning function FC and inverse reckoning function IC based on critical path method.The application result showed that the proposed method could effectively solve the multi-objective task assignment problem of large-scale engineering project under multiple work calendars.

Key words: task assignment, multiple work calendars, largescale engineering projects, multi-objective optimization, fast elitist non-dominated sorting genetic algorithm, time reckoning

摘要： 为解决多工作日历下大型工程项目任务指派问题,提出一种多目标优化方法。建立了以项目工期最短、成本最低为优化目标,考虑多工作日历约束的大型工程项目多目标任务指派优化模型;提出基于多工作日历的时间推算方法,解决了多工作日历下工程项目任务指派的关键问题。设计了带精英策略的快速非支配排序遗传算法求解优化模型,其中编码采用基于承包商号的整数编码方式,交叉操作采用两点交叉方式,变异操作采用单点变异方式。种群初始化采用拒绝策略以保证个体可行性,变异过程采用修复策略以保证子代个体的可行性。解码操作根据各任务被指派的承包商号数组,在任务成本数组中查出任务成本,对各任务成本求和得到项目成本;在任务时间数组中查出任务时间,基于关键路径法采用正向推算函数FC得到各任务最早开工时刻、最早完工时刻,进而求出项目工期。进化结束后将所得到的Pareto解集存入工作表“Pareto解集”,当决策人员双击某个Pareto解时,算法基于关键路径法采用正向顺推函数FC和反向逆推函数IC得到其对应的调度矩阵。通过案例分析验证了所提方法的有效性。

关键词: 任务指派, 多工作日历, 大型工程项目, 多目标优化, 带精英策略的快速非支配排序遗传算法, 时间推算