Multi-objective Resource Constrained Project Scheduling Problem Based On NSGA-?

With the development of social economy,the complexity of projects is increasing,the requirements for project management techniques are gradually increasing.The classic resource-constrained project scheduling problem usually considers the deterministic durations and try to find the shortest finish time of the project under the constraint conditions.Through literature review,we found that the actual project duration is usually uncertain and managers usually have to consider multiple dimensions of goals at the same time.Therefore,studying the scheduling problem of multi-objective resource-constrained projects under uncertain duration is not only of theoretical significance,but also of practical application value.First of all,through the compilation of resource-constrained project scheduling literature in recent years,this paper divides the common objective functions into three types: duration,cost and robustness,then we start from the basic model,establishing a multi-objective resource-constrained project scheduling model.Considering that different documents have different definitions of robustness,this paper defines robustness as the weighted sum of the buffer time of sub-activities.Secondly,through the comparison of the model structure analysis and the multiobjective solution method,we select the multi-objective optimization genetic algorithm NSGA-II to solve the model.In order to meet the constraints of the activity sequence,we design a set-based cross-mutation operator and chromosome encoding scheme and optimize the original crowding degree calculation method.Then we solve this algorithm through Python language.We use the solution set coverage index to compare the solution results of NSGA-II and the original NSGA-II to verify the effectiveness of the improved algorithm.After that,we build a project schedule plan that satisfies the Pareto domination relationship by modeling the project data of H company,and prove the effectiveness of the model and algorithm through examples.Finally,for the multi-mode problem,we design a multi-mode cost-duration dualobjective model combine with the previous multi-objective model and algorithm.The original NSGA-II algorithm was improved to solve the J10 and J20 data in PSPLIB,and results illustrate the relationship between construction period and cost.