دانلود رایگان مقاله انگلیسی الگوریتم ژنتیک برای زمانبندی پروژه با محدودیت منابع پیشگیرانه با تقسیم فعالیت - IEEE 2018

Abstract

Proactive scheduling aims at the generation of robust baseline schedules, which has been studied for many years with the assumption that activity splitting is not allowed. In this paper, we focus on the proactive resource-constrained project scheduling problem in which each activity can be split at discrete time instants under the constraints of a maximum number of splitting and a minimum period of continuous execution. In this problem, setup times are also considered. A mathematical model is established and analyzed, of which two properties and one lemma are proposed. As the problem is proved to be NP-hard in the strong sense, for solving the model, we develop a genetic algorithm (GA) in which the two proposed properties and the lemma are applied as local search operators. After linearizing the proposed model, we use a commercial mathematical programming solver as a benchmark to solve the problem. From the computational results, we find that the developed GA is effective and efficient in solving the defined problem, and activity splitting improves robustness. With the growth of the maximum number of splitting, the decline in the minimum execution time, the decrease in the setup times, and the extension of the project due date, robustness increases.

V. CONCLUSIONS

This paper presents a proactive RCPSP with activity splitting where each activity can be split at discrete time instants under the constraints of a maximum number of splitting and a minimum period of continuous execution. Besides, in this problem setup times are considered. Based on the analysis of the established model, two properties and one lemma are proposed and applied in our developed GA to improve the local search efficiency. In addition, after linearizing the proposed model, we use a commercial software as a benchmark to solve the problem. A computational experiment that is performed on datasets generated by the ProGen is designed and executed, from which the following conclusions are drawn.

1) The two developed properties and the proposed lemma can be used to maximize the objective function, and the GA with a combination of the three local search operators performs the best.

2) Compared with commercial software, the developed GA is much more efficient to solve the proposed scheduling problem, and the gap in terms of the objective function value is acceptable.

3) Due to the increase in flexibility of executing activities, activity splitting enhances the robustness of baseline schedules that are likely to have lower adjustment costs during project execution. Compared with the classic proactive scheduling models where activity splitting is not allowed, this paper offers a new method to improve schedule robustness when activity splitting is allowed and generates better solutions to project management.

4) With the growth of the maximum number of splitting, the decline in the minimum execution time, the decrease in the setup times, and the extension of the project due date, schedule robustness increases.