A novel non-dominated sorting genetic algorithm for solving the triple objective project scheduling problem

Abstract

Multi-objective project scheduling has attracted wide attention for approximately two decades. However, most of the existing research has focused on the double-objective project scheduling problem, while literature on project scheduling problems with more than two objectives is rather scarce. In this paper, the typical multi-mode resource-constrained project scheduling problem is extended to a new triple-objective multi-mode project scheduling problem (TOMPSP) with the objectives of minimizing the project duration, minimizing the resource investment and maximizing the robustness of the schedule. To solve the presented triple-objective problem, we resort to the latest version of the multi-objective genetic algorithm, the non-dominated sorting genetic algorithm III (NSGA-III). In the decoding process of the NSGA-III, a modified SSGS (serial schedule generation scheme), in which resource constraints are relaxed, is suggested by considering the delays of activities. Although the NSGA-III shows excellent performance in numerous multi-objective optimization problems with more than two objectives, it has a potential disadvantage in that it occasionally cannot find the intercept during the adaptive normalization process, and thus, the population cannot be normalized as expected. Since a case without an intercept is impossible in the NSGA-II, we adopt the NSGA-II normalization process rather than that of NSGA-III. The standard instances in PSPLib are modified to serve as the instances of the TOMPSP, and a computational experiment is conducted to test the algorithms. The results show that the presented algorithm not only greatly simplifies the implementation of the NSGA-III but also significantly improves the execution efficiency and calculation quality.