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The net present value (NPV)-based resource constrained project scheduling problem (RCPSP) is a well-known scheduling problem in many industries, such as construction, software development, and manufacturing. Over the last five decades, although different approaches have been proposed to solve the problem, no single approach has been shown to achieve satisfactory performances with quality solutions for a wide range of problems. This study presents a hybrid immune genetic algorithm (IGA) to solve NPV-based RCPSPs. Hybridizing a genetic algorithm (GA) with an immune algorithm (IA) enhances the overall performance of their standalone components (i.e., only GA or IA). Performance of the proposed IGA is further improved by applying a variable insertion based local search (VINS) and forward-backward improvement (FBI). A restart mechanism is presented to the algorithm which induces diversity and helps to avoid becoming trapped in local optima. Moreover, an activity move rule (AMR) is implemented to shift the negative cash flow associated activities to further improve the NPV. Taguchi Design of Experiment (DOE) is conducted to investigate the impact of various parameters and to determine the appropriate set of parameters for the proposed IGA. The performances of the proposed algorithms are tested on 17,280 standard benchmark instances ranging from 25 to 100 activities. Comparison with the state-of-art algorithms through extensive numerical experiments reveal the effectiveness of the proposed algorithms. Overall, the proposed algorithm outperforms existing algorithms, particularly the projects with 0% and 100% negative cash flow associated activities, the 75-activity instances, and the projects with two resources usage in terms of a lower value of average percentage deviation. |
