In collaboration with Payame Noor University and the Iranian Society of Instrumentation and Control Engineers

Document Type : Research Article


1 Faculty of Mathematical Sciences‎, ‎Department of Applied Mathematics, Ferdowsi University of Mashhad‎, ‎Mashhad‎, ‎Iran.

2 Mosaheb Institute of Mathematics‎, ‎Kharazmi University‎, ‎Tehran‎, ‎Iran‎.



Project portfolio selection is a critical challenge for many organizations as they often face budget constraints that limit their ability to support all available projects‎. ‎To address this issue‎, ‎organizations seek to select a feasible subset of projects that maximizes utility‎. ‎While several models for project portfolio selection based on multiple criteria have been proposed‎, ‎they are typically NP-hard problems‎. ‎In this study‎, ‎we propose an efficient Variable Neighborhood Search (VNS) algorithm to solve these problems‎. ‎Our algorithm includes a formula for computing the difference value of the objective function‎, ‎which enhances its accuracy and ensures that selected projects meet desired criteria‎. ‎We demonstrate the effectiveness of our algorithm through rigorous testing and comparison with a genetic algorithm (GA) and CPLEX‎. ‎The results of the Wilcoxon non-parametric test confirm that our algorithm outperforms both GA and CPLEX in terms of speed and accuracy‎. ‎Moreover‎, ‎the variance of the relative error of our algorithm is less than that of GA‎.


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