A novel heuristic, based on a new robustness concept, for multi-objective project portfolio optimization

•The problem of multi-objective project portfolio optimization with interval uncertainties is addressed.•A resource-wise robustness measure of a portfolio, based on the resource waste degree of that portfolio is defined.•A new objective-wise robustness index of a portfolio, based on the preferential weights of that portfolio is presented.•The relationship between the two newly defined resource-wise and objective-wise robustness index of a portfolio is deduced.•A new and accurate algorithm for generating robust portfolios is provided and applied in a case study in the port industry. In this paper, multi-objective project portfolio optimization problem, with interval uncertainties, is addressed. Due to the existence of internal and external uncertainties, the robust optimization approach is selected. We have defined and examined the robustness in terms of resources, in which, uncertainty can be the cause of wasted resources. On the other hand, the existing methods in the literature measure robustness in terms of the objective functions. These methods, which implicitly suppose equal objective weights, use the measure of the diameter of sensitivity region of a solution as robustness index. This is in contradiction to the philosophy of the posterior preferences decision-making approach. Therefore, we have proposed a novel robustness index based on the new concept of preferential weights of each portfolio and deduced a formula based on the normal vectors of bounding hyperplanes of the Pareto frontier. Then, the relationship between the two newly defined robustness indexes is investigated. Finally, an efficient heuristic is developed and applied in a case study as well as a numerical example. In addition, our proposed robustness concept is compared to an existing concept in the literature. Results show the effectiveness and efficiency of the presented concept and the proposed algorithm.