We consider a resource allocation problem in which the decision maker is responsible for selecting a group of projects to generate a portfolio, with the aim of maximizing the total benefit, and distributing the budget in a balanced way across different categories. We assume that the decision maker defines an interval for the desired share of each category. We propose augmented -constraint method to generate the nondominated solutions considering two objective functions: total benefit and balance among categories. The solution time increases with the problem size, and augmented -constraint method fails to find all nondominated solutions. We therefore develop a variable neighborhood search algorithm for the purpose of generating the nondominated frontier. Our computational experiments show that the nondominated frontier can be accurately estimated with respect to different performance measures.