In this study, a model for the selection of investment portfolios is proposed with three objectives. In addition to the traditional objectives of maximizing profitability and minimizing risk, maximization of social responsibility is also considered. Moreover, with the purpose of controlling transaction costs, a limit is placed on the number of assets for selection. To the best of our knowledge, this specific model has not been considered in the literature to date. This model is difficult (NP-Hard), and therefore, only very small instances may be solved in an exact way. This paper proposes a method based on tabu search and multiobjective adaptive memory programming (MOAMP) strategies. With this method it is possible to obtain sets of nondominated solutions in short computational times. To check the performance of our method it is compared with adaptations of the nondominated sorting genetic algorithm (NSGA-II), strength Pareto evolutionary algorithm (SPEA-II) and multiobjective particle swarm optimization (MOPSO). The results of different computational experiments show that our tabu search-MOAMP method performed best. The quality of the sets of solutions that were obtained and the speed of execution mean that our tabu search-MOAMP can be used as a tool for financial assessment and analysis (including online services). This tool, as we can see in this work with some examples, can take into account the social concerns of many clients and their overall risk profile (very conservative, conservative, moderate, or fearless). This approach is also in line with current legal regulations that oblige financial advisors to take the client profile into account to provide greater protection and propose good financial advice.