In practical engineering tasks, multi-objective topology optimization (TO) problems often arise, thus requiring the introduction of the concept of Pareto-optimal solutions. In this article, a novel gradient-informed Pareto-based multi-objective TO algorithm with binary decision variables, called GPBTO, is proposed. Without loss of generality, GPBTO is tailored to solving constrained bi-objective optimization problems (CBOPs), which represents a standard case in many engineering applications. The binary space of the decision variables together with a linearization step of objectives and constraints allows efficient integer linear programming (ILP) techniques to be used for the evolution of the decision vector. The proposed algorithm represents an effective tool for solving the TO task with traditional gradient-based formulations bypassing the limitations of weighted sum (WS) approaches usually adopted in this context. Thanks to the simple implementation, the proposed GPBTO algorithm can be readily adopted for solving multi-objective TO problems involving binary decision variables. While WS is an out-of-date technology for solving multi-objective optimization problems due to its limitations, it is well-known that in the framework of TO is still the state of the art. To the author's knowledge, this is the first time that an attempt to solve Pareto-based TO with binary variables and gradients has been proposed.