The Next Release Problem consists in selecting a subset of requirements to develop in the next release of a software product. The selection should be done in a way that maximizes the satisfaction of the stakeholders while the development cost is minimized and the constraints of the requirements are fulfilled. Recent works have solved the problem using exact methods based on Integer Linear Programming. In practice, there is no need to compute all the e cient solutions of the problem; a well-spread set in the objective space is more convenient for the decision maker. The exact methods used in the past to find the complete Pareto front explore the objective space in a lexicographic order or use a weighted sum of the objectives to solve a single-objective problem, finding only supported solutions. In this work, we propose five new methods that maintain a well-spread set of solutions at any time during the search, so that the decision maker can stop the algorithm when a large enough set of solutions is found. The methods are called anytime due to this feature. They find both supported and non-supported solutions, and can complete the whole Pareto front if the time provided is long enough.

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Metaheuristics for solving multiobjective problems can provide an approximation of the Pareto front in a short time, but can also have difficulties finding feasible solutions in constrained problems. Integer linear programming solvers, on the other hand, are good at finding feasible solutions, but they can require some time to find and guarantee the efficient solutions of the problem. In this work we combine these two ideas to propose a hybrid algorithm mixing an exploration heuristic for multiobjective optimization with integer linear programming to solve multiobjective problems with binary variables and linear constraints. The algorithm has been designed to provide an approximation of the Pareto front that is well-spread throughout the objective space. In order to check the performance, we compare it with three popular metaheuristics using two benchmarks of multiobjective binary constrained problems. The results show that the proposed approach provides better performance than the baseline algorithms in terms of number of the solutions, hypervolume, generational distance, inverted generational distance, and the additive epsilon indicator.