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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 efficient 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.

In multiobjective optimization, the result of an optimization algorithm is a set of efficient solutions from which the decision maker selects one. It is common that not all the efficient solutions can be computed in a short time and the search algorithm has to be stopped prematurely to analyze the solutions found so far. A set of efficient solutions that are well-spread in the objective space is preferred to provide the decision maker with a great variety of solutions. However, just a few exact algorithms in the literature exist with the ability to provide such a well-spread set of solutions at any moment: we call them anytime algorithms. We propose a new exact anytime algorithm for multiobjective combinatorial optimization combining three novel ideas to enhance the anytime behavior. We compare the proposed algorithm with those in the state-of-the-art for anytime multiobjective combinatorial optimization using a set of 480 instances from different well-known benchmarks and four different performance measures: the overall non-dominated vector generation ratio, the hypervolume, the general spread and the additive epsilon indicator. A comprehensive experimental study reveals that our proposal outperforms the previous algorithms in most of the instances.

In this work, we solve the problem of finding the best locations to place stations for depositing/collecting shared bicycles. To do this, we model the problem as the p-median problem, that is a major existing localization problem in optimization. The p-median problem seeks to place a set of facilities (bicycle stations) in a way that minimizes the distance between a set of clients (citizens) and their closest facility (bike station). We have used a genetic algorithm, iterated local search, particle swarm optimization, simulated annealing, and variable neighbourhood search, to find the best locations for the bicycle stations and study their comparative advantages. We use irace to parameterize each algorithm automatically, to contribute with a methodology to fine-tune algorithms automatically. We have also studied different real data (distance and weights) from diverse open data sources from a real city, Malaga (Spain), hopefully leading to a final smart city application. We have compared our results with the implemented solution in Malaga. Finally, we have analyzed how we can use our proposal to improve the existing system in the city by adding more stations.