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.This research has been partially funded by the Spanish Ministry of Economy and Competitiveness (MINECO) and the European Regional Development Fund (FEDER) under contract TIN2017-88213-R (6city project), the European Research Council under contract H2020-ICT-2019-3 (TAILOR project), the University of Málaga, Consejería de Economía y Conocimiento de la Junta de Andalucía and FEDER under contract UMA18-FEDERJA-003 (PRECOG project), the Ministry of Science, Innovation and Universities and FEDER under contract RTC-2017-6714-5, and the University of Málaga under contract PPIT.UMA.B1.2017/07 (EXHAURO Project)
