An Improved S-Metric Selection Evolutionary Multi-Objective Algorithm with Adaptive Resource Allocation

One of the main disadvantages of evolutionary multi-objective algorithms (EMOAs) based on hypervolume is the computational cost of the hypervolume computation. This deficiency gets worse either when an EMOA calculates the hypervolume several times or when it is dealing with problems having more than three objectives. In this sense, some researchers have designed strategies to reduce the number of hypervolume calculations. Among them, the use of the locality property of the hypervolume has emerged as an alternative to deal with this problem. This property states that if a solution is moving in its neighborhood, only its contribution is affected and the contributions of the rest of the solutions remain the same. In this paper, we present a novel evolutionary approach that exploits the locality property of the hypervolume. The proposed approach adopts a probability to use two or three individuals in its environmental selection procedure. In this way, it only needs to compute two or three hypervolume contributions per iteration. The proposed algorithm is evaluated by solving the standard benchmark test problems and two real-world applications where the features of the problems are unknown. According to the results, the proposed approach is a promising alternative for solving problems with a high number of objectives because of three main reasons: 1) it is competitive with respect to the state-of-the-art EMOAs based on hypervolume; 2) it does not need extra information about the problem (which is particularly essential when solving real-world applications); and 3) its computational cost is much lower than the other hypervolume-based EMOAs.