New Probabilistic, Dynamic Multi-Method Ensembles for Optimization Based on the CRO-SL

In this paper, new probabilistic and dynamic (adaptive) strategies for creating multi-method ensembles based on the coral reef optimization with substrate layers (CRO-SL) algorithm are proposed. CRO-SL is an evolutionary-based ensemble approach that is able to combine different search procedures for a single population. In this work, two different probabilistic strategies to improve the algorithm are analyzed. First, the probabilistic CRO-SL (PCRO-SL) is presented, which substitutes the substrates in the CRO-SL population with tags associated with each individual. Each tag represents a different operator which will modify the individual in the reproduction phase. In each generation of the algorithm, the tags are randomly assigned to the individuals with similar probabilities, obtaining this way an ensemble that sees more intense changes with the application of different operators to a given individual than CRO-SL. Second, the dynamic probabilistic CRO-SL (DPCRO-SL) is presented, in which the probability of tag assignment is modified during the evolution of the algorithm, depending on the quality of the solutions generated in each substrate. Thus, the best substrates in the search process will be assigned higher probabilities than those which showed worse performance during the search. The performances of the proposed probabilistic and dynamic ensembles were tested for different optimization problems, including benchmark functions and a real application of wind-turbine-layout optimization, comparing the results obtained with those of existing algorithms in the literature.