Kernel-based hybrid multi-objective optimization algorithm (KHMO)

A new hybrid evolutionary algorithm named Kernel-based Hybrid Multi-Objective Optimization Algorithm (KHMO) is introduced in this work. The main novelty of this algorithm is its updating rule based on the concept of a reproducing kernel in order to properly approximate the numerical gradient. In addition, a novel numerical strategy based on the computation of a normal vector to determine a searching target direction that guides the nondominanted solutions into more propitious regions is also introduced for the first time. IGD and HV metrics are used to evaluate the performance of KHMO algorithm against other competitive multi-objective methods such as MRBFO, FDEA-I, VMEF, BiasMOSaDE and GAMODE tested on ZDT and CEC 2009 problems. Moreover, the Wilcoxon test is carried out as a comparative statistical analysis in order to detect if a significant difference exists with respect to the rest of the algorithms. The corresponding numerical results showed that the introduced KHMO algorithm gains the best overall performance among all the compared algorithms in terms of diversity, coverage and convergence in most problems. Moreover, IGD and HV curves reveal a respectable convergence rate since nearly 200 iterations are enough to offer quality solutions.