A population-based incremental learning vector algorithm for multiobjective optimal designs

To alleviate the deficiency of crossover and mutation operations in standard genetic algorithms, the population-based incremental learning (PBIL) method is extended for multiobjective designs of inverse problems. To quantitatively measure the number of improvements in the whole objective functions and to quantify the amount of improvements in a specific objective function, a novel metric is proposed to penalize the fitness of a solution. Moreover, a selecting strategy for the best solutions of the latest iterations of an individual is introduced. Furthermore, multiple probability vectors are employed to enhance the diversity of the found solutions. Numerical experiments on low- and high-frequency inverse problems are carried out to demonstrate the feasibility of the proposed vector PBIL algorithm for hard multiobjective engineering inverse problems.