### A Multiobjective Evolutionary Algorithm Using Gaussian Process-Based Inverse Modeling

Abstract

To approximate the Pareto front, most existing multiobjective evolutionary algorithms store the nondominated
solutions found so far in the population or in an external archive during the search. Such algorithms often
require a high degree of diversity of the stored solutions and only a limited number of solutions can be achieved.
By contrast, model-based algorithms can alleviate the requirement on solution diversity and in principle, as
many solutions as needed can be generated. This paper proposes a new model-based method for representing and
searching nondominated solutions. The main idea is to construct Gaussian process-based inverse models that map
all found nondominated solutions from the objective space to the decision space. These inverse models are then used
to create offspring by sampling the objective space. To facilitate inverse modeling, the multivariate inverse
function is decomposed into a group of uni-variate functions, where the number of inverse models is reduced using a
random grouping technique. Extensive empirical simulations demonstrate that the proposed algorithm exhibits robust
search performance on a variety of medium to high dimensional multiobjective optimization test problems. Additional
nondominated solutions are generated a posteriori using the constructed models to increase the density of solutions
in the preferred regions at a low computational cost.