Incremental gaussian model-building in multi-objective EDAs with an application to deformable image registration

Estimation-of-Distribution Algorithms (EDAs) build and use probabilistic models during optimization in order to automatically discover and use an optimization problems' structure. This is especially useful for black-box optimization where no assumptions are made on the problem being solved, which is characteristic of many cases in solving complex real-world problems. In this paper we consider multi-objective optimization problems with real-valued variables. Although the vast majority of advances in EDA literature concern single-objective optimization, advances have also been made in multi-objective optimization. In this paper we bring together two recent advances, namely incremental Gaussian model building to reduce the required population size and a mixture-based multi-objective framework that has specific methods to better facilitate model-building techniques that span multiple generations. Significantly faster convergence to the optimal Pareto front is achieved on 6 out of 7 artificial benchmark problems from literature. Although results on two of these problems show that building models with higher-order interactions between variables is required, these problems are still artificial. We therefore also consider a more realistic optimization problem in image processing, namely deformable image registration. For this problem too, our results show the need for processing interactions between problem variables, stressing the importance of studying such models.