Designing the Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm and Applying it to Substantially Improve the Efficiency of Multi-Objective Deformable Image Registration

Abstract

The recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) for discrete variables has been shown to be able to efficiently and effectively exploit the decomposability of optimization problems, especially in a grey-box setting, in which a solution can be efficiently updated after a modification of a subset of its variables. GOMEA is considered to be state of the art, but currently no version of GOMEA for real-valued variables exists. In this thesis, we design a real-valued version of GOMEA, for both single-objective and multi-objective optimization. Our novel GOMEA variant is then applied to the Deformable Image Registration (DIR) problem, which was adapted to allow for efficient partial evaluations. DIR concerns the calculation of a deformation that transforms one image to another, and is of great importance for many medical applications. Experiments are performed to assess GOMEA’s performance in black-box and grey-box settings on a range of single-objective and multi-objective benchmark problems, including comparisons with it to the state-of-the-art real-valued optimization algorithm AMaLGaM. From the results of these experiments, we find that GOMEA performs substantially better on all considered single-objective and multi-objective benchmark problems in a grey-box setting, in terms of required time and number of evaluations. Moreover, the improvement becomes larger as problem dimensionality increases. In a black-box setting, GOMEA still performed better than AMaLGaM in terms of time, and comparable in terms of the number of evaluations. On DIR problems, GOMEA achieved solutions of similar quality while achieving a speed-up of up to a factor of 1600.