A novel model-based evolutionary algorithm for multi-objective deformable image registration with content mismatch and large deformations: Benchmarking efficiency and quality

Taking a multi-objective optimization approach to deformable image registration has recently gained attention, because such an approach removes the requirement of manually tuning the weights of all the involved objectives. Especially for problems that require large complex deformations, this is a non-trivial task. From the resulting Pareto set of solutions one can then much more insightfully select a registration outcome that is most suitable for the problem at hand. To serve as an internal optimization engine, currently used multi-objective algorithms are competent, but rather inefficient. In this paper we largely improve upon this by introducing a multi-objective real-valued adaptation of the recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) for discrete optimization. In this work, GOMEA is tailored specifically to the problem of deformable image registration to obtain substantially improved efficiency. This improvement is achieved by exploiting a key strength of GOMEA: iteratively improving small parts of solutions, allowing to faster exploit the impact of such updates on the objectives at hand through partial evaluations. We performed experiments on three registration problems. In particular, an artificial problem containing a disappearing structure, a pair of pre- and post-operative breast CT scans, and a pair of breast MRI scans acquired in prone and supine position were considered. Results show that compared to the previously used evolutionary algorithm, GOMEA obtains a speed-up of up to a factor of ∼1600 on the tested registration problems while achieving registration outcomes of similar quality

Niching an estimation-of-distribution algorithm by hierarchical Gaussian mixture learning

Estimation-of-Distribution Algorithms (EDAs) have been applied with quite some success when solving real-valued optimization problems, especially in the case of Black Box Optimization (BBO). Generally, the performance of an EDA depends on the match between its driving probability distribution and the landscape of the problem being solved. Because most well-known EDAs, including CMA-ES, NES, and AMaLGaM, use a uni-modal search distribution, they have a high risk of getting trapped in local optima when a problem is multi-modal with a (moderate) number of relatively comparable modes. This risk could potentially be mitigated using niching methods that define multiple regions of interest where separate search distributions govern sub-populations. However, a key question is how to determine a suitable number of niches, especially in BBO. In this paper, we present a novel, adaptive niching approach that determines the niches through hierarchical clustering based on the correlation between the probability densities and fitness values of solutions. We test the performance of a combination of this niching approach with AMaLGaM on both new and well-known niching benchmark problems and ind that the new approach properly identifies multiple landscape modes, leading to much beter performance on multi-modal problems than with a non-niched, uni-modal EDA

Exploiting linkage information in real-valued optimization with the real-valued gene-pool optimal mixing evolutionary algorithm

The recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) has been shown to be among the state-of-the-art for solving discrete optimization problems. Key to the success of GOMEA is its ability to efficiently exploit the linkage structure of a problem. Here, we introduce the Real-Valued GOMEA (RV-GOMEA), which incorporates several aspects of the real-valued EDA known as AMaLGaM into GOMEA in order to make GOMEA well-suited for real-valued optimization. The key strength of GOMEA to competently exploit linkage structure is effectively preserved in RV-GOMEA, enabling excellent performance on problems that exhibit a linkage structure that is to some degree decomposable. Moreover, the main variation operator of GOMEA enables substantial improvements in performance if the problem allows for partial evaluations, which may be very well possible in many real-world applications. Comparisons of performance with state-of-the-art algorithms such as CMA-ES and AMaLGaM on a set of well-known benchmark problems show that RV-GOMEA achieves comparable, excellent scalability in case of black-box optimization. Moreover, RV-GOMEA achieves unprecedented scalability on problems that allow for partial evaluations, reaching near-optimal solutions for problems with up to millions of real-valued variables within one hour on a normal desktop computer

Multi-objective Gene-pool Optimal Mixing Evolutionary Algorithm with the interleaved multi-start scheme

The Multi-objective Gene-pool Optimal Mixing Evolutionary Algorithm (MO-GOMEA) has been shown to be a promising solver for multi-objective combinatorial optimization problems, obtaining an excellent scalability on both standard benchmarks and real-world applications. To attain optimal performance, MO-GOMEA requires its two parameters, namely the population size and the number of clusters, to be set properly with respect to the problem instance at hand, which is a non-trivial task for any EA practitioner. In this article, we present a new version of MO-GOMEA in combination with the so-called Interleaved Multi-start Scheme (IMS) for the multi-objective domain that eliminates the manual setting of these two parameters. The new MO-GOMEA is then evaluated on multiple benchmark problems in comparison with two well-known multi-objective evolutionary algorithms (MOEAs): Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D). Experiments suggest that MO-GOMEA with the IMS is an easy-to-use MOEA that retains the excellent performance of the original MO-GOMEA