## 1 Introduction  
Deformable image registration (DIR) [1], i.e., the process of searching for the optimal non-linear transformation to align two images, plays an increasingly important role in radiotherapy [2], with applications ranging from radiotherapy planning [3], dose accumulation [4], contour propagation [5], to radiotherapy response monitoring [6]. One of the challenges of DIR in clinical practice concerns the parameter choices that need to be made for each registration instance, since the success of most registration methods depends on setting a variety of parameters well (e.g., the weights in the cost function, the number of registration levels,the control point grid spacing). The weights of the cost function are especially important, as they determine the trade-off between all the objectives of interest, including the effect of regularization of the DIR problem, which is necessary, as DIR is inherently ill-posed [7]. Optimizing these parameters for each individual DIR instance is challenging in clinical practice. Having a class solution for DIR, i.e., a configuration of parameters for which DIR performs well on all instances of a DIR problem, would facilitate wide-scale clinical application. Although several approaches have been proposed [8; 9; 10], still, often, parameters are manually tuned for each case of the DIR problem separately via trial-and-error adaptations, followed by visual inspection of the registration outcome. Finding a class solution may, however, be impossible for challenging DIR cases, as it was shown that preferred parameter settings can vary greatly even for different instances of the same type of registration problem [9; 10; 11]. Different parameter configurations lead to different DIR outcomes, due to different trade-offs between the objectives of interest in DIR, such as similarity between the images and the amount of deformation. The fact that different trade-offs may be preferable for different instances of a DIR problem indicates that DIR, although currently typically solved as a single-objective optimization problem, where all objectives of interest are combined in one cost function, is inherently a multi-objective optimization problem. In multi-objective optimization, the objectives of interest are not combined into one cost function, but optimized simultaneously, resulting in a set of DIR outcomes that represent high-quality trade-offs between the objectives of interest. If the multi-objective problem is solved to optimality, then this set of DIR outcomes is called the Pareto front. In cases where the Pareto front is not known (such as in the case of DIR), it can be said that a non-dominated front is obtained, i.e., a front where no solution is better in both objectives than any other solution in this front. Recently, it was shown that using a patient-specific multi-objective optimization approach can be useful for challenging DIR cases, for which manual tuning becomes far more complex [10]. This multi-objective, patient-specific approach can also be considered an online tuning approach: online in the sense that here, the tuning algorithm is run to search for the best parameter settings for the DIR algorithm for a specific patient. This approach removes the challenge of manual parameter tuning and provides the expert with a non-dominated front of DIR outcomes. Such a solution can be navigated to find a preferred DIR outcome insightfully. However, it can be computationally expensive, as it involves running a search algorithm on top of a DIR algorithm every time a DIR case needs to be solved. Furthermore, the more parameters to be tuned, the more time consuming this process becomes [12; 13]. In this work, we consider an alternative approach for efficient parameter tuning: an evolutionary multi-objective machine learning approach that computes, in an offline training phase, a multi-objective class solution, i.e., a set of parameter configurations, that, when used on any instance of a DIR problem, yields DIR outcomes that approximate the non-dominated front.