Counterfactual explanations are a useful tool to explain trained models. They are based on counterfactual thoughts, which are a natural human thought process that helps us reason about the past. When applied to trained models they show how to make minimal changes to a data point in order to obtain a desired output.
Most methods find these counterfactuals by optimizing a set of objectives. Previously these objectives were often combined into a loss function using an aggregation operator. This operator implicitly decides the priority between the objectives, but this ordering is not always in line with the user’s preferences.
To mitigate this the Multi-Objective Counterfactuals (MOC) method was introduced. MOC turns counterfactual generation into a multi-objective optimization problem and presents the user with a diverse set of counterfactuals that have different trade-offs for the objectives. It optimizes the set of objectives with an evolutionary algorithm called Nondominated Sorting Genetic Algorithm II.
In this thesis we optimize this problem using Multi-Objective Real-Valued Gene-Pool Optimal Mixing Evolutionary Algorithm, which is a different evolutionary algorithm. We present a single-modal method and two multi-modal methods. We compare the performance of our methods to a counterfactual generation method named Diverse Counterfactual Explanations (DiCE), which focusses on feasibility and diversity within a set of generated counterfactuals. Additionally, we also present a visualization tool for sets of counterfactuals.
The single-modal method generates counterfactuals that are realistic, but do not consistently perform well in other areas. The first multi-modal method generates diverse sets of counterfactuals, but overall performs worse. The second multi-modal method generates counterfactuals that perform similarly to the single-modal method, but are more diverse.

VanillaGP is an Inductive Program Synthesis algorithm that takes a Genetic Algorithm (GA) approach by using its 3 components: selection, mutation, and crossover. Many different alternatives exist for these components and although this is not the only application of a GAs on the Program Synthesis domain, it has not been extensively evaluated what the effects of using these different alternatives or combinations of them are. We explored this by evaluating the performance of multiple alternatives per component and comparing the results of combinations of these alternatives to VanillaGP. These evaluations were done on 3 IPS domains: robot, ASCII art, and strings. From these evaluations we conclude that Stochastic Universal Sampling combined with Queen Bee Crossover and an altered version of One Mutation Per Solution performs best on the string domain, and Down-Sampled Lexicase Selection combined with Three Parent Crossover and the same altered version of OMPS performs best on the other domains.