# Enhancing Selection Hyper-heuristics via Feature Transformations

## TL;DR

This paper proposes explicit and implicit feature transformations to enhance selection hyper-heuristics, improving their stability and performance in solving complex optimization problems like constraint satisfaction and knapsack problems.

## Contribution

It introduces two novel feature transformation methods for selection hyper-heuristics and analyzes their effects, expanding the feature set and testing across multiple problem domains.

## Key findings

- Transformations improve overall hyper-heuristic performance.
- Explicit and implicit transformations increase stability.
- Combining both transformations was less effective.

## Abstract

Hyper-heuristics are a novel tool. They deal with complex optimization problems where standalone solvers exhibit varied performance. Among such a tool reside selection hyper-heuristics. By combining the strengths of each solver, this kind of hyper-heuristic offers a more robust tool. However, their effectiveness is highly dependent on the 'features' used to link them with the problem that is being solved. Aiming at enhancing selection hyper-heuristics, in this paper we propose two types of transformation: explicit and implicit. The first one directly changes the distribution of critical points within the feature domain while using a Euclidean distance to measure proximity. The second one operates indirectly by preserving the distribution of critical points but changing the distance metric through a kernel function. We focus on analyzing the effect of each kind of transformation, and of their combinations. We test our ideas in the domain of constraint satisfaction problems because of their popularity and many practical applications. In this work, we compare the performance of our proposals against those of previously published data. Furthermore, we expand on previous research by increasing the number of analyzed features. We found that, by incorporating transformations into the model of selection hyper-heuristics, overall performance can be improved, yielding more stable results. However, combining implicit and explicit transformations was not as fruitful. Additionally, we ran some confirmatory tests on the domain of knapsack problems. Again, we observed improved stability, leading to the generation of hyper-heuristics whose profit had a standard deviation between 20% and 30% smaller.