Hyper-heuristics aim at interchanging different solvers while solving a problem. The idea is to determine the best approach for solving a problem at its current state. This way, every time we make a move it gets us closer to a solution. The problem changes; so does its state. As a consequence, for the next move, a different solver may be invoked. Hyper-heuristics have been around for almost 20 years. However, combinatorial optimization problems date from way back. Thus, it is paramount to determine whether the efforts revolving around hyper-heuristic research have been targeted at the problems of the highest interest for the combinatorial optimization community. In this work, we tackle such an endeavor. We begin by determining the most relevant combinatorial optimization problems, and then we analyze them in the context of hyper-heuristics. The idea is to verify whether they remain as relevant when considering exclusively works related to hyper-heuristics. We find that some of the most relevant problem domains have also been popular for hyper-heuristics research. Alas, others have not and few efforts have been directed towards solving them. We identify the following problem domains, which may help in furthering the impact of hyper-heuristics: Shortest Path, Set Cover, Longest Path, and Minimum Spanning Tree. We believe that focusing research on ways for solving them may lead to an increase in the relevance and impact that hyperheuristics have on combinatorial optimization problems.

Combinatorial optimization problems (COPs) are paramount for real-life problems with discrete variables. Even though the number of combinations is finite, some problems exhibit exponential growth, rendering exact approaches unfeasible. So, approximate methods, such as heuristics, are customary for making fast decisions. Despite their small computational cost, each heuristic specializes in specific kinds of problems. Hence, other approaches have appeared for merging their strengths. One of these approaches is commonly known as selection hyper-heuristics. However, a trained hyper-heuristic usually carries the following problem: it provides scarce information about its sensitivity. This makes it more difficult to estimate the effect of changing a parameter. Illumination algorithms seek to improve this issue by focusing on exploration rather than on exploitation while preserving information about the best solutions with different criteria. Still, literature falls short when merging both approaches, representing a knowledge gap. Therefore, in this work, we test the feasibility of using an illumination algorithm, the MAP-Elites (ME), for tuning a sequence-based selection hyper-heuristic model for Balanced Partition problems. We choose ME since it has been successfully applied to a different COP, and by linking it with hyper-heuristics, we may exploit upon its benefits. So, we may achieve a hyper-heuristic that represents the best combination of heuristics. Simultaneously, we can gain information about the expected performance of diverse hyperheuristics, e.g., those that begin with a different heuristic. Our approach operates by creating a multidimensional map, where each design variable represents the application of a given heuristic. Afterward, ME generates mutated sequences and tests them to determine if they represent a better-performing solution. To test our approach, we consider 1500 instances that include easy and hard instances, analyzed under different scenarios. We also include limit instances that are neither easy nor hard. Our resulting data supports the feasibility of the proposed approach. We show that this kind of hyper-heuristic can perform toe-to-toe with a synthetic oracle. Besides, under some conditions, the former may even outperform the latter. This represents an outstanding result, since such an oracle can only be obtained by a brute-force approach, and because it demonstrates that merging both approaches (ME and hyper-heuristics) is a path worth pursuing. We also present how each parameter affects the model performance, concluding that some parameters can be critical while others are virtually irrelevant. This is also a relevant result, since it serves as the groundwork for future works so that they can focus on exploiting the most relevant parameters.