Although the number of solutions in combinatorial optimization problems (COPs) is finite, some problems grow exponentially and render exact approaches unfeasible. So, approximate methods, such as heuristics, are customary. Each heuristic usually specializes in specific kinds of problems. Hence, other approaches seek to merge their strengths. One of them is selection hyper-heuristics. However, they usually provide scarce information about their sensitivity. Illumination algorithms may fix this issue since they focus on exploration rather than exploitation while preserving the best solutions under different criteria. Still, literature falls short when merging both approaches, representing a knowledge gap. This work tests the feasibility of using an illumination algorithm, MAP-Elites (ME), for tuning a sequence-based selection hyper-heuristic model for Balanced Partition problems. We choose ME since other researchers have successfully applied it to a different COP. So, we may achieve a hyper-heuristic that represents the best combination of heuristics while simultaneously gaining intel on the performance of diverse alternatives. Our approach operates by creating a multi-dimensional map, where each design variable represents the application of a heuristic. Afterward, ME generates mutated sequences and tests them to determine if they represent a better-performing solution. We consider 1500 instances that include easy and hard instances, analyzed under different scenarios to test our approach. We also include limit instances that are neither easy nor hard. Our resulting data support the proposed approach, as it performs toe-to-toe with a synthetic oracle and may even outperform it. This represents an outstanding result, since a brute-force approach is needed to achieve such an oracle. So, merging ME and hyper-heuristics is a path worth pursuing. We also present how each parameter affects the model performance and identify the critical and virtually irrelevant ones. This serves as the groundwork for future works that focus on exploiting the most relevant parameters.
AuthorCombinatorial 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 hyper-heuristics, e.g., those that begin with a different heuristic. Our approach operates by creating a multi-dimensional 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.
