TLDR: This research paper introduces a novel approach to improve cross-domain hyper-heuristics by focusing on transforming the set of low-level heuristics (LLHs) rather than just their adaptive selection. The authors identify and analyze three key principles: solution acceptance, LLH repetitions, and perturbation intensity. By systematically applying transformations based on these principles, even a trivial random selection mechanism can outperform state-of-the-art hyper-heuristics on challenging real-world problems and the CHeSC benchmark, finding 11 new best-known solutions. The findings suggest that the design and properties of the LLH set are as crucial, if not more, important than the selection mechanism itself.
In the realm of artificial intelligence and optimization, hyper-heuristics are designed to create general-purpose search strategies that can tackle a wide range of complex problems. Traditionally, much of the research in this area has focused on how to adaptively select the best low-level heuristics (LLHs) from a given set. However, a recent paper challenges this conventional wisdom by shifting the focus to the composition and strategic transformation of these LLH sets themselves.
The research, titled “Key Principles in Cross-Domain Hyper-Heuristic Performance”, introduces a groundbreaking perspective. Instead of merely picking the right tools, the authors argue that modifying the tools themselves can lead to significantly better outcomes. They systematically analyze transformations based on three fundamental principles: solution acceptance, LLH repetitions, and perturbation intensity.
Understanding the Key Principles
Solution Acceptance: This principle dictates when a newly generated solution, even if slightly worse, should be accepted. In cross-domain problems, objective function values can vary wildly, making standard acceptance methods difficult to apply. The paper proposes novel cross-domain acceptance mechanisms by normalizing solution qualities using a ‘mean improvement statistic’ (µ-normalization). This allows for consistent application of strategies like Metropolis acceptance, Threshold acceptance, and Record-to-Record Travel across diverse problem types.
LLH Repetitions: The idea here is to apply low-level heuristics repeatedly for a certain duration. This not only allows for a more thorough exploration of the search space but also implicitly normalizes the computational resources allocated to each LLH. By replacing overly aggressive discarding of worse solutions with more nuanced acceptance, this approach fosters better ‘collaboration among heuristics’.
Perturbation Intensity: Perturbative LLHs introduce changes to a solution. The intensity of these changes can significantly impact the search process. The paper suggests duplicating perturbative LLHs with a predefined set of varying intensity settings. This effectively offers a range of perturbations, from subtle to aggressive, allowing the hyper-heuristic to choose the appropriate level of disruption without complex adaptive mechanisms.
A Trivial Method Outperforms State-of-the-Art
Perhaps the most striking finding of this research is the performance of a ‘trivial unbiased random selection mechanism’ when combined with appropriately constructed transformations based on these three principles. This simple method, which merely selects an LLH category and then an LLH within that category uniformly at random, was shown to outperform all available state-of-the-art hyper-heuristics on three challenging real-world domains. Furthermore, it found 11 new best-known solutions and was competitive with the winner of the CHeSC competition, a standard cross-domain benchmark.
This remarkable result strongly suggests that the inherent properties and design of the LLH set play a comparable, if not more important, role than the sophisticated adaptive selection mechanisms that have been the focus of much prior research. By providing a ‘reasonably safe environment’ (through acceptance), ‘normalized granularity’ (through repetitions), and ‘varying perturbation intensity’, even a basic selection process can achieve superior performance.
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Impact on Existing Hyper-Heuristics
The authors also demonstrated that accompanying several recent hyper-heuristics with these strategic transformations significantly improved their performance on both the CHeSC benchmark and real-world domains. In many cases, this approach also simplified their designs by replacing complex internal adaptation mechanisms with transparent LLH set modifications.
The experiments covered a range of hyper-heuristics, including those based on Q-learning, Luby sequence restarts, and iterated local search schemes. The real-world applications included a pickup-delivery problem with time windows, a minimum shift design problem, and a bus driver scheduling problem, further validating the generality of the proposed methodology.
In conclusion, this research provides a fresh perspective on hyper-heuristic design, emphasizing that control over what low-level heuristics are available and how they are structured is as crucial as, if not more than, learning how to select them. This work offers a general tool for enhancing cross-domain search performance through strategic LLH set transformations. You can read the full paper for more details here.
