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The wikipedia page on meta-heuristics states that they are "heuristics designed to find, generate, or select a heuristic".

The wikipedia page on hyper-heuristics states that they are "heuristic search methods that seeks to automate [...] the process of selecting, combining, generating or adapting several simpler heuristics".

Moreover, it also states that "The fundamental difference between metaheuristics and hyper-heuristics is that most implementations of metaheuristics search within a search space of problem solutions, whereas hyper-heuristics always search within a search space of heuristics."

This leaves me confused: it seems like the hyper heuristic page is contradicting the meta-heuristic page. How can a meta-heuristic search for heuristics, if its search space is the problem space rather than the space of heuristics?

What really is the difference between metaheuristics and hyperheuristics?

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  • $\begingroup$ Does this answer your question? $\endgroup$ – Bruce Adams Dec 28 '18 at 8:18
  • $\begingroup$ @BruceAdams, the answers seem to primarily distinguish meta-heuristic from heuristic, but not clarify the difference betwen meta- and hyper- heuristics $\endgroup$ – user626625 Dec 28 '18 at 19:10
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Defining meta-heuristics as "heuristics designed to find, generate, or select a heuristic" seems too broad. A meta-heuristic is commonly understood as an algorithmic template that defines how different low-level heuristic components (e.g. constructive procedures, local searches, solutions recombinations) interact in the search. After instantiating these components for a specific problem, you get a heuristic which searches in the solution space.

Gendreau, Potvin, Handbook of Metaheuristics define them as

solution methods that orchestrate an interaction between local improvement strategies and higher-level strategies to create a process capable of escaping from local optima and performing a robust search of a solution space

and chapter "Defining the term 'Metaheuristic'" of Zäpfl, Braune, Bögl, Metaheuristic Search Concepts summarizes

  • A metaheuristic relies on a high-level strategy which builds upon a particular basic search principle
  • The high-level strategy is problem-independent and can be seen as an abstract framework
  • The high-level strategy has to properly realize a balance between the two forces intensification and diversification.

Thus, a short answer could be: in a meta-heuristic the designer instantiates low-level heuristics; a hyper-heuristic automates the selection or generation of the low-level heuristics.

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