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Local smoothness is often mentioned in literature analysing different heuristics and meta-heuristics for combinatorial optimisation. What is meant precisely by local smoothness is often left out, but one definition is "A landscape with small (average) fitness differences between neighboring points is called smooth". Additionally I have read of at least one measure (auto-correlation) that quantifies this.

I am interested however in the relationship between smoothness and optimisation processes. The extent of the detail in literature seems to be local smoothness is good for optimisation and ruggedness is bad. Could anyone further explain the relation between effective optimisation and local smoothness, and/or point to literature that delves into this more deeply.

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  • $\begingroup$ This question seems a little broad to me. I wonder if it might be possible to focus it a little, so that one doesn't end up with trivial answers ? $\endgroup$ – Suresh Venkat Sep 1 '11 at 16:43
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It sounds like you need to make your question much more precise or pick up a good book on smooth optimization and marvel at what smoothness makes possible. See for instance "Numerical Optimization" by Nocedal and Wright (Springer).

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