The BBOB (2009) benchmark functions include functions that are unimodal, have "adequate global structure", and have "weak global structure". From the problem definitions, these search space structures can be easily determined.
What are real-time techniques (i.e. during the search process) available to identify unimodal, globally convex, and non-globally convex search spaces?
This is a good question.
In addition to what @Chin-Chang Yang has observed, consider
C.J. Convey, Towards efficient stochastic optimization of functions of convex sets, Ph.D. thesis, University of Rhode Island, 2013:
http://homepage.cs.uri.edu/faculty/hamel/pubs/theses/phd-christian-convey.pdf
The significance of Corollary 5.3.5 [this corollary establishes that the internal path closure of a set X is the smallest convex set containing the set X] (page 53) is considered in Section 5.3, starting on 49. Thls result is useful for search algorithms that establish convexity by adding vertices to a concave set but strive to modify the original set as little as possible (page 50). Internal path closure is defined on page 49 (mid-page).
Hi, very interesting question!
I'm dealing with a similar issue right now, as I design a “hybridization schedule” to combine two different heuristics. One of the methods is good on unimodal problems and the other on multimodal ones. I guess Chin-Chang Yang is right, you could see it as a classification problem. Actually by measuring some performance parameter of two (very) different heuristics I believe it shouldn’t be so hard to classify the problem in some of the categories…. the issue is, that once you are done classifying you will also be done with your entire function evaluations budget. So, for optimization purposes the classification needs to be done dynamically as you optimize (and the sooner the better). Perhaps reviewing the “reactive (meta)heuristic” literature could shed some light upon this problem. Summarizing… I’ve no answer for this question.
But I hope someone does.
Hi all,
I do not have a complete answer to this question, but I happen to know a paper about the topic.
T. Takahama and S. Sakai, "Differential evolution with dynamic strategy and parameter selection by detecting landscape modality." IEEE CEC 2012.
http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6256613
Hope it is helpful.
https://www.researchgate.net/publication/296636431_Codes_in_MATLAB_for_Particle_Swarm_Optimization
Code Codes in MATLAB for Particle Swarm Optimization
https://www.researchgate.net/publication/297245624_Particle_Swarm_Optimization_Algorithm_and_its_Codes_in_MATLAB
Research Particle Swarm Optimization: Algorithm and its Codes in MATLAB
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