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Mathematical Problems in Engineering
Volume 2014, Article ID 184540, 10 pages
Research Article

Geometric Generalisation of Surrogate Model-Based Optimisation to Combinatorial and Program Spaces

1Department of Computer Science and Engineering, Kwangwoon University, Nowon-gu, Seoul 139-701, Republic of Korea
2Department of Computer Science, Streatham Campus, University of Exeter, Exeter EX4 4QF, UK
3Computer Science Department, Umm Al-Qura University, Makkah 21955, Saudi Arabia
4Department of Computer Engineering, Gachon University, Seongnam-si, Gyeonggi-do 461-701, Republic of Korea

Received 14 March 2014; Accepted 31 March 2014; Published 29 April 2014

Academic Editor: Ker-Wei Yu

Copyright © 2014 Yong-Hyuk Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Surrogate models (SMs) can profitably be employed, often in conjunction with evolutionary algorithms, in optimisation in which it is expensive to test candidate solutions. The spatial intuition behind SMs makes them naturally suited to continuous problems, and the only combinatorial problems that have been previously addressed are those with solutions that can be encoded as integer vectors. We show how radial basis functions can provide a generalised SM for combinatorial problems which have a geometric solution representation, through the conversion of that representation to a different metric space. This approach allows an SM to be cast in a natural way for the problem at hand, without ad hoc adaptation to a specific representation. We test this adaptation process on problems involving binary strings, permutations, and tree-based genetic programs.