Approximation based curvilinear local search for optimization problems

Abstract

Purpose

At this work, we propose a local approximation based search method to optimize any function. For this purpose, an approximation method is combined with an estimation filter, and a new local search mechanism is constituted.

Design/methodology/approach

RBF network is very efficient interpolation method especially if we have sufficient reference data. Here, reference data refers to the exact value of the objective function at some points. Using this capability of RBFs, we can approximately inspect the vicinity each point in search space. Meanwhile, in order to obtain a smooth, rapid and better trajectory toward the global optimum, the alpha-beta filter can be integrated to this mechanism. For better description and visualization, the operations are defined in 2-dimensional search space; but the outlined procedure can be extended to higher dimensions without loss of generality.

Findings

When compared with our previous studies using conventional heuristic methods, approximation based curvilinear local search mechanism provide better minimization performance for almost all benchmark functions. Moreover computational cost of this method too less than heuristics. The number of iteration down to at least 1/10 compared to conventional heuristic algorithm. Additionally, the solution accuracy is very improved for majority of the test cases.

Originality/value

This paper proposes a new search approach to solve optimization problems with less cost. For this purpose, a new local curvilinear search mechanism is built using RBF based approximation technique and alpha-beta estimation filter.

Citation

Yaman, F., Yilmaz, A.E. and Leblebicioğlu, K. (2016), "Approximation based curvilinear local search for optimization problems", Engineering Computations, Vol. 33 No. 2. https://doi.org/10.1108/EC-05-2014-0122