Hybridizing mesh adaptive search algorithm and artificial immune systems for discrete rational Bézier curve approximation

This paper is an extension of a previous one presented at the conference Cyberworlds 2014. In that work we addressed the problem of obtaining the rational Bézier curve that fits a given set of data points better in the least-squares sense. Our approach was based on the clonal selection theory principles to compute all parameters of the problem, namely, the control points of the approximating curve, their corresponding weights, and a suitable parameterization of data points. Although we were able to obtain results with good accuracy, this scheme can still be significantly improved by hybridizing it with an efficient local search procedure. This is the approach proposed in this paper. In particular, we consider the mesh adaptive search algorithm, a direct search method aimed at improving the local search step to refine the quality of the solution. This hybrid strategy has been applied to six illustrative free-form shapes exhibiting challenging features, including the three examples in previous paper. A comparative analysis of our results with respect to the previous methodology is also reported. Our experimental results show that this hybrid scheme performs extremely well. It also outperforms the previous approach for all instances in our benchmark.

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