Abstract: his paper presents a new method called multilayer embedded bat algorithm (ME-BAT) to solve the general curve reconstruction problem with free-form parametric B-splines. Opposed to previous approaches in the literature, this method computes the optimal values of all free variables (data parameters, breakpoints, and poles), a very difficult task because they are strongly intertwined in a highly nonlinear way. The method is based on the idea of applying the bat algorithm at different layers: a main bat algorithm at an upper layer to compute the breakpoints and a second bat algorithm at a lower layer to compute the data parameters. This second bat algorithm is embedded into the first one and executed for each breakpoint vector of the population and at each iteration step of the main algorithm. Then, the poles are calculated by least-squares minimization through SVD. The method has been applied to three real-world engineering examples. The experimental results show that the method performs very well, being able to recover the underlying shape of data with high accuracy. A comparison with eleven alternative methods (including six classical methods in the field and all the metaheuristic methods applied so far to this problem) shows that this method outperforms the previous approaches in the field for all instances in the benchmark.

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