Four Adaptive Memetic Bat Algorithm Schemes for Bézier Curve Parameterization

This paper is an extension of a previous one presented at the conference Cyberworlds 2015. In that work we addressed the problem to fit a given set of data points in the least-square sense by using a polynomial Bezier curve. This problem arises in many scientific and industrial domains, such as numerical analysis, statistical regression, computer-aided design and manufacturing, computer graphics, virtual reality, etc. A critical issue to address this least-squares minimization problem is that of curve parameterization. In our previous work we solve it by applying a powerful nature-inspired optimization method called the bat algorithm. Although we obtained pretty good results on a number of examples, the method can still be further improved by considering a memetic approach, in which the global search bat algorithm is hybridized with a local search procedure to enhance the exploitation phase of the minimization process. In this paper we extend our previous method through two local search strategies: Luus-Jaakola and ASSRS. In both cases, the adaptive and self-adaptive versions are considered, leading to four memetic schemes. A comparative analysis of our results on the previous benchmark for these four memetic schemes and our previous method has been carried out. It shows that the memetic approaches improve the efficiency of the previous method at different extent for all instances in our benchmark.