Enhanced tunicate swarm algorithm for optimizing shape of C2 RQI-spline curves

Abstract

The shape optimization of interpolation curves is a crucial and intractable technique in scientific visualization, data analysis, manufacturing and computer-aided design and is potentially used in many engineering fields involving geometric modeling. In this paper, an enhanced hybrid tunicate swarm algorithm (TSA) is used to optimize the shape of complex rational quartic interpolation spline (RQI-spline, for short) curves. Firstly, to modify the shape of the interpolation curve more flexibly, a novel multi-parameter RQI-spline curve with local and global shape parameters is presented. Then the corresponding combined RQI-spline curves with 2th-order parametric continuity denoted C2 are constructed. In addition, considering that the optimization of shape parameters for RQI-spline curves is a complex optimization problem, an enhanced hybrid version of TSA called DQTSA is developed. The introduction of differential evolution and quadratic interpolation strategies enhances the ability of the TSA to jump out of local minima, thus effectively solving the shape parameter optimization of RQI-spline curves. DQTSA and some popular comparison algorithms are used to solve the set of 23 benchmark functions and CEC2019 test functions. The experimental results show that DQTSA performs the best in 7 (30.43%) of the 23 test problems, while DQTSA performs the best in 3 of the 10 CEC2019 suites. Meanwhile, applying DQTSA to three engineering optimization problems, the best value, mean and significantly better than other search algorithms are obtained from 20 optimized designs, which verifies the applicability and stability of DQTSA in solving engineering optimization problems. Finally, the proposed DQTSA is used to solve the shape optimization model for the combined C2 RQI-spline curve. Numerical results find that DQTSA obtains the optimal RQI-spline curve with minimum energy. Some representative numerical examples illustrate that DQTSA is a potentially excellent algorithm for solving curve optimization.