Differential Evolution Based On Local Search And Its Application In Surface Reconstruction

Differential evolution (DE) and the related heuristic algorithms have been widely used to solve complex nonlinear optimization problems for recent years. However, the classical DE exists some shortcomings, such as the limited local search ability or the diversity of the population can not be maintained at an appropriate level. Considering these shortcomings in the DE, this dissertation studied how to design effective evolu-tionary algorithms to solve complex optimization problems, and how to apply these algorithms to solve two important problems in engineering field, that is, surface recon-struction and surface extending. The main works of this dissertation are as follows:In the second chapter of this dissertation, two effective evolutionary algorithms are proposed to solve continuous and discrete optimization problems, respectively. On one aspect, the classical gradient operator is integrated into the searching strategies of the DE, and a new mutation operator is designed to maintain the diversity of the popu-lation in the evolution procedure. Based on18benchmark continuous test problems, numerical comparisons of the proposed algorithm and five related algorithms in other references show that the proposed algorithm achieves significantly better performance on the searching ability, the average runtime and the population diversity. To solve discrete optimization problems, on the other aspect, the difference information between stochastic individuals are embedded into the DE algorithm and a new binary evolution-ary algorithm is obtained. Furthermore, the convergence of this algorithm in probability is proved and numerical results show the effectiveness of the new algorithm.In the third chapter of this dissertation, the non-uniform rational B-spline function integrated with optimization algorithms is employed to reconstruct three dimension-al surface. With respect to the general unorganized points (disordered points), two methods for obtaining the initial parameterization are proposed, one is based on the projection of the given points on a plane, the other is to employ the form of "segment-parameterization’". The accuracy on five sets of classical organized points can reach10-5-10-9; for two sets of unorganized points from complex surfaces, the accuracy reaches an order of10-4. Moreover, the accuracy on real-measured data from Mashan pump station can reach10-4. Furthermore, the effect of noise on the algorithm is s- tudied, numerical results on perturbed points with noise intensities of1%.5%10%and20%demonstrate the robustness of the proposed algorithm.In the fourth chapter of this work, a general method of surface extending by uti-lizing DE algorithm is proposed, which is specialized into two algorithms for two real applications, one is for hole filling, and the other is for surface extrapolation. On a care-fully chosen section plane, this method predicts the points in the considered region by predicting the average distances and intersection angles between the prediction points. With respect, to these two problems, the predicted points are further added into the provided model by constrained triangulation or surface reconstruction, moreover, the obtained local models are improved by smoothing operation or the mesh optimization. On the aspect of hole filling, numerical comparisons of the proposed algorithm and two recently introduced algorithms on the runtime and the prediction accuracy w.r.t. the sphere and elephant models are conducted, and these results demonstrate that our algo-rithm is competitive on the prediction accuracy. On the aspect of surface extrapolation, the proposed algorithm is employed to obtain the complete characteristic data of flow rate, torque and rotational speed at small and large guide vane openings for the pump stations of Guangxu. Mashan and Bailianhe, the prediction accuracies reach10-2-10-3on average.