Hybrid collaborative optimization based on selection strategy of initial point and adaptive relaxation

There are two problems in Collaborative optimization (CO): (1) the local optima arising from the selection of an inappropriate initial point; (2) the low efficiency and accuracy root in inappropriate relaxation factors. To solve these problems, we first develop the Latin hypercube design (LHD) to determine an initial point of optimization, and then use the non-linear programming by quadratic Lagrangian (NLPQL) to search for the global solution. The effectiveness of the initial point selection strategy is verified by three benchmark functions with some dimensions and different complexities. Then we propose the Adaptive relaxation collaborative optimization (ARCO) algorithm to solve the inconsistency between the system level and the disciplines level, and in this method, the relaxation factors are determined according to the three separated stages of CO respectively. The performance of the ARCO algorithm is compared with the standard collaborative algorithm and the constant relaxation collaborative algorithm with a typical numerical example, which indicates that the ARCO algorithm is more efficient and accurate. Finally, we propose a Hybrid collaborative optimization (HCO) approach, which integrates the selection strategy of initial point with the ARCO algorithm. The results show that HCO can achieve the global optimal solution without the initial value and it also has advantages in convergence, accuracy and robustness. Therefore, the proposed HCO approach can solve the CO problems with applications in the spindle and the speed reducer.