This paper focuses on a multi-objective model of Vehicle Routing Problem with Time Windows (VRPTW), where the total distance, the vehicle number, and the time penalty of customers are taken into account. NSGA-II has been performed as an efficient algorithm in solving multi-objective problems, and the Or-opt heuristic is well-known as one of the classic optimization algorithms. A hybrid algorithm involving both two algorithms above is introduced in this article. Data from the distribution center in Utica (Michigan, US.) has been tested with this hybrid algorithm in MATLAB. Faster running speed has been proved and some improvements in solutions have been shown.

The VX gasket is an important part of the wellhead connector for a subsea Christmas tree. Optimization of the gasket’s structure can improve the connector’s sealing performance. In this paper, we develop an optimization approach for the VX gasket structure, taking into consideration working load randomness, based on the Kriging surrogate model-NSGA-II algorithm. To guarantee the simulation accuracy, a random finite element (R-FE) model of the connector’s sealing structure was constructed to calculate the gasket’s sealing performance under random working load conditions. The working load’s randomness was simulated using the Gaussian distribution function. To improve the calculation efficiency of the sealing performance for individuals within the initial populations, Kriging surrogate models were constructed. These models accelerated the optimization speed, where the training sample was obtained using an experimental method design and the constructed R-FE model. The effectiveness of the presented approach was verified in the context of a subsea Christmas tree wellhead connector, which matched the 20'' casing head. The results indicated that the proposed method is effective for VX gasket structure optimization in subsea connectors, and that efficiency was significantly enhanced compared to the traditional FE method.