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Variable-fidelity optimization (VFO) frameworks generally aim at taking full advantage of high-fidelity (HF) and low-fidelity (LF) models to solve computationally expensive problems. The purpose of this paper is to develop a novel modified trust-region assisted variable-fidelity optimization (MTR-VFO) framework that can improve the optimization efficiency for computationally expensive engineering design problems.

Though the LF model is rough and inaccurate, it probably contains the gradient information and trend of the computationally expensive HF model. In the proposed framework, the extreme locations of the LF kriging model are firstly utilized to enhance the HF kriging model, and then a modified trust-region (MTR) method is presented for efficient local search. The proposed MTR-VFO framework is verified through comparison with three typical methods on some benchmark problems, and it is also applied to optimize the configuration of underwater tandem wings.

The results indicate that the proposed MTR-VFO framework is more effective than some existing typical methods and it has the potential of solving computationally expensive problems more efficiently.

The extreme locations of LF models are utilized to improve the accuracy of HF models and a MTR method is first proposed for local search without utilizing HF gradient. Besides, a novel MTR-VFO framework is presented which is verified to be more effective than some existing typical methods and shows great potential of solving computationally expensive problems effectively.

It is shown in natural gas proportion mixing experiments that a mixed-source natural gas is the physical combination of end member gas. Both the carbon and hydrogen isotopes in the mixed-source natural gas can be expressed by the weighted average of corresponding components content and isotopes of end member gas. Under certain geological setting, the selection of end member gas is the key to mixed-source ratio calculation. Then, it's better to estimate the mixed-source ratio with δ¹³C₁ and component data according to the weighted average calculation formula. The analysis on natural gas geochemistry characteristics show that the natural gas extracted from Jingbian Gas Field in the Ordos Basin is mainly an upper Paleozoic coal-derived gas. In the analysis of geological conditions for reservoir forming and characteristics of natural gas, natural gas from Longtan 1 Well and Tao 6 Well were selected as the end member gases of lower Paleozoic oil-type gas and upper Paleozoic coal-type gas respectively to calculate the mixed-source ratio of natural gas in Jingbian Gas Field. The ratio of upper Paleozoic coal-derived gas mostly accounts for over 70% and its average ratio reaches 81%. Therefore, the exploration of natural gas of Ordos Basin should be focused on the upper palaeozoic coal source rock, and attention should be paid to the matching of coal source rock in the exploration of weathered crust gas deposit.

“Originally as a business providing community life services since its founding in 2017, Dingdong (Cayman) has transformed itself into a fresh e-commerce company. After making adjustments to its business model and operating strategy for three times, Dingdong (Cayman) has completed the strategic transition from grocery surrogate shopping to comprehensive self-operation, and built its own commercial fortress. In 2019, the total revenue of the company was five billion yuan. Upon the outbreak of COVID-19, its monthly revenue exceeded 1.2 billion yuan in February 2020, and the year's total revenue was expected to hit 15∼18 billion yuan. To date, Dingdong (Cayman) has formed a supply chain fully based on digital operation and built a commercial fortress in the fresh e-commerce industry. Despite this, its future prospect is not free from challenge. This case mainly deals with the following questions: How about the strategic positioning and core competitiveness of Dingdong (Cayman) in its early days? In the process of rapid expansion, what are the advantages and problems in its business model? How can the digitally operated supply chain support its continuous expansion in the future?”