Research on Sustainable Tourism Development based on Multivariate Model Optimization

In order to promote the sustainable development of tourism in Juneau, the article constructs a series of models to balance multiple factors in tourism development. By integrating the data of the past 15 years, a two-period moving average method is used to build a model of tourist numbers; the Pearson correlation coefficient is used to determine the strong positive correlation between residents' income and the number of tourists, so that the income model is abstracted as a linear function of the residents' model; and simplified differential equations are used to simulate the process of glacier degradation and build an environmental pressure model. Further, the Tourist Happiness Index (THI), Resident Happiness Index (RHI) and Sustainable Development Index (SDI) are developed to quantify the above models. Considering the constraints of environment, infrastructure, number of tourists and hidden financial expenditures, the TOPSIS model was applied to screen the relative optimal strategies. In addition, the social satisfaction index (SSI) was constructed using principal component analysis (PCA), and the tourism economic benefit function (EBT) was introduced under the Nash equilibrium framework, and the optimal sustainable development model was obtained by taking the maximization of “SSI + SDI + EBT” as the objective function, which provided the sustainable development of Juno tourism with theoretical support and decision-making basis.