# An Optimization Model for a Desert Railway Route Scheme Based on Interval Number and TOPSIS
###### Abstract
There is little research on the evaluation index system and quantitative decision-making method of the desert railway alignment scheme, which is not conducive to the high-quality construction of the desert railway. The accurate quantification of the qualitative indicators and the unified calculation of all indicators are the key points for the railway scheme decision. Quantitative indicators refer to those that can be expressed in specific numerical values, such as project quantity, project investment, and land occupation. Qualitative indicators refer to those that can only be described qualitatively by linguistics, such as vegetation destruction and water pollution. Qualitative language expression has fuzziness and randomness. In the present research, the quantitative methods of qualitative indicators include expert scoring and triangular fuzzy number methods [11]. The expert scoring methodology is convenient to use, but it overlooks the fuzziness of qualitative linguistic expression. This quantitative method may make the evaluation results inconsistent with the actual results. In contrast to this approach, the method based on triangular fuzzy numbers considers fuzziness. However, in calculating the comprehensive distance between the alternative scheme and the ideal scheme, the qualitative and quantitative indexes should adopt various distance formulas, which increase the complexity and uncertainty of the calculation. Interval numbers are defined as those numbers expressed in interval form [12]. Essentially, these all represent a set of real numbers in a closed interval. Because interval number description can realize the uncertainty of quantitative expression, interval number theory has been extensively employed in uncertain multi-attribute decision-making and uncertain mathematical programming [13; 14]. The factors affecting the selection of desert railway routes include not only quantitative indicators such as railway length and proportion of bridges and tunnels, but also qualitative indicators such as environmental impact and wind-sand hazard. Therefore, the evaluation and optimization of the desert railway alignment scheme is a multi-attribute decision-making problem involving qualitative and quantitative indicators. By applying the interval number theory to the quantitative expression of qualitative indicators, the unified calculation of two types of indicators can enhance the accuracy of qualitative indicators and the efficiency of railway scheme decision-making. The technique for order preference by similarity to an ideal solution (TOPSIS) is a commonly used comprehensive evaluation methodology based on the original data information [15]. This method ranks the evaluation objects according to the proximity of the limited evaluation objects to the idealized goals. The calculated results can precisely reveal the gap between various evaluation schemes. A brief literature survey and the explanations given above indicate that it is necessary to establish a quantitative decision-making method to optimize the desert railway alignment scheme. Let us consider the Minfeng-Yuhu section of the Hotan-Ruoqiang railway as the research object. With the aim of the technical problem of comprehensive quantification and optimization of the design of the desert railway route, the evaluation index system of the desert railway alignment plan is established. To this end, various crucial factors including railway design, wind-blown sand hazards, environmental impact, and operation condition are taken into account by analyzing the main factors affecting the design of desert railway. According to the principle of minimum discrimination information, the subjective and objective weights are appropriately combined to obtain the comprehensive weights of the index. The interval number is then exploited to realize the quantitative expression of the qualitative indexes of the railway scheme. The comprehensive distance between the alternative scheme and the ideal scheme is then evaluated based on the TOPSIS method.