# Multi-Objective Optimization Model of Industrial Lubricants Based on Integer Nonlinear Programming
###### Abstract  
Based on actual lubricating oil production data and the base oil performance indexes of an enterprise, two nonlinear blending schemes corresponding to viscosity and freezing point and four linear blending schemes corresponding to acid value, flash point, oxidation stability, and carbon residue are given in this paper. On the premise that the error of each index is less than 5%, a linear weighted multi-objective optimization model based on integer nonlinear programming considering cost and performance is established, and the lubricating oil blending scheme is obtained. The results show that the blending formula is simple in form and convenient in calculation, and that the overall consistency between the calculated value and the measured value is good. At the same time, the relative error of each performance index, except residual carbon, of the scheme with weight value of (0.5, 0.5) is far less than 5%. Although the performance index is slightly inferior to that of the scheme with a weight value of (0, 1), it is far higher than that of the scheme with a weight value of (1, 0). The linear weighted multi-objective optimization model based on integer nonlinear programming proposed in this paper can well-optimize the blending scheme of industrial  
The physical and chemical properties of oil products change when they are blended. The linear or nonlinear relationship between this change and the properties of each blending component is expressed as an additive effect between the components. A certain physical and chemical property equal to the superposition of each component according to its composition ratio is called linear harmony; otherwise, it is called nonlinear harmony. The chemical composition of oil products and additives [5] is very complex, and their physical and chemical properties generally do not have an additive effect, so the blending of lubricating oil is mostly nonlinear. In addition, the performance indexes of lubricating oil mainly include viscosity [6; 7; 8], freezing point [9], acid value [10], flash point [11], oxidation stability [12; 13], residual carbon [14], and so on. Therefore, the optimization of the design of a lubricating oil blending scheme [15] mainly includes two aspects: one is to select the base oils reasonably to meet the performance index requirements of the blended product; the other is to establish the blending mathematical model [16] and determine the blending scheme of each base oil on the premise of meeting the product performance indexes.  
The blending formula of early lubricating oil was mainly optimized by the linear programming method. However, many important technical indexes of lubricating oil do not show a simple linear relationship with the content of each component. If the oil products are blended according to the linear programming method, the prediction accuracy of the performance of the blended product will be poor, and unable to meet the actual needs of production. In recent years, many experts and scholars in the field of lubricating oil have studied the nonlinear [17; 18] relationship between important indexes of lubricating oil and the content of each component, and have obtained many accurate prediction models.  
The blending of lubricating oil is a relatively complicated process. This paper ignores the production technology and process of lubricating oil, and does not consider the issue of additives. A certain index of lubricating oil is only related to the corresponding index of the base oil. In this paper, a multi-objective optimization model of lubricating oil based on integer nonlinear programming is established to optimize the design of the blending scheme so that it meets various performance indexes and, at the same time, is lower in cost.