# Thermal Conductivity of Low-GWP Refrigerants Modeling with Multi-Object Optimization
## 1 Introduction
Several methods available in the literature are based on this approach, such as the Random Search method [22] or advanced intelligent algorithms [25; 26]. On the other hand, the multi-objective optimization problem comprises a group of objective functions that must be simultaneously maximized or minimized. This approach is used in many engineering problems. An example is the cost minimization of a manufactured item and the simultaneous maximization of its performance. Another is the maximization of an engine's performance with a simultaneous decrease in fuel consumption. Finding the best coefficients for an equation could be considered a MOO problem if multiple objective functions are simultaneously considered. In this particular case, we simultaneously optimize the Average Absolute Relative Deviation (AARD) and the coefficient of determination (R\({}^{2}\)). The advantage of multi-objective optimization is that it allows us to consider several criteria when designing a new equation and enables us to find a better approximation of the experimental values and a more robust equation. In [27], it is possible to find a review of the various uses of the MOO for chemical process engineering problems and a detailed explanation of all the steps to build, resolve, and select the optimum result. The algorithm used to solve the multi-objective problem is NSGAII [28] which is a popular nondominated genetic algorithm in genetic algorithms. NSGAII is based on multi-objective optimization. It is a very effective algorithm used in various engineering and scientific fields. In this study, the NSGA-II is used to obtain the Pareto frontier [29; 30] that solves the problem of simultaneous optimization of the two objectives, AARD and the coefficient of determination. It yields more consistent solutions to the problem, simultaneously considering more statistical parameters. Such a method is a novelty in the field of thermophysical properties and it achieves a very good performance. In fact, the statistical parameters of AARD and Root Mean Square Error (RMSE) were improved in the entire database, and good results were also obtained for single fluids having a large number of data points. The final result of the optimization is the Pareto front (Figure 1) which is a set of points representing the best trade-offs between the different objective functions, i.e., the most feasible solutions which satisfy the constraints while satisfying as many of the objectives as possible. A drawback of this approach is that the selection of the best solution among the ones on the Pareto front is not a trivial problem. Indeed, in a single-objective minimization problem, the best solution is the smallest. However, in a multi-objective problem, the optimal solution cannot be easily selected since some of the solutions that optimize one objective may not be satisfactory for the others. A tool developed by [31; 32] that implements ten methods to select an optimal solution from the Pareto front was used in this regard. This useful tool allowed us not only to weigh the two objective functions but also to choose which weight was the most significant and which solutions were optimal in solving the problem of finding the best solution for minimizing the distance between calculated and experimental values. In this regard, the ten selection methods available in the tool were used to choose the optimal solution within the Pareto frontier regarding their capability to manage objectives with significantly different magnitudes and were able to rank among the best solutions. In the end, the obtained model was compared with literature models to determine its effectiveness for predicting the thermal conductivity of low GWP refrigerants. The paper has been organized as follows: after the introduction, the algorithms used to perform the MOO task are described. Then, the results obtained in different cases are presented. Finally, the main conclusions are presented with future works on the studied topic.