###### Abstract
This goal was achieved by performing thermal simulation on the models and then using various data to conduct a regression analysis and finally, multi-objective optimization using Minitalo 21.4.2 (64-bit). TPMS modeling: Design considerations for modeling in this study are based on lattice-influenced geometry that has the resemblance of a crystal structure. This can be divided into two sub-groups: graphic unit cell and TPMS. Graphic unit cells are structures that are composed of beams with no thickness that include graph properties of valencies, edge counts, and more. TPMS are structures created out of sine and cosine equations and create periodic structures when stacked in the x-, y-, or z-directions [13]. For example, Gyroid, Schwartz, Diamond, Lidinoid, SplitP, Nevovious, and all these TPMS have their unique equations (Figure 1). In nTop, a TPMS can be also custom-built from an equation as well as custom unit cells can be created to build custom lattice structures. Minimal surfaces are surfaces with the smallest area among all possible surfaces for a given boundary [14]. Minimal Surfaces are also defined as surfaces with a mean curvature of zero. TPMS are Minimal Surfaces that are periodic in three different directions. This mathematically defined periodic minimal surface is also found in nature. For example, highly curved TPMS is found in giant amoeba (_Chaos carolinensis_) mitochondria [15] that suggests structural adaptation and survival. Gyroid cubic membranes are found in the chloroplast of green alga _Zygnema_ (LB923) [16] and their formation indicates the adaptability of the chloroplast membrane to different environmental stresses such as limited nutrients, temperature fluctuations, and UV exposure, etc. Gyroid is observed in the wings of the _Callophrys rubi_ butterfly and primitive TPMS is found in the microstructure of sea urchin skeletons [17]. Another research introduces an innovative approach of combining TPMS with varying axial elastic moduli to achieve isotropic mechanical properties that were supported by simulations and experiments [18]. A formalized parametric design is applied [19] to create and assess TPMS identifying key design parameters such as equation, volume fraction, unit cell, number of cells, orientation, etc. A comprehensive topology optimization was developed for functionally graded TPMS-based structures [20]. The research uses numerical homogenization and material interpolation laws for transversely isotropic elastic bulk properties of the structures. These TPMS structures demonstrate remarkable adaptability and functionality in both biological and engineered systems. Extracting data such as the volume of the solid and the surface area of the TPMS is straight forward with simple commands in nTop. One of the crucial factors of this study (surface area to volume ratio) is determined by the data which are used in the later stage of data analysis. nTopology for modeling and thermal simulation: According to a master's thesis, nTop platform and Inspire emerged as the top two topology optimization software tools compared to SolidWorks 2019 Student Edition by Dassault Systems, Fusion 360 V.2.0.7824 by Autodesk, and Ansys Student 2020 R1 by Ansys- all student licenses [22]. nTop made it easy to automate the homogenization process for TPMS in a large number for mechanical properties analysis [23]. This software is known for its advanced capabilities of handling complex geometries that are widely used in heat exchangers and are for additive manufacturing [24]. This is why nTop was selected to design and perform steady-state thermal analysis of the TPMS models in this study. A study conducted a numerical simulation of a Gyroid heat exchanger employing the SST K-\(\omega\) turbulence model [25]. The effects of lattice size, unidirectional lattice size, and the hot/cold fluid porosity ratio were investigated, and the porosity ratio was found to be crucial for optimizing heat transfer coefficients and flow dynamics of the system.