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Knowledge-based potentials were developed to investigate the differentiation of native structures from their decoy sets. This work presents the construction of two different distance-dependent potential energy functions based on two fundamental assumptions using mathematical modeling. Here, a model was developed using basic mathematical methods, and the carbon-alpha form is the simplest form of protein representation. We aimed to reduce computational volume and distinguish the native structure from the decoy structures. For this purpose, according to Anfinsens dogma, we assumed that the energy of each model structure should be more favorable than the corresponding native type. In the second one, we thought that the energy difference between the native and decoy structures changes linearly with the root-mean-square deviation of structures. These knowledge-based potentials are expressed by the B-spline basis functions of the pairwise distances between Ca-Ca of inter-residues. The potential function parameters in the above two approaches were optimized using the linear programming algorithm on a massive collection of Titan-HRD and tested on the remainder. We found that the potential functions produced by Anfinsens dogma detect native structures more accurately than those developed by the root-mean-square deviation. Both linear programming knowledge-based potentials (LPKP) successfully detect the native structures from an ensemble of decoys. However, the LPKP of the first approach can correctly identify 130 native structures out of 150 tested cases with an average rank of 1.67. While the second approach LPKP detects 124 native structures from their decoys. We concluded that linear programming is promising for generating knowledge-based potential functions. All the training and testing sets used for this work are available online and downloaded from http://titan.princeton.edu/HRDecoys.