Combinatorial problems are ubiquitous in engineering design and manufacturing. These problems typically arise whenever it is necessary to determine an optimum sequence of steps that maximizes or minimizes a quantity of interest. Examples include the optimal sequence of welding operations to minimize weld-induced distortion or simply the tightening sequence for a pattern of bolts to minimize contact-induced stresses. This project poses a mathematical method of conversion from a combinatorial problem to a differentiable, non-combinatorial problem that can be efficiently solved using gradient-based nonlinear programming methods. In its initial stages, it was decided to use a classic combinatorial problem known as the Traveling Salesman problem as a proxy. This problem evaluates the shortest distance traveled between "cities" or a random set of points. To make the evaluation more realistic, the points were then randomized to allow for the program to evaluate unique cases after the initial evaluation period. Then, by creating a new mathematical method that focuses on a history-dependent solution, we were able to create and implement an equation that creates one linear solution based on the desired parameters.