A Lagrangian Approach to Loss Function Optimization on Traffic Network Regularity

The optimization of traffic networks is a valuable tool for every major industry. Optimizing these networks is inherently difficult due to sheer scale, yet developing techniques at smaller scales with more feasible models makes the process manageable. To approach optimizing irregularity on graphs, we construct a method to randomly generate networks by controlling the probability and distribution of node connections. Next, by including constant flow from the borders of the graph, we introduce real-world complexity. We then develop a regularity loss function and analyze its convex gradient to create a minimization algorithm. Our novel solution to this problem is the use of Lagrange multipliers to approximate the gradient's minima, abiding by a defined constraint function. Thus, our methods reduce irregularity by 31.3% and will help industry and academia understand how to evaluate traffic networks through a computer-generated example and set up a framework for future research.