FORWARD: Feasibility Oriented Random-Walk Inspired Algorithm for Radial Reconfiguration in Distribution Networks

We consider an optimal flow distribution problem in which the goal is to find a radial configuration that minimizes resistance-induced quadratic distribution costs while ensuring delivery of inputs from multiple sources to all sinks to meet their demands. This problem has critical applications in various distribution systems, such as electricity, where efficient energy flow is crucial for both economic and environmental reasons. Due to its complexity, finding an optimal solution is computationally challenging and NP-hard. In this paper, we propose a novel algorithm called FORWARD, which leverages graph theory to efficiently identify feasible configurations in polynomial time. By drawing parallels with random walk processes, our method simplifies the search space, significantly reducing computational effort while maintaining performance. The FORWARD algorithm employs a combination of network preprocessing, intelligent partitioning, and strategic sampling to construct radial configurations that meet flow requirements, finding always a feasible solution. Numerical experiments demonstrate its effectiveness, highlighting its potential for real-world applications in optimizing distribution networks.