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

TL;DR

The paper introduces FORWARD, a novel polynomial-time algorithm inspired by random walks, for efficiently finding feasible radial configurations in distribution networks to minimize resistance costs.

Contribution

It presents a new graph-theoretic algorithm that simplifies the complex NP-hard problem of optimal flow distribution in radial networks, enabling practical solutions.

Findings

Successfully finds feasible configurations in polynomial time

Reduces computational effort compared to traditional methods

Effective in real-world distribution network optimization

Abstract

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 on electricity networks, 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 a feasible solution in polynomial time. Numerical experiments demonstrate the effectiveness of our approach, highlighting its potential for real-world applications in optimizing distribution networks.