The Algorithm for Solving Shortest-Path Problems Based on Electrical Circuit Laws

Shortest-path problem is one of the well-known optimization problems that has been studied by many scientists in recent years. Applications of this problem such as transportation and communication are generally solved by Dijkstra's Algorithm (Labeling). In this paper, two separate scientific fields, electronics and operation research have been linked to each other and a new algorithm has been created for to find the optimization solution of a shortestpath problem by using electric networks and rules. The proposed algorithm can solve the shortest-path problem in directed graphs and no order ones, and also can solve the longest path problems in directed graphs. In this algorithm, electrical network are used in a way that the resistance value of each branch is equal to each edge weights in the shortest-path problems. Then with using Ohm Law and Kirchhaff's Voltage Law (KVL), the current in each circuit cycle is calculated. Then the branches that contain the most passing current are specified, and according to Ohm’s Law, have the lowest resistance or weight. Thus, the shortest path in the network is achieved. Advantage of this algorithm is faster convergence to the answer and less computing time than the conventional method, specially in networks with more nods. The mentioned algorithm has been described for three examples.