New Algorithm Permitting the Construction of an Effective Spanning Tree

Abstract

In this paper, we have done a rapid and very simple algorithm that resolves the multiple objective combinatorial optimization problem. This, by determining a basic optimal solution, which is a strong spanning tree constructed, according to a well-chosen criterion. Consequently, our algorithm uses notions of Bellman’s algorithm to determine the best path of the network, and Ford Fulkerson’s algorithm to maximise the flow value. The Simplex Network Method that permits to reach the optimality conditions manipulates the two algorithms. In short, the interest of our work is the optimization of many criteria taking into account the strong spanning tree, which represents the central angular stone of the network. To illustrate that, we propose to optimize a bi-objective distribution problem.

Keywords

• bi-objective minimum cost flow problem
• network flows
• linear programming
• minimum spanning tree
• efficient extreme point