A fast algorithm to solve large-scale matrix games based on dimensionality reduction and its application in multiple unmanned combat air vehicles attack-defense decision-making

Abstract

In the scenario of attack-defense involved with unmanned combat air vehicles (UCAVs), it is often envisioned that a large group of UCAVs is deployed to complete some complex tasks which could be specifically modeled as large-scale matrix games. Solving such matrix games by the traditional linear programming approaches, however, could be quite time-consuming and thus cannot be implemented in real-time which is, in fact, a key requirement for real air combat. On this account, an algorithm, termed as dimensionality reduction based matrix game solving algorithm (DR-MG), is proposed in this paper to solve large-scale matrix games in a timely manner. Our algorithm builds on the technique of dimensionality reduction which inherently finds the convex hull vertices of a vector set. Through establishing the connection between Nash equilibria of the matrix games before and after dimensionality reduction, the proposed algorithm is capable of finding the solutions while only dealing with the matrix game with reduced dimensions. As a consequence, it is expected the time complexity of the proposed algorithm is significantly decreased, and thus the algorithm could be applicable in real air combat. Finally, numerical results are provided to show the effectiveness of our algorithm.