关键词: Lanchester方程, 军事想定, 非线性整数规划, 最优决策, 混合对策

Abstract: The strategy analysis based on mathematical description for a battle usually stresses the consistency of the outcome of a battle with the strategy schemed for it. However, as a whole, the decision-making analysis of the battle disposition is rarely involved, such as force grouping and allocation. Taking the historically famous Trafalgar naval battle as example and virtual background with some reasonably military settings given, the Lanchester square equations are introduced in combination with nonlinear integer programming to develop a mathematical model to solve the maximum remaining force problem when the total force is not superior to the enemy. Matlab simulation result and solution to the model both verified the effectiveness of the model we developed and, therefore, the optimal strategy is decided from the exemplification with the naval battle. The reasonable analysis and research on the hybrid game by exemplification with naval battles are also made to complement the war game simulation and foreshadow its outcome.