基于Lanchester方程的一类海战实例的决策分析

Analysis of Optimum Strategy Using Lanchester Equation for Naval Battles like Trafalgar

利用数学描述来研究作战决策分析注重结局和预设策略的一致性,作战的整体决策分析很少被涉及,如兵力分组及兵力配置等问题.在做出合理的军事想定的基础上,以著名的特拉法尔加海战为实际背景,引入Lanchester方程理论,利用非线性整数规划,建立了在总兵力不占优的情况下求解最大剩余兵力的数学模型.Matlab仿真实现和求解结果验证了模型的有效性,从而获得了海战实例的最优决策.同时合理地分析和研究了海战实例的混合对策问题,为作战模拟的研究做了必要的补充和铺垫.

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.