Optimising structure in a networked Lanchester model for fires and manoeuvre in warfare

We present a generalisation of the classical Lanchester model for directed fire between two combat forces but now employing networks for the manoeuvre of Blue and Red forces, and the pattern of engagement between the two. The model therefore integrates fires between dispersed elements, as well as manoeuvre through an internal-to-each-side diffusive interaction. We explain the model with several simple examples, including cases where conservation laws hold. We then apply an optimisation approach where, for a fixed-in-structure adversary, we optimise the internal manoeuvre and external engagement structures where the trade-off between maximising damage on the adversary and minimising own-losses can be examined. In the space of combat outcomes this leads to a sequence of transitions from defeat to stalemate and then to victory for the force with optimised networks. Depending on the trade-off between destruction and self-preservation, the optimised networks develop a number of structures including the appearance of so-called sacrificial nodes, that may be interpreted as feints, manoeuvre hubs, and suppressive fires. We discuss these in light of Manoeuvre Warfare theory.