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

Abstract

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.

Adversarial decision strategies in multiple network phased oscillators: The Blue-Green-Red Kuramoto-Sakaguchi model

“…Finally, the coupling of this model into a representation of the outcomes of decisions will yield a means of quantifying risks through the interplay between probability and consequences. In particular, in view of the military contextualisation we adopt with this model there is an opportunity to couple this model with well-known mathematical representations of combat and network generalisations of them [46]. Above all, through a compact mathematical model of complexity such as this, at least partially analytical insights may be gained into otherwise surprising and rich behaviours.…”

`Friend or foe’ and decision making initiative in complex conflict environments

“…The top-left panel of Fig 4 displays continuously connected regions of Blue or Red victory, boundary regions of stalemate, and regions of significantly variable outcome with abrupt shifts between Blue and Red victory with small parameter variations. Similar outcome representations were employed in [ 35 ], deliberately constructed akin to a phase space in thermodynamics, distinct from the phase of an oscillator. These phase boundaries in B − R also match the structures seen in T end (top right).…”

“…Previous studies have attempted to validate Lanchester outputs to World War II data-sets [ 31 ], and the recent Syrian civil war [ 32 ]. Recent generalisations of the Lanchester equations for heterogeneous forces include MacKay’s mixed forces model [ 33 , 34 ] and a fully networked Lanchester model [ 35 ].…”

Adversarial Decisions on Complex Dynamical Systems using Game Theory

“…Note that this model may be called a global model, where the resources of the two sides are homogeneous. In [21] a heterogeneous form of the model is also given, where the resources may also be structured through network parameters using the generalisation of the Lanchester model in [26]. We do not treat this model here in this first application of computational game Theory to such a system.…”

“…Having now characterised particular regimes of behaviour of the BKL model and the computational performance of the Game Theory solver, we now test the behaviour of the model across a range of parameter values. The aim here is to see transitions in the parameter space through a heatmap in Lanchester outcomes, as originally used in [26], from one-side having advantage to the other side, within an equilibrium solution and subject to the constraints that each side brings into the scenario (size of initial resources and their respective network C2 design, for example). Treating this as a larger meta-game, the designer of a system may detect then where risks are incurred given their design choices.…”