Planning for Theatre Air Warfare can be represented as a hierarchy of decisions. At the top level, surviving airframes must be assigned to roles (e.g., Air Defense, Counter Air, Close Air Support, and AAF Suppression) in each time period in response to changing enemy air defense capabilities, remaining targets, and roles of opposing aircraft. At the middle level, aircraft are allocated to specific targets to support their assigned roles. At the lowest level, routing and engagement decisions are made for individual missions. The decisions at each level form a set of time-sequenced Courses of Action taken by opposing forces. This paper introduces a set of simulation-based optimization heuristics operating within this planning hierarchy to optimize allocations of aircraft. The algorithms estimate distributions for stochastic outcomes of the pairs of Red/Blue decisions. Rather than using traditional stochastic dynamic programming to determine optimal strategies, we use an innovative combination of heuristics, simulation-optimization, and mathematical programming. Blue decisions are guided by a stochastic hill-climbing search algorithm while Red decisions are found by optimizing over a continuous representation of the decision space. Stochastic outcomes are then provided by fast, Lanchester-type attrition simulations. This paper summarizes preliminary results from top and middle level models.
KEYWORDS: Computer simulations, Optimization (mathematics), Cognitive modeling, Expectation maximization algorithms, Data modeling, Matrices, Systems modeling, Information operations, Manufacturing, Data integration
This paper describes initial research to define and demonstrate an integrated set of algorithms for conducting high-level Operational Simulations. In practice, an Operational Simulation would be used during an ongoing military mission to monitor operations, update state information, compare actual versus planned states, and suggest revised alternative Courses of Action. Significant technical challenges to this realization result from the size and complexity of the problem domain, the inherent uncertainty of situation assessments, and the need for immediate answers. Taking a top-down approach, we initially define the problem with respect to high-level military planning. By narrowing the state space we are better able to focus on model, data, and algorithm integration issues without getting sidetracked by issues specific to any single application or implementation. We propose three main functions in the planning cycle: situation assessment, parameter update, and plan assessment and prediction. Situation assessment uses hierarchical Bayes Networks to estimate initial state probabilities. A parameter update function based on Hidden Markov Models then produces revised state probabilities and state transition probabilities - model identification. Finally, the plan assessment and prediction function uses these revised estimates for simulation-based prediction as well as for determining optimal policies via Markov Decision Processes and simulation-optimization heuristics.
KEYWORDS: System identification, Systems modeling, Computer simulations, Data modeling, Chemical elements, Statistical modeling, Weapons, Stochastic processes, Matrices, MATLAB
In this paper we report on state-space system identification approaches to dynamic behavioral abstraction of military simulation models. Two stochastic simulation models were identified under a variety of scenarios. The `Attrition Simulation' is a model of two opposing forces with multiple weapon system types. The `Mission Simulation' is a model of a squadron of aircraft performing battlefield air interdiction. Four system identification techniques: Maximum Entropy, Compartmental Models, Canonical State-Space Models, and Hidden Markov Models (HMM), were applied to these simulation models. The system identification techniques were evaluated on how well their resulting abstractions replicated the distributions of the simulation states as well as the decision outputs. Encouraging results were achieved by the HMM technique applied to the Attrition Simulation--and by the Maximum Entropy technique applied to the Mission Simulation.
KEYWORDS: System identification, Systems modeling, Data modeling, Mathematical modeling, Computer simulations, Chemical elements, Matrices, Dynamical systems, Signal processing, Telecommunications
This paper describes preliminary research into the applicability of system identification techniques to simulation model abstraction. Model abstraction enables the construction of a valid, low-resolution surrogate to a more detailed, high-resolution simulation model. When rapid, approximate results will suffice, we can also apply system identification directly to actual system data, bypassing the simulation stage. Four non-traditional system identification techniques are discussed in relation to their ability to produce linear, time-invariant, state-space formulations of multivariable random systems. A simple example is provided in which one of the techniques, Hidden Markov Models, is used to identify the transition probabilities within a simulated Markov Chain. The example is used to illustrate the challenges in general simulation model abstraction caused by model transformation procedures, problem size, uncertainty, and computational complexity. At this stage, we can say that the application of systems identification to simulation model abstraction is promising, yet challenging.
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