Information geometry-based optimization models for decision analysis in cyber-physical infrastructure networks

Abstract

Cyber-physical infrastructure networks comprise physical assets, sensors, communication means, computation resources, and control mechanisms leading to complex decision-making environments where there are uncertainty, heterogeneity, and dynamism in observation and operation. Traditional optimization methods usually model system states as points in Euclidean space, and such traditional methods might be unable to appropriately account for the intrinsic property of uncertain probability distributions. This research work has developed an Information Geometry-Based Optimization Model for Decision Analysis in Cyber-Physical Infrastructure Networks through the use of statistical manifolds, Fisher information geometry, information geometric divergence, and minimax optimization. The heterogeneity of infrastructure observation is converted into probabilistic state representation modelled as points in a statistical manifold. The Fisher information geometry is then used to describe the local geometric characteristics of uncertain states. In order to tackle the distributional uncertainties, an admissible uncertainty set is devised and embedded into a minimax decision approach in which the maximum value of the operational objective function is minimized. The developed model takes into account decision cost, geometric discrepancy, operational risk, and violation of constraints under resource, capacity, safety, and stability constraints. To assess the convergence, robustness, computation characteristics, sensitivity analysis, and component importance, a synthetic 50-node cyber-physical infrastructure network is utilized as test cases. Some representative results confirm that the proposed IG Minimax model outperforms the classical minimax and Euclidean approaches with respect to the worst-case objective value, equal to 51.27 and 56.84, respectively. The results indicate that information geometry is a mathematical sound tool for representing uncertain states of the infrastructure network, while the minimax optimization increases the robustness of the decision to distributional uncertainty.