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Research Questions

  1. What methods and metrics for measuring complexity exist in the literature?
  2. How can these metrics be used to give the United Sates an operational advantage across battlespace domains?

Modern warfare is characterized by an environment of complex, multidomain operations deployed against an adversary who, likewise, responds with a complex array of tactics. Although the challenges of operating in this environment have long been recognized, the complexities of this environment have rarely been framed or studied in a structured way.

In this report, the authors assess mathematical strategies for quantifying complexity in wartime environments. After comparing approaches based in linear algebra with Monte Carlo simulation strategies, they were able to provide a general road map that defined the advantages and limitations of each. These methods are demonstrated in two operational vignettes: one examining a simplified suppression of enemy air defenses scenario and a second examining the Cuban Missile Crisis.

Note: As a component of this project, researchers created a Julia implementation for some Markov chain processes, including defining and implementing transition matrix from a sparse text file using variables, finding steady states and absorption probabilities, and simulating random walks. Research teams that would like to apply these processes to their own work can find the underlying code in this GitHub repository:

View the repository on GitHub

Key Findings

  • There are useful metrics of complexity that can be used to assess complexity both at the level of overall systems and at the level of individual decisionmakers.
  • Systems-level complexity measures the increasing convolution of decision processes and captures the overall difficulty faced by decisionmakers.
  • A second, more granular approach examines the use of different metrics to identify the key points within simulated decision processes to identify specific points of influence that could be targeted to leverage their potential for outsized impact on adversary operations.

Research conducted by

The research described in this report was prepared for the Department of the Air Force and conducted by the Force Modernization and Employment Program within RAND Project AIR FORCE.

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