Optimization and Simulation

Optimization is important for efficient system design, allocation of resources, and decision making. Minimizing waste and maximizing utility helps to improve system performance. Optimization can focus on a single metric (cost, profit, etc.) or consider multiple metrics that might be in tension (cost, speed, etc.) providing a range of options with different trade-offs but each an optimal combination in its own way. Optimization under uncertain conditions can help one find the safest option with the least downside or conversely, the option with the highest expected return.

Simulation can be used alone or paired with optimization to better understand a system’s dynamics, assess potential risks, and provide insights into where process improvements can have the greatest impact on performance. Simulation can be paired with data analytics to improve the accuracy of the simulation by using real-world data to improve the detail of the output by analyzing ranges of simulated behavior.

Primary Techniques

Optimization techniques include global optimization methods, such as GROPE, and the full range of mathematical programming methods, from linear programs and mixed integer programs to generalized non-linear programs. Some problems are tractable using algorithmic methods such as the simplex method, column generation, cutting-plane methods, or branch and bound. Other problems are too complex or large for such methods requiring the use of meta-heuristics to find good (but not provably optimal) solutions, these include powerful methods such as genetic algorithms, simulated annealing, and particle swarm optimization.

Simulations can take a variety of forms, from the abstract mathematical models used to simulate pandemics (e.g., SIR models) to detailed models that try and capture individual interactions between components of the system (Agent Based Models and Discrete Event Simulation).

General Applications

Optimization: Resource allocation, Advertising portfolio, Investment portfolio, scheduling, routing…

Simulation: Transportation and logistics networks, Hospitals, Out-patient facilities, Social Networks, …

Case Studies

  • Peregrine
  • Hammer