Numerical Optimization

Simulation-based Numerical Optimization

In science and engineering, simulation is a powerful tool that predicts the behavior of physical systems. Moreover, progress made with algorithms and computational hardware yielded further improvements in simulation. Today's simulation tools have become more practical in dealing with complex design problems, for which you want to determine the large system parameters that maximize a specific objective.

Such design problems are in fact optimization problems. Instead of optimizing mathematical expressions, the optimization treats the simulation model as a black box to the optimizer. The simulation-based optimization process incorporated into Optimus, a numerical optimization software solution, adjusts the input variables of the simulation model to identify the levels that achieve the best possible outcome.

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Usually, simulation-based optimization sets specific challenges because of their large size, inexact derivatives when available, and expensive computing time. Many conflicting objectives must be optimized simultaneously, which makes it even more challenging.

Categories of Numerical Optimization

Based on the number of objective functions, Optimus numerical optimization can be classified into subfields:

  • Single-objective optimization: Single-objective optimization contains one single objective that needs to be optimized.
  • Multi-objective optimizationMulti-objective optimization has multiple objectives to be optimized, and usually a so-called Pareto set or a compromised solution is generated.

And based on the search methods, Optimus categorizes optimization methods into:

  • Local optimization methods: Local optimization methods search for an optimum based on the local information, such as gradient and geometric information, of the optimization problem. A local optimum can be found using these algorithms.
  • Global optimization methods: Global optimization methods search for the optimum based on global information about the optimization problem. These are usually probability-based searching methods. These methods have a good possibility to find the global optimum, but this is not guaranteed.
  • Hybrid optimization methods: Hybrid optimization methods combines the local and the global approach in a seamless approach. These usually rely on response surface approximation to find a global optimum with minimum effort.