Optimization and simulation

Optimization and simulation are two commonly used approaches in system modeling and analysis, but they serve different purposes.

• Optimization aims to find the best possible solution to a given problem, by maximizing or minimizing an objective function. For example, this could involve minimizing costs, maximizing profit, or achieving the best trade-off between multiple criteria.

• Simulation, on the other hand, is used to model the behavior of a real or hypothetical system under various conditions without necessarily seeking the optimal solution. It allows for understanding how a system works, evaluating the impact of different scenarios or conditions, and testing hypotheses.

As they serve different purposes, the two techniques implies different inputs and methods.

• An optimization problem requires an objective function to optimize and a set of variables and constraints, that defines together a set on finite solution.

• In a simulation, an initial state and a control are defined, and a set of equation describe the position of the system in the next state, depending of the past and the boundary conditions.

These two approaches are complementary.