Hello Andrea,
To perform a Pareto optimization of three parameters—costs, emissions, and efficiencies of different types of energy generation plants—you'll need to define a multi-objective optimization problem. The Viennet function you found is a classic test function used for benchmarking multi-objective optimization algorithms, but it may not directly apply to your specific problem. Instead, you'll want to create a custom objective function that reflects your parameters.
Here's a general approach to setting up your optimization problem:
1) Define Objective Functions: You need to create three objective functions representing the parameters you want to minimize or maximize:
- Cost: Typically, you want to minimize costs.
- Emissions: You likely want to minimize emissions.
- Efficiency: Usually, you want to maximize efficiency (or equivalently, minimize the inverse of efficiency).
2) Formulate the Optimization Problem: If you're using MATLAB, you can define these objectives in a single function file or as separate functions.
3) Use an Optimization Solver: MATLAB provides several solvers for multi-objective optimization. For example, you can use the gamultiobj function, which is part of the Global Optimization Toolbox, to find the Pareto front.
Best,
Umang
