From a real problem to an optimization model
Before choosing GA, DE, or a numerical solver, make the problem itself precise.
Learning goal
Translate a decision problem into decision variables, an objective function, and constraints.
Prerequisites
- Elementary algebra
Model structure
A model states what we choose, what we want to minimize or maximize, and which choices are feasible.
Production example
Let x₁ and x₂ be production quantities with unit profits 40 and 30. A natural objective is to maximize total profit under resource limits.
Why modeling comes before the algorithm
If the objective is wrong, the optimizer returns the best answer to the wrong problem. If a real constraint is omitted, the result may be mathematically valid but operationally impossible.
Connection to the Convex QP Solver
The solver project takes this modeling step to a more structured form and then applies numerical methods. The algorithm is the end of the chain, not the starting point.
Exercises
- Model a two-task scheduling problem.
- Write both a cost objective and a delay objective.
- Find one real constraint whose removal would make the model unrealistic.
Related project
Convex Quadratic Programming Solver
A real project taking a convex QP model into a numerical solver.
Open sourceRelated solutions
Have a decision problem?
We can make the model precise before choosing an algorithm.