A genetic algorithm (GA) mimics natural selection — evolve candidate solutions, keep the best, mutate and cross them — to find near-optimal answers to hard problems, including fitting algebraic functions to data. Here is how they work and where they shine.
What Is a Genetic Algorithm?
It starts with a population of random candidate solutions, scores each on a fitness function, then selects, crosses and mutates survivors over many generations until good solutions emerge. No gradients or clean maths required.
Restoring/Fitting Algebraic Functions
To recover a function from noisy data, you encode candidate parameters (coefficients, exponents) as a 'genome', score each by error against the data, and let the GA evolve better fits. It works even on nonlinear or non-differentiable problems.
Advantages
- Works without gradients.
- Escapes local optima better than greedy methods.
- Flexible encoding for complex domains.
Limitations
- Computationally heavy for large problems.
- Results are heuristic — no guarantee of the global optimum.
- Requires careful design of representation and fitness.
FAQ
Is a genetic algorithm exact?
No — it seeks good approximations, not proven optimums.
When should I use one?
For messy search/optimisation problems where classical methods fail or need tuning.
Related: Forecasting and Strategy Optimization.