Many optimization problems are inherently continuous, where . In such problems, binary encoding introduces artificial discretization of a continuous space, and long chromosomes are needed to achieve acceptable precision. With real-valued GA, we can work directly in the problem’s native space.
Note that with real-valued genetic algorithms, we no longer have to do encoding, so the genotype = phenotype. We can represent a solution directly as a real-valued vector, where each gene corresponds to a real-valued problem variable.
- Example: Tuning controller gains
Real-valued genetic algorithms are particularly effective when:
- Objective function is continuous
- Gradient information is unavailable
- Search space is multimodal, noisy, or rugged
- Global exploration is more important than local optimality
Note that our variation operators for binary genetic algorithms no longer work, as we can’t do things like bit-level crossover. Thus, we turn to variation operators for real-valued genetic algorithms.
Constraints in Real-Valued GA
Most real0-valued optimization problems impose box contraints:
After mutation or crossover, variables may violate these bounds. Thus, we need some constraint-handling strategies:
- Repair (clipping): Force values back to nearest bound
- Reflection: Mirror excess back into feasible region
- Rejection & resampling: Discard and withdraw offspring
