The main difference between a genetic algorithm and an optimization algorithm based on a directly defined cost function lies in the way solutions are searched for and how the optimization process is guided.
Inspired by natural evolution and genetics, a genetic algorithm searches for solutions in a search space by selecting, recombining (crossover), and mutating individuals (candidate solutions) in a population.
The cost function (or fitness function) is used to evaluate the quality of candidate solutions in the population. Solutions with better fitness values are more likely to be selected for reproduction and thus pass on their traits to subsequent generations.
Genetic algorithms do not require information about the gradient of the cost function and are capable of exploring a wide and diverse search space.
These algorithms are particularly useful in complex, nonlinear, and high-dimensional optimization problems where conventional optimization techniques may struggle.
Algorithm based on a directly defined cost function:
These optimization algorithms, such as gradient descent or optimization algorithms based on quadratic programming, seek solutions by directly minimizing the defined cost function in the search space.
Information about the gradient of the cost function, if available, is used to guide the search towards the local or global minimum. In the case of gradient descent, for example, the parameters are updated following the direction of the negative gradient.
These algorithms may be faster and more efficient than genetic algorithms when the cost function is differentiable and the gradient is known.
However, they may struggle with non-convex or constrained optimization problems, as they can get stuck in local minima.
In summary, the main difference between genetic algorithms and algorithms based on a directly defined cost function is the way solutions are searched for and how the optimization process is guided. Genetic algorithms are more suitable for complex and nonlinear problems, while algorithms based on a directly defined cost function may be more efficient in convex and differentiable problems.