It is well known that nonlinear models can be extremely difficult to optimize. Problems of local optima or inherent discontinuities are often compounded by the need to impose constraints on parameter values to ensure that results are meaningful or feasible. Each heuristic rule, or operator , acts on one or more trial solutions from the current population to produce one or more trial solutions to be included in the new population. The many variations of these kinds reflect the variety of codes best suited for different applications.
Mutation randomly changes the values of elements of a single selected code-string.
Used in suitable combinations, the genetic operators tend to improve the average fitness of each successive generation. There is no guarantee that the average fitness will improve between every pair of successive generations. The average fitness may well decline. And in general, the code-string with the greatest fitness in one generation will not appear in the next one. The theorems do not imply that GAs converge to global optima.