A local optimum is a solution to a problem that appears to be a global optimum, but is not. Complex fitness landscapes can have deep valleys surrounded by mountains. The optimization method may very well get caught in one of these valleys with no way to get over the mountains to see if the next valley is a better solution. For example, in the following image, imagine the optimal solution to the function is at point A. If the optimization method finds point C or B it must climb the hill (or be able to accept less optimal solutions) before seeing improvements again. The more complex the problem, the more likely optimization methods will have to overcome local optimum problems.