The Optimization problem is a search problem. Generally, information has a cost and management wants to maximize goals while minimizing cost and time spent.
Complicating the problem is that fact that there are "permissible" regions and "not permissible" regions. For example, if you were trying to optimize fuel economy of a vehicle, a zero-to-sixty time of more than 8.0 seconds might be "not permissible" due to lack of consumer acceptance. Interesting problems will have many, intersecting "not permissible" constraints.
|Gold star denotes highest point. Permissible region is the area inside the red triangle.|
Because of the frequency that optimum solutions are found in the vertices, it is absolutely critical that the boundaries between the permissible and not-permissible regions be defined with great care.
This problem is addressed by running the optimization routine many times, the difference being that our blind man starts at several different locations. For example, you might find the absolute, optimum spouse at a dance, a laundromat, a church, a college classroom, a bar or an Appleseed shoot. The diligent searcher should exhaust all venues and compare results.
An even harder optimum to find is if the tops of the trees are "permissible". The chances of our blind man stumbling into a tree is very remote because the tree trunk is not very large. Yet the top of the tree is the highest elevation inside the red polygon.
Those "trees in the golf course" often seem to be the result of synergistic behaviors of otherwise, predictable inputs. There are a lot of ways to combine organic materials and nitrogen salts. Only a few of them result in gunpowder. The trees are often found by the two-guys-in-a-garage because they have the freedom to look in unlikely places.