Additional information is available at the end of the chapter http://dx.doi.org/10.5772/53700
. IntroductionThe process of selecting objects, activities, people, projects, resources, etc. is one of the activities that is frequently realized by human beings with some objective, and based on one or more criteria economical, space, emotional, political, etc. For example, as a daily experience people should select what means of transportation and routes to utilize to arrive at a determined destination according to the price, duration of the trip, etc. In these cases, one must select the best subset of elements based on a large set of possibilities, the best in some sense, and in many cases there is an interest in the selected elements not appearing amongst themselves, if not it is better that they have different characteristics so that they can represent the existing diversity in the collection of original possibilities. Of course at this level people make these decisions intuitively, but commonsense, generally, is not a good advisor with problems that require optimized decision-making, and simple procedures that apparently offer effective solutions lead to bad decisions, thus this can be avoided by applying mathematical models that can guarantee obtainable effective solutions. In other human activities the selection of this subset has economic implications that involve a selection of a more diverse subset, a crucial decision, and difficult to obtain, which requires a correct process of optimization guided by a methodical form.In the Operations Research literature, the maximum diversity problem MDP can be formulated by the following manner If V = { , , ⋯ , n } is the original set, and M is the selected subset, M ⊂ V , the search for optimizing the objective is as follows
