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Optimization and Decision Theory (Hardcover)
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Optimization and Decision Theory (Hardcover)
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The theory of decision deals with analyzing how a person chooses an
action that, among a set of possible actions, leads to the best
result given the preferences. If a person should invest or not in
capital goods, what career a person is going to choose, what car is
foing to buy, are very common problems that affect us in our daily
life and to the which - in formal terms - is faced with the theory
of decision. On the other hand, in recent years its influence in
disciplines such as psychology and economics has been so great,
along with applied mathematics, sociology, political science and
philosophy - which have that it is very difficult to address some
of these specialties without having a knowledge of theory of the
decision. Decision theory has become an indispensable working tool
in disciplines as varied as economics, psychology, science
politics, sociology or philosophy. Nevertheless, he remains a great
stranger for many social scientists despite its great influence. In
this work the basic elements of decision theory are presented first
then focus on decision theory in situations of uncertainty. Thus,
after explaining some classic decision criteria under uncertainty,
we discuss the normative model of expected subjective utility
(SEU). The limitations of this theory lead us to the more recent
descriptive models that are Support of Herbert Simon's limited
rationality theory as the model the adaptive decision maker or the
theory of ecological rationality. Life abounds in situations where
it is necessary to make decisions. In some cases, the consequences
of decisions depend only on one side, which makes the decision. For
example, a programmer makes a decision in any programming language
will encrypt algorithm that solves a given problem. However, the
consequences of decisions often depend not only on one side but
also on the interaction with the decisions taken by the other side,
so that the outcome of the decision on the one hand depends on the
decisions of others or other parties. It is often the case that
such a situation characterized by conflicting-antagonistic
interests of the participants in decision-making, ie. we say that
the parties to make decisions in the conflict. In the game of
chess, the result of the game depends not only moves one player
more than another move and their interests are conflicting, because
each side wants to win another. This situation of uncertainty in
decision-making in mathematical games is the field of operations
research that deals with the analysis of these problems and finding
optimal solutions, and is called game theory. Game theory means the
mathematical theory of decision-making process by the opponent (the
participants, players) that are in conflict (conflict) or are
involved in competitive conditions. The term game means a model of
real conflict situations. The game can be added to the relevant
rules, which define the rules of conduct of participants in the
game, and the goal of game theory is that the exact mathematical
algorithm analyzes the conflict situation and determine the
reasonable behavior of the players and the course of the conflict,
ie. to determine the optimal strategy for each of the participants
in the game. Game theory has the task of finding solutions in
situations of competition, which is partially or completely
conflicting interests are at least two opponents (ie. According to
this theory among the participants in the game). The solution of
the conflict is determined by the actions of all parties involved
in the conflict. Game theory deals with situations that have the
following characteristics: a) there must be at least two players;
b) The game starts by having one or more players choose between
defined alternatives; c) after the selection is associated with the
first move, the result is determined by the situation that
determines who makes the next selection and what are his options
open; d) the rules of the game are certain rules for determining
which specifies the mode of behavior of players; e) any move in the
game ends the situation that determines the payout of each
bonificiranog player (extra nine player is the one who makes
choices and receive payments). There are many examples in different
areas of life that can be observed and studied as a conflict
situation. A good number of economic problems in the field of
market - competitive relations contain conflicts of different
interests, so they can be analyzed and solved using game theory. In
this book the solutions of multiobjective problems are considered
through genetic algorithms, which consist of random searches in the
search space marked by the restrictions, obtaining solutions
increasingly efficient. In order to achieve this, two new
methodologies are proposed, the first one (MOEGA), which elitism as
an interesting concept not to lose the good results that are have
achieved and obtain a Pareto border close to the real and the
second (MOEGA-P) which considers the preferences of the decision
maker in an interactive way, such that the decision maker can
direct the search of the algorithm towards the area of its
interest. MOEGA get better solutions in the problem of the backpack
comparing it with algorithms like the SPEA2 and NSGAII and MOEGA-P
allows the decision- maker to obtain only a portion of the pareto
according to your preferences acquiring knowledge of the problem,
such that for it will be much easier for him to decide between this
small group of alternatives. In addition to in the case of the
backpack, MOEGA-P offers the decision maker alternative solutions
that does not consider an algorithm without preferences and much
closer to the Pareto frontier real, because restricting the search
area with preferences, takes advantage of the cost to find more
efficient solutions instead of looking at areas that are no longer
are of interest to the decision maker. In this book, the problem of
multiobjective optimization is described, mentioning some classic
techniques of optimization as well as some meta techniques -
heuristics that are used to solve such problems. Since the interest
of this research are the genetic algorithms, will be deepened in
this type of methodology. The following chapter will describe the
main methodologies of multiobjective genetic algorithms and will
mention how the preferences of the decision maker. Taking into
account the weaknesses and strengths of these methodologies, the
next chapter describes an interactive methodological proposal where
the decision-maker intervenes in the search process for better
results and according to your preferences; But not before proposing
another new methodology of algorithms genetic algorithm that
obtains better results comparing it with the already existing ones.
Then, the results obtained with the two methodological proposals
are described along with the conclusions and some ideas of possible
future work.
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