Systematic Evolutionary Algorithm for a general Multilevel Stackelberg Problems with bounded decision variables (SEAMSP
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Date
2013-07-01
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Addis Ababa University
Abstract
Multilevel Stackelberg Problems (MSPs) are nested optimization problems which
reply hierarchical decisions of subproblems. Each decision maker (DM) in the hierarchy
admits the decision of those above its level (if exist), observes the response of those be-
low (if exist) for each possible value of its decision variable and returns the best variable
value/s of its interest. These kind of problems are known to be common in distinct areas
of study. Linear MSPs are shown to be NP-hard problems by di_erent authors. The
inclusion of non-linear, non-convex, non-di_erentiable and other undisciplined property
of functions add further complexity to the problem. Unfortunately, real life situations
are crowded with such kind of functions. Most existing algorithms in MSPs are proposed
for bilevel stackelberg problems (BSPs), specially the linear version of BSPs. Systematic
evolutionary algorithm for a general multilevel stackelberg problems (SEAMSP) having
bounded decision spaces, has been proposed in this work. A unique feature of the algo-
rithm is that it is not a_ected by the behavior of the objective and constraint functions
involved in a problem. The proposed algorithm apply evolutionary algorithm concepts
to MSPs, with systematic way of selecting initial populations at each iteration and a
newly constructed mutation operator, which is suitable to the selection of populations.
In SEAMSP, each decision space is controlled by \intelligent spies" having a nice
cooperation with the spies on the other decision spaces, for representing the whole con-
straint region in a random, unique, diverse and systematic way. The numerical results
on various problems demonstrated that the proposed algorithm is very much promis-
ing to MSPs without any limitation of the included functions, and it can be used as a
benchmark for a comparison of approximate results by other algorithms
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Keywords
Systematic Evolutionary, Algorithm for a general Multilevel