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The methodic of comparative analysis of optimization
methods
When evaluating the efficiency of optimization methods for different
test problems it is necessary to find some “rule” how to take into account the
“complexity” of the problem, or its “performances” – the number of design
variables and constraints, their type (equality or inequality), the topological complexity
of goal function and constraints. In our investigations we are used the following rule of
this index evaluation.
Error = (CurrObj - BestObj) / Abs(BestObj) + Penalty;
Score = (10*Nx+5*Nineq+10*Neq)*SQRT[LOG(Error0/Error1)]/Ncalls,
(***)
where Error0 is starting Error, Error1 - final
Error (zero values were replaced by 1e-16). Scores for each test problem were added for
each algorithm, and then normalized by the highest total score. Next step is an evaluation
of Comparative Score:
CompScore=Score+K/R,
K=1, if this task was solved succesfuly; K=0, if algorithm
was failed (the algorithm did not improve Error value below 1e-2); R - rating according to
score for this problem.
The important place in optimization process is taken by the choice of
search starting point. It can effect significantly upon the optimization process itself,
and, consequently, upon the effectiveness indices when carrying out the comparative
analysis. As known, most of the algorithms require starting point. However, there is a
number of algorithms (IOSO algorithms are among them), which do not require this value.
During the starting stage of extremum search these algorithms use the following
hypothesis: ”I know that I know nothing about the researched object”. In practice
usually it is known some basic solution, which can be assumed as the starting point.
However, we can sight a number of real-life problems, for which the starting point and any
information about the object is unavailable.
(***) The main theses of such effectiveness
evaluation approach were proposed by Oleg Golovinov.
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