Reduction of computational costs of optimization of real industrial processes is crucial, because the models of these processes are often complex and demand time consuming numerical computations. Iterative optimization procedures have to run the simulations many times and therefore the computational costs of the optimization may be unacceptable high. This is why a new optimization methods and strategies which need less simulation runs are searched. The paper is focused on the problem of reduction of computational costs of optimization procedure. The main goal is the presentation of developed by the Authors new, efficient Approximation Based Optimization (ABO) and Modified Approximation Based Optimization (MABO) methods which allow finding the global minimum in smaller number of objective function calls. Detailed algorithm of the MABO method as well as the results of tests using several benchmark functions are presented. The efficiency of MABO method was compared with heuristic methods and the results show that MABO method reduces the computational costs and improve the optimization accuracy.

1.
J.
Kusiak
,
J. Mat. Proc. Techn.
57
,
79
84
(
1996
).
2.
J.
Kusiak
,
A.
Danielewska-Tułecka
, and
P.
Oprocha
,
Optimization. Chosen methods with applications
(
PWN Wydawnictwo Naukowe
,
Warszawa
,
2009
- in Polish).
3.
L.
Sztangret
, “
Reduction of computational costs of the metallurgical processes optimization
,” PhD thesis - in Polish,
AGH University of Science and Technology
,
Krakow, Poland
2014
.
4.
T.
Back
,
Evolutionary algorithms in theory and practice
(
Oxford University Press
,
New York
,
1996
).
5.
R. C.
Eberhart
and
J.
Kennedy
,
Proc. Conf. Sixth International Symposium on Micromachine and Human Science
39
43
(
1995
).
6.
J.
Holland
,
Adaptation in natural and artificial systems
(
MIT Press
,
1975
).
7.
J.
Kennedy
and
R. C.
Eberhart
,
Proc. IEEE International Conference on Neural Networks
1942
1948
(
1995
).
8.
H.
Schwefel
,
Evolution and optimum seeking
(
Wiley
,
Chichester
,
1995
).
9.
M. D.
Vose
,
The simple genetic algorithm: Foundations and Theory
(
MIT Press
,
Cambridge
,
1998
).
10.
L.
Sztangret
and
J.
Kusiak
,
Lecture Notes in Artificial Intelligence
2
,
600
607
(
2012
).
11.
E.
Rafajłowicz
,
Algorytmy planowania eksperymentu: z implementacjami w środowisku Mathematica
(
Akademicka Oficyna Wydawnicza PLJ
,
Warszawa
,
1996
- in Polish).
12.
R. H.
Myers
and
D. C.
Montgomery
,
Response Surface Methodology: Process and Product Optimization Using Designed Experiments
(
Wiley
,
New York
,
1995
).
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