STANDARD EXAMPLES OF OPTIMIZATION PROBLEMS

Problem
The purpose and restrictions
Type of object
representation
Number
of 
variables
-----------
restrictions
The class of
goal function
Optimization of geometrical 
parameters of the multistage axial compressor
1. The magnification of efficiency on rated operational model of gas-turbine engine or power installation at observance of restrictions on air consumption, compressor operation stability and strength of details. 
Mathematical
model
4-99
-----
8-220
Multiextreme, 
non-
differentiable
--"--
2. The magnification of compressor efficiency on several operational modes of gas-turbine engine at observance of restrictions on air consumption, operation stability and strength of details. (Multicriteria approach). 
Mathematical
model
4-99
----
8-600
Multiextreme, 
non-
differentiable
--"--
3. The maximization of efficiency ensured with specific probability at a specific accuracy of details manufacturing and specific probability of restrictions observance.
Mathematical
model
4-63
----
12-280
Stochastic 
The joint optimization of geometrical parameters and 
blades rows control laws of multistage axial compressor
The maximization of efficiency for a specific range of operational modes at observance of restrictions on air consumption, compressor operation stability and strength of details 
Mathematical
model
4-63
----
8-250
Multiextreme, 
non-
differentiable
The optimization of work process parameters of 
gas-turbine engine of versatile aircraft
The choice of optimal values of design and gas-dynamic parameters of gas-turbine engine for given totality of aircraft flight modes
Mathematical
model
3
--
4
Nonconvex
The searching of Pareto- optimal for a specified series of engine operational modes totality of multistage axial compressor geometric parameters and blades rows control laws. (Multicriteria optimization). The minimization of fuel consumption for each of specified operational modes at observance of restrictions on operation stability and strength of details
Mathematical
model
6-18
---
6
Multiextreme
The optimization of control program of the serial gas-turbine engine controllable elements (multicriteria approach). Searching of positions of controllable elements to be Pareto- optimal on "thrust" and "fuel consumption" criteria at observance of restrictions on components stability margins and on gas temperature at turbine inlet
Mathematical
model
3-4
----
5
Nonconvex
The multipurpose optimi-zation of STOVL aircraft power plant design parameters and controllable elements positions The magnification of vertical thrust and low pressure compressor stability margins at observance of restrictions on remaining ele-ments stability margins, temperatures of gas at turbine inlet and nozzles outlets, on rotors rotation rates and on the thrust modulation margin
Mathematical model
8
-----
6
Nonconvex
The multipurpose optimization of time control laws of power plant of STOVL aircraft for it’s short take-off The decreasing of take-off run length and fuel consumption for STOVL aircraft short take-off from it’s start to evolutive velocity and safe altitude reaching at observance of restrictions on stability margins, temperature of gas and rotors rotation rates
Mathematical model
Up to 53
---------
8
Multiextreme
The optimization of control laws of controllable ele-ments of aircraft gas-turbine engine at non-stationary perturbations of inlet stream 1. The preservation of steady engine operation at minimum losses of thrust impulse for specified parameters of perturbation.
Mathematical model
48-216
--------
26
Multiextreme
--"--
2. The maximization of probability of steady operation security and minimization of expectation of thrust impulse losses for specified perturbation probability perform-ances
Mathematical model
24-112
-------
26
Stochastic
--"--
3. Raise of probability of steady operation security at a lack of information about per-turbation parameters.
Mathematical model
16-48
-------
5
Multiextreme
The optimization of aircraft gas-turbine engine controllable elements control laws at maneuvering of aircraft The minimization of maneuver execution time and fuel consumption at restriction on aircraft overload and admissible angles of attack and on engine operation stability
Mathematical model
20 - 70
-------
5
Multiextreme
The optimization of parameters and control programs of gas-turbine engines, which have completed resource, in a structure of ground power installations The minimization of fuel consumption, the minimization of thrust and maximization of outlet temperature for gas-turbine engine in a structure of the thermal machine. (Multicriteria approach)
Mathematical model + actual plant
3 - 5
------
3
Multiextreme
The optimization of sizings of microsystems of automobile engine control The minimization of fuel consumption at specified restrictions on exhaust toxicity
Actual plant on the experimental bench
3
---
3
Stochastic
The optimization of multilayer optical coatings Minimization of surface reflection (absorption) coefficient in a specified range of lengths of waves
Mathematical model
6-20
-----
57
Multiextreme, ravine
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