||Moderate dimension implies up to 20-50 design variables.
Large dimension implies up to 100-200 design variables.
|Nonlinear inequality constraints
||For problems of moderate dimension the number of inequality
constraints should be up to 20-50. For large dimension problems, there
is no limit on the number of inequality constraints.
|Nonlinear equality constraints
||Each equality constraint should be transformed into
two inequality constraints. Alternatively, the penalty function approach
could be used. Any types of penalty functions could be employed, including
discontinuous ones. The reason for such a variety is that our optimization
algorithms are insensitive to the topology
of the objective function.
|The number of objective functions
||For problems of moderate dimension the number of objectives
should be up to 10. For large dimension problems up to 20-40. If
the user will require, this number could be increased.
|The number of processors that can be
used with parallel optimization algorithms
||No restrictions. For example, for 5 design variables
problem 2, 9, 23, 100, and more processors can be employed.
|The number of levels that can be used
in multilevel optimization algorithms
||Up to 3 levels of mathematical models can be used: low
fidelity models (LFM), moderate fidelity models (MFM), and high fidelity
models (HFM). Their use is adaptively determined by our response surface
algorithms without users input. MFM and HFM mathematical models should
be developed by the user. For example, MFM 2D CFD, HFM 3D CFD.
If the user requires, more fidelity levels can be employed. For example,
2D CFD, quasi 3D CFD, and 3D CFD. Also, the difference in the fidelity
of the mathematical model could be determined by the discretization
|Requirements for the topology of the
objective function and constraints
||There are no restrictions on topology of the objective
function and constraints except for one: the capability to determine
the value of the objective function and constraints at least in some
subspace of the design space.
|Requirements for a starting point of
||No starting point is required.
|Use of previously obtained information
in optimization process.
||It is possible in the optimization process to make use
of the information obtained prior to the optimization, including use
|Specifics of the optimization process
||It is possible to stop the optimization process at any
iteration and then ontinue it at any other time without any extra
information from the user. It is also possible to change the method
of optimization when starting the continuation process. In the last
case, however, the user may be required to provide some extra information.
|Information about existence of the solution
in the design space
||There is no need to provide any information about existence
of the solution in the design space. In case of incorrectly posed
optimization problem (no feasible solution), the algorithms will find
the solution with minimal possible violation of the constraints.
|Requirements to the computational reliability
of the analysis program
||Our optimization process is very insensitive to fluctuations
in computational process. That is why it is allowed for the users
analysis program to fail during optimization process. It is also allowed
to have some regions in the design space where it is not possible
to evaluate objective function and constraints. In this case the only
requirement for the analysis program is not to go into the infinite
loop in these regions.
|Requirements to the user
||The user has to be able to correctly formulate an optimization
- Choose the objective functions (optimization criteria);
- Define constraints;
- Choose design variables and their allowable bounds;
- Prepare the analysis code for information exchange with optimization
module: be able to get the design variables from the optimization
module and provide objective function and constraints to the optimization
It is not required to specifically modify analysis code when preparing
for integration with optimization module. That is why integration
|Requirements to knowledge of optimization
||IOSO Technology control parameters are defined within
the algorithm and are adaptively changed during optimization process
without users interference.
|Requirements to programming language
of the analysis code
||The information exchange between users analysis code
and optimization module is accomplished by means of external files.
That is why analysis code can be written in any programming language.
The user can take into account this information when analyzing the optimal
solution. Particularly, the user may choose some other point, rather than
the optimal, as the best point, according to his other considerations.
The objective function value at the chosen point, however, will have the
value close to the one at the optimal point. This information may also
help in formulating new optimization problems at a later stage, which
results in cost reduction for obtaining the new solution.