56
4 Design Optimization of Micromixers
N
(Problem Formulation)
Max
subject to
(Design of Experiments)
Selection of design points using LHS
(Numerical Analysis)
Calculation of objective function for each
design point
Training data
(Model set)
Set of candidate models
Error Analysis
(Search for optimal point)
SQP, PSO, GA
Is optimal point within
design space?
(Optimal Design)
(Final Surrogate Model)
Fig. 4.7 Single-objective optimization procedure (an example)
4.6 Multi-Objective Optimization
The standard form of a multi-objective optimization problem is:
maximi ze
x
/ minimi ze
x
f (x)
subject to x min ≤ x ≤ x max
where f (x) =
f 1 (x), f 2 (x), . . . , f p (x)
is a vector of objective functions and x
is a vector of design variables. x min and x max are vectors for the lower and upper
bounds of the design variables, respectively.
A multi-objective problem yields many solutions, which are known as Paretooptimal solutions. Each feasible solution set x of the multi-objective optimization
4 Design Optimization of Micromixers
N
(Problem Formulation)
Max
subject to
(Design of Experiments)
Selection of design points using LHS
(Numerical Analysis)
Calculation of objective function for each
design point
Training data
(Model set)
Set of candidate models
Error Analysis
(Search for optimal point)
SQP, PSO, GA
Is optimal point within
design space?
(Optimal Design)
(Final Surrogate Model)
Fig. 4.7 Single-objective optimization procedure (an example)
4.6 Multi-Objective Optimization
The standard form of a multi-objective optimization problem is:
maximi ze
x
/ minimi ze
x
f (x)
subject to x min ≤ x ≤ x max
where f (x) =
f 1 (x), f 2 (x), . . . , f p (x)
is a vector of objective functions and x
is a vector of design variables. x min and x max are vectors for the lower and upper
bounds of the design variables, respectively.
A multi-objective problem yields many solutions, which are known as Paretooptimal solutions. Each feasible solution set x of the multi-objective optimization