Single versus Multi-Objective - The Systems Realization 单与多目标系统的实现.ppt

Training course design
Single versus Multi-Objective - The Systems Realization 单与多目标系统的实现
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Model Formulations
Different types of optimization model formulations exist:
Classical non-linear formulation
Linear Programming formulation
Baseline model formulation
Goal Programming formulation
Compromise Decision Support Problem formulation
etc.
Basic classifications are:
Constrained versus unconstrained
Linear versus non-linear
Single objective versus multi-objective
Another classification can be made by variables:
continuous/discrete/mixed-integer
2
Introduction to Multi-Objective Optimization
3
Single versus Multi-Objective
What should you use and what is available?
Most important rule:
Never restrict yourself in modeling!
Design is multi-objective by nature, so we will look at some multi-objective formulations first.
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Different formulations
There are different ways to formulate a multi-objective optimization model
Some covered are:
Baseline model
Goal Programming (GP) model
Compromise Decision Support Problem model
Others exist
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Baseline Model
Ignizio proposes the following “baseline” model:
He argues that this is one of the most generic and flexible mathematical programming models.
What is missing?
Find
The vector of problem variables
X
Satisfy
The goals
A
t
(
X
)
= T
t
for all t
Maximize:
A
r
(
X
)
for all r
Minimize:
A
s
(
X
)
for all s


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Goal Programming (GP)
Another multiobjective mathematical “programming” technique is Goal Programming (GP)
The term "goal programming" is used by its developers to indicate the search for an "optimal" program (i.e., a set of policies to be implemented) for a mathematical model that is composed solely of goals.
Developers argue that any mathematical programming model may find an equivalent representation in GP.
“GP provides an alternative representation that often is more effective in capturing the nature of real world problems.”
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Difference b