Hello, everybody.
In this lecture, we want to talk about the optimization applications, so there are many applications
that we need, optimization techniques to find out what is the optimal decision for doing that.
Let me give you a very simple example.
Suppose you want to construct a bridge and you want to find out how you should do it.
Definitely.
You want to do it in an optimal way.
So the decision variables are some, let me name some of these decision variables.
For example, you want to know if you want to create a bridge between two points, how many piles are
needed?
What is the optimal distance between these two piles and and also how much cost is needed for doing that
construction?
How many workers do you need for doing that in a minimum time and which materials you have to use in
order to minimize the environmental undesired impacts and so on and so on?
OK, so you can see here that, uh, there are several issues associated with each optimization problem.
So those objective functions and decision variables are dependent on the application.
So let me give you another example.
Suppose you want to, build an aircraft.
OK, and also you want to know, for example, how much fuel does it need?
What is the aerodynamic constraints that should be satisfied?
How much material do you need?
What is the cost of building such a huge, um, an object?
OK, and what are the safety issues?
So you want to decide in an optimal way to better use your resources.
OK, so for this purpose, you need to know how to deal with different kinds of constraint creation and
how to find out what is the optimal decisions in this regard.
OK, So, different optimization problems can be categorized into some categories.
For example, single objective optimization.
So in these types of optimization, you only have one objective function and also you have a multiple
number of constraints.
OK, so this is one way of dealing with the optimization.
The other way is, for example, you have multiple objective functions and you want to find out what
is the optimal decision variables in order to not only satisfy the decision and constraints, but also
the objective functions are both optimized that can be minimized or they can be maximized.
OK, and sometimes the objective function is inside the constraint.
So you can see here the objective function too is inside the concept.
For example, let's say we want to maximize or have one and we have an additional constraint.
Saying that of two should be, for example, less than something or bigger than something.
OK, so this is called multilevel optimization.
So at the upper level, we have some objectives and the lower level we have other objectives.
And for each type of optimizations, we need to know how to deal with them.
OK, that's it.