1 00:00:00,600 --> 00:00:01,480 Hello, everybody. 2 00:00:02,160 --> 00:00:08,490 In this lecture, we want to talk about the optimization applications, so there are many applications 3 00:00:08,490 --> 00:00:15,210 that we need, optimization techniques to find out what is the optimal decision for doing that. 4 00:00:15,570 --> 00:00:17,370 Let me give you a very simple example. 5 00:00:17,370 --> 00:00:22,590 Suppose you want to construct a bridge and you want to find out how you should do it. 6 00:00:23,010 --> 00:00:23,550 Definitely. 7 00:00:23,550 --> 00:00:25,260 You want to do it in an optimal way. 8 00:00:25,950 --> 00:00:32,370 So the decision variables are some, let me name some of these decision variables. 9 00:00:32,700 --> 00:00:39,780 For example, you want to know if you want to create a bridge between two points, how many piles are 10 00:00:39,780 --> 00:00:40,220 needed? 11 00:00:40,710 --> 00:00:49,200 What is the optimal distance between these two piles and and also how much cost is needed for doing that 12 00:00:49,200 --> 00:00:49,980 construction? 13 00:00:50,050 --> 00:00:57,870 How many workers do you need for doing that in a minimum time and which materials you have to use in 14 00:00:57,870 --> 00:01:04,080 order to minimize the environmental undesired impacts and so on and so on? 15 00:01:04,110 --> 00:01:12,260 OK, so you can see here that, uh, there are several issues associated with each optimization problem. 16 00:01:13,500 --> 00:01:19,870 So those objective functions and decision variables are dependent on the application. 17 00:01:20,220 --> 00:01:21,930 So let me give you another example. 18 00:01:22,830 --> 00:01:28,320 Suppose you want to, build an aircraft. 19 00:01:28,500 --> 00:01:34,080 OK, and also you want to know, for example, how much fuel does it need? 20 00:01:34,540 --> 00:01:38,370 What is the aerodynamic constraints that should be satisfied? 21 00:01:38,400 --> 00:01:40,110 How much material do you need? 22 00:01:40,560 --> 00:01:46,250 What is the cost of building such a huge, um, an object? 23 00:01:46,260 --> 00:01:49,290 OK, and what are the safety issues? 24 00:01:49,290 --> 00:01:55,440 So you want to decide in an optimal way to better use your resources. 25 00:01:55,770 --> 00:02:05,850 OK, so for this purpose, you need to know how to deal with different kinds of constraint creation and 26 00:02:05,850 --> 00:02:10,200 how to find out what is the optimal decisions in this regard. 27 00:02:10,320 --> 00:02:18,270 OK, So, different optimization problems can be categorized into some categories. 28 00:02:18,270 --> 00:02:21,050 For example, single objective optimization. 29 00:02:21,060 --> 00:02:28,020 So in these types of optimization, you only have one objective function and also you have a multiple 30 00:02:28,020 --> 00:02:29,190 number of constraints. 31 00:02:29,220 --> 00:02:32,280 OK, so this is one way of dealing with the optimization. 32 00:02:32,290 --> 00:02:38,730 The other way is, for example, you have multiple objective functions and you want to find out what 33 00:02:38,730 --> 00:02:46,920 is the optimal decision variables in order to not only satisfy the decision and constraints, but also 34 00:02:46,920 --> 00:02:52,960 the objective functions are both optimized that can be minimized or they can be maximized. 35 00:02:52,980 --> 00:02:58,860 OK, and sometimes the objective function is inside the constraint. 36 00:02:58,870 --> 00:03:02,520 So you can see here the objective function too is inside the concept. 37 00:03:02,520 --> 00:03:09,360 For example, let's say we want to maximize or have one and we have an additional constraint. 38 00:03:09,360 --> 00:03:14,010 Saying that of two should be, for example, less than something or bigger than something. 39 00:03:14,320 --> 00:03:18,570 OK, so this is called multilevel optimization. 40 00:03:18,570 --> 00:03:24,090 So at the upper level, we have some objectives and the lower level we have other objectives. 41 00:03:24,630 --> 00:03:30,390 And for each type of optimizations, we need to know how to deal with them. 42 00:03:30,420 --> 00:03:31,950 OK, that's it.