Introduction to Mathematical Optimization
Optimization Vocabulary Your basic optimization problem consists of •The objective function, f(x), which is the output you’re trying to maximize or minimize •Variables, x 1 x 2 x 3 and so on, which are the inputs – things you can control They are abbreviated x n to refer to individuals or x to refer to them as a group
Introduction to Optimization Models
optimization models • Decision variables • Parameters (data) • Constraints • Performance objective • Linear problems = constraints and performance objective are linear functions of decision variables 2
Part 1 Examples of optimization problems
The cost of optimization algorithms is dominated by evaluating f(x), g(x), h(x) and derivatives: Traffic light example: Evaluating f(x) requires us to sit at an intersection for an hour, counting cars Designing air foils: Testing an improved wing design in a wind tunnel costs millions of dollars How expensive is every iteration?
Introduction to Constrained Optimization
Graphical Optimization The overlap of these graphs is known as the feasible region A solution to the problem must lie in the region in order to obey both of the constraints x 1 x 2 And, because the constraints are linear, the maximum and minimum must lie on the boundary
OVERVIEW OF HEURISTIC OPTIMIZATION
OPTIMIZATION (Eberhart Kennedy -1995) A robust stochastic optimization technique inspired by the social behavior of swarms of insects or flocks of birds –maximize “food” Apply the concept of social interaction to problem solving Developed in 1995 by James Kennedy (social-psychologist) and Russell Eberhart (electrical engineer)
Optimization Practice Problems
Optimization Practice Problems – Pike Page 3 of 15 n n Use the First Derivative Test to determine if each critical value is a maximum, minimum, or neither 3 475 x 2 is a minimum because the derivative changes from negative to zero to positive Answer the question 1 3 3 3 2 2 3 5 3 22 0 6 r 475 2
Optimization, Validation and Troubleshooting Single and
•Initial optimization efforts should identify good control or standard RNA or DNA that you can rely upon throughout data generation •Generate a range of acceptable QPCR performance data •Controls should dictate what data is good or bad •Practice setting up assay, its not a trivial task •Always try and start with good RNA or DNA of known
The Value of Optimization in Asset Management
Before discussing the value of asset optimization, a few key terms require definition: • Asset is an item of value owned • Optimization is an act, process, or methodology of making something as fully perfect, functional or effective as possible • Perfect means having all the qualities you want, rather than making every asset as close
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