## Application Project

The first project for this course is similar in scope and size as the prior homework problems but is of the student's own creation.

1️⃣ Develop a mathematical model for the problem that describes the objectives and constraints of the optimization.

2️⃣ Select a suitable optimization algorithm to solve the problem.

3️⃣ Develop a computer program to implement the algorithm.

4️⃣ Test the program to ensure it meets the objectives and constraints.

5️⃣ Analyze the results and refine the model and algorithm as needed.

6️⃣ Create a visualization of the feasible region, objective contours, and optimal solution.

7️⃣ Document the optimization project and the results.

The project should have the following characteristics as general guidelines:

- Involve an application from engineering
- Preferably involve an application from prior work experience or current research interests
- Problem size guidelines
- 3-10 design variables
- 10-50 equations

- Problem type guidelines
- Continuous variables preferred (LP, QP, NLP)
- Can include discrete variables (MILP, MIQP, MINLP)
- Empirical equations
- Equations from first principles
- Hybrid models: mix of empirical and first principles

For the project report, turn in the following content:

- A 2-3 page write-up of the problem in a way that a student can solve the problem in 1-2 hours. Include figures, equations, and problem background sufficient to allow an engineer from any discipline to be able to understand and formulate the mathematical model and solve the optimization problem. If the project builds upon another problem, include the relevant citation in the project write-up.
- A copy of the solution key with the optimal solution, relevant contour plots, a description of the meaning of the results, and any other relevant information.
- A copy of the source code used to generate the solution.

The project reports will be graded on originality, technical difficulty, clarity of the problem statement, accuracy of the solution, description of the solution, and professionalism of the report.

#### Optimization Problem Statements

- Bolt Pattern
- Building Design
- Catalyst Design
- Chemical Reactor Design
- Compliant Knee Simulator
- Compliant Window Shutters
- Concrete Beam
- Drone Aircraft EMI Shielding
- Fin Array Heat Transfer
- Flying Wing
- Flywheel Design
- Helical Spring
- Jet Engine
- Masonry Shear Wall
- Reactor Design
- Refinery Production
- Rocket Fin Design
- Snow Ski Design
- Sprinkler System Design
- Synthetic Diamond Anvil
- Trebuchet Design
- Turbomachinery Efficiency
- Water Heater