Assignment 5

Published

March 11, 2024

Abstract
Exploration of MDO architectures and their implementation

Due: 19-04-2024

Problem Statement

\[\begin{aligned} \text{minimize} &\ \ & x_1^2 + x_2 + y_1 + e^{-y_2} \\ &\ \ & \\ \text{w.r.t} &\ \ & z_1, x_1, x_2 \\ &\ \ & \\ \text{such that}&\ \ & y_1 = z_1^2 + x_1 + x_2 - 0.2y_2\\ &\ \ & y_2 = \sqrt{y_1} + z_1 + x_2 \\ &\ \ & \\ &\ \ & \frac{y_2}{24} - 1 \le 0\\ &\ \ & 1 - \frac{y_1}{3.16} \le 0\\ &\ \ & \\ &\ \ & -10 \le z_1 \le 10\\ &\ \ & 0 \le x_1 \le 10 \\ &\ \ & 0 \le x_2 \le 10 \\ \end{aligned}\]

The global optimum is located at \((z_1, x_1, x_2) = (1.9776, 0, 0)\).

So this question seems straight forward. Solve the problem using MDF, IDF and AAO architectures.

Questions

  1. Clearly state the mathematical formulation of each architecture and the results obtained.
  2. Compare the performance of the different architectures in terms of convergence and computational cost.
  3. Experiment with different initial guesses for each problem and comment on the robustness of each architecture.
  4. Comment on the ease of implementation and the potential for parallelization of each architecture.

Deliverables

  • A pdf report with source code and a discussion of your implementation methodology and results.