Description: Optimization in the context of engineering Design. Non-linear and linear, static and dynamic, constrained and unconstrained formulation and solution of practical problems. Structural optimization. Multi-objective optimization. Genetic Algorithms. Simulated Annealing.

Textbook: "Elements of Structural Optimization" - Haftka and Gurdal. Kluwer Academic Publishers, latest edition.

References: Genetic Algorithms in Search, Optimization and Machine learning. Goldberg, Addison Wesley, 1992.
Engineering Optimization. Ragsdell, Reklaitis, Ravindran, Wiley, 1983.

Objectives: To provide engineering students interested in CAE/CAD an engineering view of optimization as a tool for design. The course will concentrate on the mathematical and numerical techniques of optimization as applied to engineering problems. It is designed to provide students with a strong background in optimization which can be complemented by more specialized courses in Mathematics.

Topical Outline: 1. Introduction to the formulation of optimization problems. Unconstrained optimization. Zero order search. Random walk.
2. Adaptive creep. Powell’s method. First order search.
3. Gradient, Conjugate gradient methods.
4. Second order search. Newton-Raphson, Davidon-Fletcher-Powell.
5. Constrained optimization. Penalty methods. Direct methods of constrained optimization.
6. Linear programming.
7. Sensitivity analysis. Multi-objective - pareto - optimization. Equality constraints, Cumulative constraints.
8. Law of diminishing returns and function approximation concepts. Sensitivity of objective function and Lagrange Multipliers.
9. Goal Programming. Primal Dual Methods.
10. Generalized Reduced Gradients. Dynamic Programming. Integer Programming. Sensitivity of optimum to problem parameters.
11. Multi-level optimization. Optimization of complex engineering problems.
12. Non-traditional tools of optimization - Genetic algorithms, Simulated annealing.

Grading: Programming projects (4 or 5 hw projects) 60%
1 Semester Project 30% (due on Finals day)
1 paper presentation 10%