Special Topics
- Part One: Historical Review
Earlier Optimization, Minimum Weight, Linear Programming Application, Optimality Criteria Methods, Mathematical Programming Methods, Generalized Optimality Criteria, Discrete Optimization
Shape Optimization, Software Packages
- Problem Formulation, Component and system level optimization
- classical optimization; differential calculus, Lagrange multipliers, calculus of variations
- Linear Programming formulation, Simplex method, sequential linear programming,
- Unconstrained optimization (Direct search methods: univariate search, conjugate directions,
- Gradient methods: steepest descent, conjugate gradients, Newton methods: Newton-Raphson, Variable-Metric
- Constraint optimization
Tucker conditions, Gradient Projection methods, feasible directions methods, penalty-function methods: Exterior method, interior method, Gauss-Newton method
- Part Four: Approximation Concepts
Basic concepts, Sensitivity Analysis (stress and Displacement sensitivities, Pseudo-load and virtual load methods, sensitivity of vibration frequencies), variable
selection, Constraint approximations (conservatives and hybrid approximations), The synthesis process
- The Dual method, Discrete variable optimization, Optimality Criteria method (Intuitive methods, rigorous methods), shape optimal design
- Part Five: Genetic Algorithms
Modeling the evolutionary process (artificial life, evolution strategies), Application of a genetic algorithm (coding a decision variable, evaluating fitness, genetic
erations, one-generation operation of GA), Genetic algorithms for engineering design (trussed-beam roof strictures, cable-stayed bridge, Michell truss, composite
laminate plate