Page 184 - Using ANSYS for Finite Element Analysis Dynamic, Probabilistic, Design and Heat Transfer Analysis

Design optimization • 171
of design variables, g is a vector of inequality constraints, h is a vector of
equality constraints, x and x are vectors of lower and upper bounds on
ub
lb
the design variables. Maximization problems can be converted to min-
imization problems by multiplying the objective by constraints can be
reversed in a similar manner. Equality constraints can be replaced by two
inequality constraints.
Optimization Tree: The optimization is divided into three types,
namely, the continuous, discrete, and multi-objective optimization. The
various ways for optimization along with the procedures to be followed
are listed in Figure 5.1.
Problem solution: The problem is normally solved using appropriate
techniques from the field of optimization. These include gradient-based
algorithms, population-based algorithms, or others. Very simple problems
can sometimes be expressed linearly; in that case, the techniques of linear
programming are applicable.

Gradient-based
methods Population-based Other methods
• Newton’s method
• Random search • Genetic algorithms • Steepest descent
• Grid search • Memetic • Conjugate
• Simulated annealing algorithms gradient sequential
harmony search direct • Particle swarm quadratic
search optimization
programming

Figure 5.1. Optimization tree listing the optimization methods.