Optimization

Design and analysis optimization methods use specialized algorithms to iteratively search the design space for the best values of input variables to achieve a specified goal. In many cases, optimization can be applied to everyday design problems to improve product performance/quality while simultaneously reducing manufacturing cost, weight, etc.

Multidisciplinary Design Optimization (MDO) simply refers to the use of optimization methods on system-level models. For example, MDO methods can be used to minimize a product’s predicted cost, while satisfying engineering, manufacturing, and logistics variables and constraints. There are special methodologies that can be utilized to aid in exploration and simplification of complex MDO problems, such as Design of Experiments (DOE) and Response Surface Methodology (RSM).

Optimization algorithms that are used for engineering problems can be grouped into two categories: deterministic and stochastic.

Deterministic methods include gradient-based and simplex algorithms. Gradient-based algorithms attempt to find an optimum by searching along the direction of steepest descent of the objective function, until some convergence criterion is met. Some gradient-based methods are designed to handle constraints. If used properly on the right kinds of problems, gradient-based algorithms usually require the fewest evaluations to find a solution. However, these algorithms are susceptible to finding a local (rather than global) optimum if a poor start point is selected. Also, gradient-based methods are ill-suited for problems with discrete variables or noisy objective functions.

Stochastic methods include genetic algorithms, simulated annealing, Monte Carlo, and random walk. All of these algorithms employ probabilistic methodologies (randomness) in their search. Due to the probabilistic nature of stochastic methods, it is often possible to parallelize evaluations of the objective function in order to speed up the solution. This is a major advantage over gradient-based optimization, which is impossible to parallelize.

Genetic algorithms, for example, are very useful for engineering problems with multiple optima, a noisy objective function, multiple objectives, and/or discrete design variables. Genetic algorithms start with a more global search and eventually converge to an optimal population of designs. However, they have the disadvantage of requiring more evaluations to converge, compared to gradient-based methods. In addition, many genetic algorithm implementations do not handle constraints.

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