Editing Multidisciplinary design optimization (section)

==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===
*[[Adjoint equation]]
*[[Newton's method]]
*[[Steepest descent]]
*[[Conjugate gradient]]
*[[Sequential quadratic programming]]

===Gradient-free methods===
* Hooke-Jeeves pattern search
* [[Nelder-Mead method]]

===Population-based methods===
*[[Genetic algorithm]]
*[[Memetic algorithm]]
*[[Particle swarm optimization]]
*[[Harmony search]]
*[[ODMA]]

===Other methods===
*Random search
*[[Grid search]]
*[[Simulated annealing]]
*[[Brute-force search|Direct search]]
*[[IOSO]] (Indirect Optimization based on Self-Organization)

Most of these techniques require large numbers of evaluations of the objectives and the constraints. The disciplinary models are often very complex and can take significant amounts of time for a single evaluation. The solution can therefore be extremely time-consuming. Many of the optimization techniques are adaptable to [[parallel computing]]. Much current research is focused on methods of decreasing the required time.

Also, no existing solution method is guaranteed to find the [[global optimization|global optimum]] of a general problem (see [[No free lunch in search and optimization]]). Gradient-based methods find local optima with high reliability but are normally unable to escape a local optimum. Stochastic methods, like simulated annealing and genetic algorithms, will find a good solution with high probability, but very little can be said about the mathematical properties of the solution. It is not guaranteed to even be a local optimum. These methods often find a different design each time they are run.