Shape optimization is part of the field of optimal control theory. The typical problem is to find the shape which is optimal in that it minimizes a certain cost functional while satisfying given constraints. In many cases, the functional being solved depends on the solution of a given partial differential equation defined on the variable domain.
Topology optimization is, in addition, concerned with the number of connected components/boundaries belonging to the domain. Such methods are needed since typically shape optimization methods work in a subset of allowable shapes which have fixed topological properties, such as having a fixed number of holes in them. Topological optimization techniques can then help work around the limitations of pure shape optimization.
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Famous quotes containing the word shape:
“This whole day have I followed in the rocks,
And you have changed and flowed from shape to shape,
First as a raven on whose ancient wings
Scarcely a feather lingered, then you seemed
A weasel moving on from stone to stone....”
—William Butler Yeats (1865–1939)