and "inverse optimization"

The amazing rationality of biological ``constructions" calls for the use of mathematical methods of structural optimization to model them. For example, trunks of trees, feathers, leafs, muscle system, or bones are mechanical structures made of composites with variable parameters that adapts itself to the environment. Similarly to an engineering construction, they support weight, must sustain certain external loadings, and they have been perfected by the Evolution.

Studying bio-structures, it may be postulated that they
are optimal with respect to some goal, which means that they are best adapted
to the environment. The question is: **In what sense is the structure
optimal?**

It would be natural to apply optimization methods developed for engineering constructions to biological structures. However, the two problems are mutually inverse. The biological structure is known, but it is not clear in what sense (if any) the structure is optimal. In contrast, in engineering problems, the goal is the minimization of a given functional that is not the subject of a search or even a discussion; the problem is to find the optimal structure.

The problem is formulated as an "i**nverse optimization problem**":

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