JOURNAL PUBLICATION: Symmetry and asymmetry of solutions in discrete variable structural optimization

In this paper symmetry  and asymmetry  of opti­ mal solutions insymmetric structural optimization problems is investigated, based  on the choice of variables. A group theory approach is used to define the symmetry of the struc­ tural problems  in a general  way. This approach  allows the set of symmetric structures to be described and related to the entire search space of the problem. A relationship  between the design variables and the likelihood  of finding symmet­ric or asymmetric solutions to problems is established. It is shown that an optimal symmetric  solution (if any) does not necessarily  exist in the case of discrete  variable problems, regardless  of  the size of the  discrete,  countable  set  from which variables can be chosen. Finally a number of examples  illustrate  these  principles  on  simple  truss structures with discrete topology and sizing variables.