A structural optimization solution to a branch-and-bound problem

A simple algorithm, developed for a least-weight structural optimization problem, is used to force the selection of the same $n$ components of the vectors $X$ and $Y$, containing $b$ elements $(b > n)$ so that the objective function $\tilde L {\max _{xi,yi}}\left \{ {\left | X \right |,\left | Y \right |} \right \}$ is minimized subject to $n$ equality constraints on each vector, $AX = {b_1}$ , $AY = {b_2}$. The method has an obvious advantage over integer programming or branch-and-bound techniques that would, in this case, seek the best selection of $n$ out of $b$ elements which satisfy the constraints.