In many optimum design cases, we look for a set of design variables selected from a given list which assure the optimum of objective function together with satisfaction of the constraints. That is, optimum conceptual design mostly consists of selecting the best combination of a finite number of structural elements and the available parameters. In this paper a novel technique is presented for the conceptual design optimization of framed buildings with a rectangular plan. The method supports all the buildings with grid pattern column layout. To that end, we take advantage of the knapsack problem as a basic applied combinatorial optimization problem. The objective is to find a rectangular column layout of maximum profit for the frames that also satisfy the imposed geometric constraints. The method is presented in a general form and is not confined to optimization under a certain type of action effect and/or geometrical constraints. It gives the methodology the ability of being formulated for various objective functions and constraints and different structural systems. Civil-Comp Press, 2013.