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In this paper we formulate the problem of packing unequal rectangles/squaresinto a fixed size circular container as a mixed-integer nonlinear program. Herewe pack rectangles so as to maximise some objective (e.g. maximise the numberof rectangles packed or maximise the total area of the rectangles packed). Weshow how we can eliminate a nonlinear maximisation term that arises in one ofthe constraints in our formulation. We indicate the amendments that can be madeto the formulation for the special case where we are maximising the number ofsquares packed. A formulation space search heuristic is presented andcomputational results given for publicly available test problems involving upto 30 rectangles/squares. Our heuristic deals with the case where therectangles are of fixed orientation (so cannot be rotated) and with the casewhere the rectangles can be rotated through ninety degrees.

Packing unequal rectangles and squares in a fixed size circular container using formulation space search