Arbitrary rectilinear block packing based on sequence pair

Based on the sequence pair structure, this paper proposes a novel method to represent arbitrary shaped rectilinear blocks. The necessary and sufficient conditions are derived such that non-overlapped packing of arbitrary rectilinear blocks can always be guaranteed regardless of the dimensions of the blocks. A stochastic search is applied, three sequence pair operations are defined to search the feasible solution space both continuously and exhaustively. Theoretical results derived in this paper show that an optimal solution can always be reachable through finite steps of the stochastic search. As such, the algorithm becomes a significant breakthrough in the general packing problem both theoretically and practically.