Almost square packing

摘要: The almost square rectangle packing problem involves all rectangles with sizes 1×2 to n×(n+1) (almost squares) into an enclosing of minimal area. This extends the previously studied by adding additional degree freedom for each rectangle, deciding in which orientation item should be packed. We show how extend model and search strategy that worked well solve new problem. Some adapted versions known redundant constraints improve overall times. Based on a visualization tree, we derive decomposition method initially only looks at subproblem given one cumulative constraints. leads further modest improvements execution find solution size 26 first time dramatically best times finding solutions smaller up three orders magnitude.