On Improved Least Flexibility First Heuristics Superior for Packing and Stock Cutting Problems

Two dimensional cutting and packing problems have applications in many manufacturing and job allocation problems. In particular, in VLSI floor planning problems and stock cutting problems, many simulated annealing and genetic algorithms based methods have been proposed in the last ten years. These researches have mainly been focused on finding efficient data structures for representing packing results so the search space and processing time of the underlying search engine can be minimized. In this paper, we tackle the problem from a different approach. Instead of using stochastic searches, we introduce an effective deterministic optimization algorithm for packing and cutting. By combining an improved Least Flexibility First principle and a greedy search based evaluation routine, we can obtain very encouraging results: In stock cutting problems, our algorithm achieved over 99% average packing density for a series of public rectangle packing data sets, which is significantly better than the 96% packing density obtained by meta-heuristics (simulated annealing) based results while using much less CPU time; whereas in rectangle packing applying the well-known MCNC and GSRC benchmarks, we achieved the best (over 96%) packing density among all known published results packed by other methods. Our encouraging results seem to suggesting a new experimental direction in designing efficient deterministic heuristics for some kind of hard combinatorial problems.