A beam search implementation for the irregular shape packing problem

Abstract

This paper investigates the irregular shape packing problem. We represent the problem as an ordered list of pieces to be packed where the order is decoded by a placement heuristic. A placement heuristic from the literature is presented and modified with a more powerful nofit polygon generator and new evaluation criteria. We implement a beam search algorithm to search over the packing order. Using this approach many parallel partial solutions can be generated and compared. Computational results for benchmark problems show that the algorithm generates highly competitive solutions in significantly less time than the best results currently in the literature.

Column generation and sequential heuristic procedure for solving an irregular shape cutting stock problem

“…Since the sub-problem cannot be solved using the traditional optimization techniques like dynamic programming or branch and bound, we propose a beam search heuristic to generate feasible layouts based on Bennell and Song (2010). This section includes details of the algorithmic procedure for this step.…”

“…We describe a beam search algorithm based on Bennell and Song (2010) to find near optimal solution for this problem in the next section. Note that, the elements x 1 , x 2 , · · · , x m in solution vector x found by our CG are not generally integral.…”

“…We describe the SHP in section 5. Bennell and Song (2010) demonstrated that beam search is an effective approach for solving the irregular strip packing problem and has the advantage of generating many alternative solutions in parallel. First, we introduce the main steps of the beam search algorithm for irregular packing and then describe our implementation for the KP sub-problem.…”

“…The contribution of this paper includes directly solving the irregular cutting stock problem, without pre-constructing stencils, applying Beam Search (BS) algorithm (Bennell and Song (2010)) within CG, and developing the CG methodology to deal with matrices that have more rows than columns. Each approach implemented includes methodology innovations to either make the approach capable of handing the irregular shape packing problem directly, or deal with the additional set up constraint.…”

An effective heuristic for the two-dimensional irregular bin packing problem

“…Dowsland et al (2002) use eight static orderings, which have the common strategy of trying to place the difficult-to-place pieces first. Dynamic selection permits all pieces to be available to be placed next Bennell and Oliveira (2009), for example, Bennell and Song (2010) use beam search. This approach searches the breadth first tree, and prunes the tree at each level according to two evaluation functions.…”