One-dimensional heuristics adapted for two-dimensional rectangular strip packing

Abstract

We consider two-dimensional rectangular strip packing without rotation of items and without the guillotine cutting constraint. We propose a single-pass heuristic which fills every free space in a onedimensional knapsack fashion, i.e. considering only item widths. It appears especially important to assign suitable heuristic "pseudo-values" as profits in this knapsack problem. This simple heuristic improves the results for most of the test classes from the literature, compared to the results of Bortfeldt (2004) and . Moreover, we describe a simple modification of the Bottom-Left heuristic and call it Bottom-Left-Right. Executing it iteratively with different input sequences generated by the randomized framework BubbleSearch of , we obtain the best results in some classes with smaller number of items (20, 40). For larger instances, the pseudo-value-based algorithm is the best one in most cases.

Bidirectional best-fit heuristic considering compound placement for two dimensional orthogonal rectangular strip packing

“…In the case that an approach is stochastic, the average performance reported is used to calculate %-gap to compare to our deterministic method. nice0050 50 1000 1000 nice0100 100 1000 1000 nice0200 200 1000 1000 nice0500 500 1000 1000 nice1000 1000 1000 1000 path0025 25 1000 1000 path0050 50 1000 1000 path0100 100 1000 1000 path0200 200 1000 1000 path0500 500 1000 1000 path1000 1000 1000 1000 Burke et al (2004) N1 10 40 40 N2 20 50 30 N3 30 50 30 N4 40 80 80 N5 50 100 100 N6 60 100 50 N7 70 100 80 N8 80 80 100 N9 100 150 50 N10 200 150 70 N11 300 150 70 N12 500 300 100 N13 3152 960 640 BBFM has similar performance many of the techniques in the literature in terms of %-gap including SVC(SubKP) (Belov et al, 2008) and GRASP (Alvarez-Valdes et al, 2009) which up until recently were considered state of the art. Although the performance in terms of %-gap initially looks poor, using such a metric for comparison can be misleading when working with instances with varied optimal solution values.…”

“…Local search is then applied to improve the solution generated in the constructive phase. Belov et al (2008) describe the SVC(SubKP) framework which iteratively applies a single constructive heuristic (SubKP) updating a number of parameters at each step. Burke et al (2011) used a simple squeaky wheel optimisation methodology (SWP) for the oriented version of the strip packing problem where no rotations are allowed.…”

“…Burke et al (2011) used a simple squeaky wheel optimisation methodology (SWP) for the oriented version of the strip packing problem where no rotations are allowed. Leung et al (2011) introduced a two-stage stochastic 'intelligent search algorithm' (ISA) which again relies on a constructive phase and improvement phase based on simulated annealing resulting in some improvement on average over reactive GRASP (Alvarez-Valdes et al, 2009) and SVC(SubKP) (Belov et al, 2008). A simplified parameterless adaptation of this algorithm (SRA) is described by Yang et al (2013).…”

“…The techniques from the literature are: Best-fit (BF) (Burke et al, 2004), Best-fit with simulated annealing (BF-SA) (Burke et al, 2009), squeaky wheel optimisation (SWP) (Burke et al, 2011), SVC(SubKP) (Belov et al, 2008), GRASP (Alvarez-Valdes et al, 2009), an 'intelligent search algorithm' (ISA) (Leung et al, 2011) and iterative doubling binary search (IDBS) (Wei et al, 2011). In the case that an approach is stochastic, the average performance reported is used to calculate %-gap to compare to our deterministic method.…”

“…This is unfortunate for methods such as ours which excel in the larger instances of the set. When compared directly, BBFM has equal performance SVC(SubKP) (Belov et al, 2008) in 10 instances, outperforms SVC in 5 instances and is outperformed by SVC in 6 instances showing very similar performance. When compared to the second best metaheuristic, BBFM matches the performance of ISA (Leung et al, 2011) in 13 of the 21 instances.…”