Linear one-dimensional cutting-packing problems: numerical experiments with the sequential value correction method (SVC) and a modified branch-and-bound method (MBB)
Abstract:Two algorithms for the one-dimensional cutting problem, namely, a modified branch-and-bound method (exact method) and a heuristic sequential value correction method are suggested. In order to obtain a reliable assessment of the efficiency of the algorithms, hard instances of the problem were considered and from the computational experiment it seems that the efficiency of the heuristic method appears to be superior to that of the exact one, taking into account the computing time of the latter. A detailed descri… Show more
“…in which the formula defines each new pseudo-price value to be the weighted sum of its previous value and the material consumption norm within the last obtained pattern. Some years later the SVC scheme was employed again by Mukhacheva et al [97] in one-dimensional CSP, and by Verkhoturov and Sergeyeva [131] for the two-dimensional CSP with irregular shapes. The latter dealt the issue of the item placement by defining the pseudo-prices as functions of the angle of rotation and such angles are chosen in order to maximize the pseudo-price values.…”
Section: Sequential Value Correction Heuristicmentioning
4.3 instances in I B : bin size and assortment of item sizes for each class. . 4.4 SVC-DD, SVC2BPRF and best H solutions of 2BP on I B : n mean values 4.5 MXGA and SVC-DD solutions of 2RBP-DD on I B : G N and G L gaps (%) 4.6 MXGA, CPMIP and SVC-DD π ℓ solutions of 2RBP-DD on I B : G L gaps
“…in which the formula defines each new pseudo-price value to be the weighted sum of its previous value and the material consumption norm within the last obtained pattern. Some years later the SVC scheme was employed again by Mukhacheva et al [97] in one-dimensional CSP, and by Verkhoturov and Sergeyeva [131] for the two-dimensional CSP with irregular shapes. The latter dealt the issue of the item placement by defining the pseudo-prices as functions of the angle of rotation and such angles are chosen in order to maximize the pseudo-price values.…”
Section: Sequential Value Correction Heuristicmentioning
4.3 instances in I B : bin size and assortment of item sizes for each class. . 4.4 SVC-DD, SVC2BPRF and best H solutions of 2BP on I B : n mean values 4.5 MXGA and SVC-DD solutions of 2RBP-DD on I B : G N and G L gaps (%) 4.6 MXGA, CPMIP and SVC-DD π ℓ solutions of 2RBP-DD on I B : G L gaps
“…In the early noughties Mukhacheva et al [222] proposed a pattern oriented branchand-bound algorithm for both the BPP and the CSP, while Korf [179,180] proposed a "bin completion" algorithm (later improved on by Schreiber and Korf [252]) in which decision nodes are produced by assigning a feasible set to a bin. However, starting from the late nineties, branch-and-price (see Section 2.6) proved to be very effective, and became the most popular choice for the exact solution of the BPP.…”
Section: Chapter 2 Bpp and Csp: Mathematical Models And Exact Algorimentioning
“…Here we adapt the method sequential value correction (SVC), already well-known e.g. for 1D stock cutting (Mukhacheva et al, 2000, Belov andScheithauer, 2003).…”
Section: W ∈ Rmentioning
confidence: 99%
“…A similar algorithm from (Mukhacheva and Valeeva, 2000) fills every hole by solving a subset-sum problem with item widths; then, items are ordered by non-increasing heights. Inspired by Sub and the 1D-CSP heuristic SVC (Mukhacheva et al, 2000, Belov andScheithauer, 2003), we propose the following modification SubKP of Sub. Namely, to fill the empty spaces solving a one-dimensional knapsack problem.…”
Section: The Knapsack Substitution Heuristic (Subkp)mentioning
confidence: 99%
“…A thorough investigation of SVC for 1D cutting has been done in (Mukhacheva et al, 2000, Belov andScheithauer, 2003). The idea is to fill every bin by solving a knapsack problem while assigning some heuristic "pseudo-values" to the items.…”
Section: Sequential Value Correction (Svc)mentioning
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.
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