Pattern based diving heuristics for a two-dimensional guillotine cutting-stock problem with leftovers
CLAUTIAUX, François
Reformulations based algorithms for Combinatorial Optimization [Realopt]
Université de Bordeaux [UB]
Reformulations based algorithms for Combinatorial Optimization [Realopt]
Université de Bordeaux [UB]
VANDERBECK, François
Reformulations based algorithms for Combinatorial Optimization [Realopt]
Université de Bordeaux [UB]
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Reformulations based algorithms for Combinatorial Optimization [Realopt]
Université de Bordeaux [UB]
CLAUTIAUX, François
Reformulations based algorithms for Combinatorial Optimization [Realopt]
Université de Bordeaux [UB]
Reformulations based algorithms for Combinatorial Optimization [Realopt]
Université de Bordeaux [UB]
VANDERBECK, François
Reformulations based algorithms for Combinatorial Optimization [Realopt]
Université de Bordeaux [UB]
Reformulations based algorithms for Combinatorial Optimization [Realopt]
Université de Bordeaux [UB]
VIAUD, Quentin
Université de Bordeaux [UB]
Reformulations based algorithms for Combinatorial Optimization [Realopt]
< Leer menos
Université de Bordeaux [UB]
Reformulations based algorithms for Combinatorial Optimization [Realopt]
Idioma
en
Article de revue
Este ítem está publicado en
EURO Journal on Computational Optimization. 2019-09, vol. 7, n° 3, p. 265–297
Springer
Resumen en inglés
We consider a variant of two-dimensional guillotine cutting-stock problem that arises when different bills of order (or batches) are considered consecutively. The raw material leftover of the last cutting pattern is not ...Leer más >
We consider a variant of two-dimensional guillotine cutting-stock problem that arises when different bills of order (or batches) are considered consecutively. The raw material leftover of the last cutting pattern is not counted as waste as it can be reused for cutting the next batch. The objective is thus to maximize the length of the leftover. We propose a diving heuristic based on a Dantzig-Wolfe reformulation solved by column generation in which the pricing problem is solved using dynamic programming (DP). This DP generates so-called non-proper columns, i.e. cutting patterns that cannot participate in a feasible integer solution of the problem. We show how to adapt the standard diving heuristic to this " non-proper " case while keeping its effectiveness. We also introduce the partial enumeration technique, which is designed to reduce the number of non-proper patterns in the solution space of the dynamic program. This technique helps to strengthen the lower bounds obtained by column generation and improve the quality of solutions found by the diving heuristic. Computational results are reported and compared on classical benchmarks from the literature as well as on new instances inspired from industrial data. According to these results, proposed diving algorithms outperform constructive and evolutionary heuristics.< Leer menos
Palabras clave en inglés
Cutting and Packing
Diving Heuristic
Dynamic Programming
Orígen
Importado de HalCentros de investigación