An improved best-first branch-and-bound algorithm for unconstrained two-dimensional cutting problems

Abstract

The two-dimensional cutting problem requires maximising the sum of the profits of small rectangular pieces, each of which has its own profit and size, obtained from a large rectangular plate. In this paper, a best-first branch-and-bound algorithm is proposed for the unconstrained problem, which has no limit on the number of pieces cut. Each small piece can have its own profit or can use the area of the piece instead of the profit. The proposed algorithm extends the concept of dominated patterns to remove the dominated patterns efficiently. Our proposed algorithm can also remove duplicate patterns and reduce the search space. The existing upper bound is revised and a new bounding strategy that can prune several nodes simultaneously is proposed. Additionally, new data structures are introduced to improve the performance of the algorithm. Computational results using the proposed algorithm on some benchmark examples were compared to the performance of previous algorithms to show the efficiency of the new algorithm. The proposed algorithm reduced the average computational time by up to 93% for 48 sample problems, excluding those problems that required almost no time using existing algorithms. Additionally, a large-scale problem that could not be solved in a reasonable time by the existing exact algorithms was solved successfully using the proposed algorithm.

An improved best-first branch-and-bound algorithm for constrained two-dimensional guillotine cutting problems

“…To avoid the construction of a dominated pattern, Kang and Yoon (2011) proposed three methods for UTDC by setting a limit to the width or height of a pattern combining with R in O. All of these cannot be applied to CTDC International Journal of Production Research 1683 because CTDC is bound by a constraint on the number of pieces.…”

“…w A and the newly generated unoccupied area of A is large enough to contain a piece that is available. A constraint on the number of pieces should be added compared with the method of Kang and Yoon (2011).…”

“…However, this is offset by the small amount of computational time required and the ease with which various additional constraints can be handled (Cung et al 2000). G et al (2003) and Kang and Yoon (2011) also used this approach to solve UTDC and dramatically reduced the amount of memory required by using efficient branching strategies and upper bounds. The algorithm proposed here also uses this approach.…”

“…Additionally, more efficient upper bounds and a bounding strategy are proposed. We also propose a method of preventing the formation of unpromising patterns, which can be dominated by other patterns, based on the work of Kang and Yoon (2011).…”

Recent Advances of Intelligent Optimization Algorithm in Manufacturing

“…In the solving process of large-scale complex problem, finding a general method to simplify large-scale solution space for various kinds of special complex problems is still a big challenge. For the existing studies in simplification of large-scale solution space, refer to references [96][97][98][99][100][101][102].…”