A heuristic, dynamic programming-based approach for a two-dimensional cutting problem with defects

An improved heuristic-dynamic programming algorithm for rectangular cutting problem

“…Discretization sets of C-blocks. If a sub-block is a C-block, the discretization sets defined by the equations 2, 3, and (4) are quite same with the discretization sets proposed by Afsharian et al [11]. They are established by the solution of a onedimensional knapsack problem with the width and height of the small rectangular blocks.…”

“…Neidlein and Wäscher (2008) [10] reduce the size of discretization sets in the algorithm proposed by Vianna and Arenales (2006) [9], however, their algorithms do not obtain optimal solutions. Afsharian et al (2014) [11] modify the predecessor's heuristic dynamic programming algorithm to solve the problem with 4 defects. Their discretization sets size are cumbersome, which means the computational efficiency is not high.…”

“…In this paper, inspired by the previous algorithms [7,11], an improved heuristic dynamic programming algorithm is proposed to solve the problem with multiple defects in the way of guillotine cut. The algorithm reduces the discretization sets size of Afsharian et al (2014) [11]. However, the cut positions at one unit from the four boundaries of the defect are added to the new discrete set.…”

Simulated Annealing Algorithm and Implementation Software for Fabric Cutting Problem

“…The work in our paper, as will be elaborated later, will be referred to in the other group in the future, because of carrying many specific features. Some of the two-dimensional problems and their solutions in the literature are Rodrigo et al [4], Fathy et al [5], Andrade et al [6], Cui and Zhao [7], Kim et al [8], Afsharian et al [9]. Javanshir et al [10] focused on the field of readymade of the textile sector.…”

“…Although the number of dimensions decreases, the constraints arising from the problem structure increase complexity. In the study of Afsharian et al [9], these problem variants are called as "more specialized, less standardized" because of considering large defective objects. For the glass cutting problem, which can be classified in this category, the researchers developed a dynamic programming algorithm [17], mixed integer programming based algorithm [18], and genetic algorithm based solution [19].…”