Approximate algorithms for constrained circular cutting problems

Abstract

In this paper, we study the problem of cutting a rectangular plate R of dimensions ( L, W) into as many circular pieces as possible. The circular pieces are of n different types with radii r i , i=1,…, n. We solve the constrained circular problem, where d i the maximum demand for piece type i is specified, using two heuristics: a constructive procedure-based heuristic and a genetic algorithm-based heuristic. Both of these approaches search for a good ordering of the pieces and use an adaptation of the best local position procedure (Studia. Inform. Univ. 2 (1) (2002) 33) to find the “best” layout of this ordered set. This positioning procedure is specifically tailored to circular cutting problems. It acts, for constrained problems, as one of the mutation operators of the genetic algorithm. We compare the performance of both proposed approaches to that of existing approximate and exact algorithms on several problem instances taken from the literature. The computational results show that the proposed approaches produce high-quality solutions within reasonable computational times. The genetic algorithm-based heuristic is easily parallelizable; one of its important features to be investigated in the near future. Scope and purpose In many industrial sectors, minimizing waste is a critical issue. This is particularly the case for the packing, textile, naval, and aerospace industries, where minimizing the waste of packing and cutting is a frequent problem. Our paper studies the constrained circular packing problem where a set of circles needs to be cut on a rectangular stock sheet of fixed width and length. The objective is to maximize the usage of the rectangular sheet while respecting the upper demand value for each circle type. We propose two approximate algorithms to solve this problem and prove their efficiency.