This work presents a genetic symbiotic algorithm to solve the one-dimensional cutting stock problem with multiple objectives. We considered two important objectives for an industry (1) cost of trim loss and (2) cost of setup. We use a symbiotic relationship, between the population of solutions and the population of cutting patterns, together with a niche strategy to obtain an approximation of t...

A branch-and-cut-and-price algorithm for one-and two-dimensional two-staged cutting (stock) problems

We confront a practical cutting stock problem from a production plant of plastic rolls. The problem is a variant of the well-known one dimensional cutting stock, with particular constraints and optimization criteria defined by the experts of the company. We start by giving a problem formulation in which optimization criteria have been considered in linear hierarchy according to expert preferenc...

It is well known that the one-dimensional cutting stock problem (1DCSP) a combinatorial optimization with nondeterministic polynomial (NP-hard) characteristics. Heuristic and genetic algorithms are two main used to solve (CSP), which has problems of small scale low-efficiency solutions. To better improve stability versatility solution, mathematical model established, objective minimum raw mater...

We address a 1-dimensional cutting stock problem where, in addition to trimloss minimization, we require that the set of cutting patterns forming the solution can be sequenced so that the number of stacks of parts maintained open throughout the process never exceeds a given s. For this problem, we propose a new integer linear programming formulation whose constraints grow quadratically with the...

We present an asymptotic fully polynomial approximation scheme for strip-packing, or packing rectangles into a rectangle of xed width and minimum height, a classical NP-hard cutting-stock problem. The algorithm nds a packing of n rectangles whose total height is within a factor of (1 +) of optimal (up to an additive term), and has running time polynomial both in n and in 1==. It is based on a r...

In this paper, the authors present a hybrid genetic approach for the two-dimensional rectangular guillotine oriented cutting-stock problem. In this method, the genetic algorithm is used to select a set of cutting patterns while the linear programming model permits one to create the lengths to produce with each cutting pattern to fulfil the customer orders with minimal production cost. The effec...