New Stabilization Procedures for the Cutting Stock Problem
نویسندگان
چکیده
In this paper, we deal with a column generation based algorithm for the classical cutting stock problem. This algorithm is known to have convergence issues, which are addressed in this paper. Our methods are based on the fact that there are interesting characterizations of the structure of the dual problem, and that a large number of dual solutions are known. First we describe methods based on the concept of dual cuts, proposed by Valério de Carvalho (2005). We introduce a general framework for deriving cuts, and we describe a new type of dual cuts, which exclude solutions that are linear combinations of some other known solutions. We also explore new lower and upper bounds for the dual variables, and we present a procedure to set some of these variables to zero. Then we show how the prior knowledge of a good dual solution helps improving the results. It tightens the bounds around the dual values, and makes the search converge faster if a solution is sought in its neighborhood first. A set of computational experiments on very hard instances are reported at the end of the paper. They confirm the effectiveness of the methods proposed.
منابع مشابه
An Algorithm for Two Dimensional Cutting Stock Problems with Demand
In this paper, two-dimensional cutting stock problem with demand has been studied.In this problem, cutting of large rectangular sheets into specific small pieces should be carried out hence, the waste will be minimized. Solving this problem is important to decrease waste materials in any industry that requires cutting of sheets. In most previus studies, the demand of pieces has not been usually...
متن کاملAn Algorithm for Two Dimensional Cutting Stock Problems with Demand
In this paper, two-dimensional cutting stock problem with demand has been studied.In this problem, cutting of large rectangular sheets into specific small pieces should be carried out hence, the waste will be minimized. Solving this problem is important to decrease waste materials in any industry that requires cutting of sheets. In most previus studies, the demand of pieces has not been usually...
متن کاملA simple approach to the two-dimensional guillotine cutting stock problem
Cutting stock problems are within knapsack optimization problems and are considered as a non-deterministic polynomial-time (NP)-hard problem. In this paper, two-dimensional cutting stock problems were presented in which items and stocks were rectangular and cuttings were guillotine. First, a new, practical, rapid, and heuristic method was proposed for such problems. Then, the ...
متن کاملAn ACO algorithm for one-dimensional cutting stock problem
The one-dimensional cutting stock problem, has so many applications in lots of industrial processes and during the past few years has attracted so many researchers’ attention all over the world. In this paper a meta-heuristic method based on ACO is presented to solve this problem. In this algorithm, based on designed probabilistic laws, artificial ants do select various cuts and then select the...
متن کاملThe trim loss concentration in one-dimensional cutting stock problem (1D-CSP) by defining a virtual cost
Nowadays, One-Dimensional Cutting Stock Problem (1D-CSP) is used in many industrial processes and re-cently has been considered as one of the most important research topic. In this paper, a metaheuristic algo-rithm based on the Simulated Annealing (SA) method is represented to minimize the trim loss and also to fo-cus the trim loss on the minimum number of large objects. In this method, the 1D-...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- INFORMS Journal on Computing
دوره 23 شماره
صفحات -
تاریخ انتشار 2011