We introduce an evolutionary stochastic-local-search (SLS) algorithm for addressing a generalized version of the so-called 1 V D R cutting-stock problem. Cutting-stock problems are encountered often in industrial environments and the ability to address them efficiently usually results in large economic benefits. Traditionally linear-programming-based techniques have been utilized to address such problems, however their flexibility might be limited when nonlinear constraints and objective functions are introduced. To this end, this paper proposes an evolutionary SLS algorithm for addressing one-dimensional cutting-stock problems. The contribution lies in the introduction of a flexible structural framework of the optimization that may accommodate a large family of diversification strategies including a novel parallel pattern appropriate for SLS algorithms (not necessarily restricted to cutting-stock problems). We finally demonstrate through experiments in a real-world manufacturing problem the benefit in cost reduction of the considered diversification strategies.
Due to the fact that many different types of cutting stock problems can be found in the literature, e.g. with respect to dimensionality, characteristics of large and small objects, shape of figures and so forth, it is highly desirable that the scientific community is using the same language and terminology when describing problems and the corresponding solution approaches. In @cite_36 a typology that covered the most important four characteristics at the time to classify optimization problems like the cutting stock problems was introduced. This typology was improved by @cite_25 . An overview of characteristics how to classify the problems in the literature can be found in @cite_24 . The problem can further be distinguished whether it is off-line (full knowledge of the input) or on-line (no knowledge of the next items) @cite_0 .
@cite_36 @cite_0 @cite_25 @cite_24
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Abstract Cutting and packing problems appear under various names in literature, e.g. cutting stock or trim loss problem, bin or strip packing problem, vehicle, pallet or container loading problem, nesting problem, knapsack problem etc. The paper develops a consistent and systematic approach for a comprehensive typology integrating the various kinds of problems. The typology is founded on the basic logical structure of cutting and packing problems. The purpose is to unify the different use of notions in the literature and to concentrate further research on special types of problems. The number of publications in the area of Cutting and Packing (C&P) has increased considerably over the last two decades. The typology of C&P problems introduced by Dyckhoff [Dyckhoff, H., 1990. A typology of cutting and packing problems. European Journal of Operational Research 44, 145–159] initially provided an excellent instrument for the organisation and categorisation of existing and new literature. However, over the years also some deficiencies of this typology became evident, which created problems in dealing with recent developments and prevented it from being accepted more generally. In this paper, the authors present an improved typology, which is partially based on Dyckhoff’s original ideas, but introduces new categorisation criteria, which define problem categories different from those of Dyckhoff. Furthermore, a new, consistent system of names is suggested for these problem categories. Finally, the practicability of the new scheme is demonstrated by using it as a basis for a categorisation of the C&P literature from the years between 1995 and 2004. � 2006 Elsevier B.V. All rights reserved. This paper presents a tabu search and best-fit decreasing (BFD) algorithms to address a real-world steel cutting problem from a retail steel distributor. It consists of cutting large steel blocks in order to obtain smaller tailored blocks ordered by clients. The problem is addressed as a cutting & packing problem, formulated as a 3-dimensional residual bin packing problem for minimization of stock variation. The performance of the proposed approaches is compared to an heuristic and ant colony optimization (ACO) algorithms. The proposed algorithms were able to reduce the stock variation by up to 179 . The comparison of results between the tabu search and BFD algorithm shows that a multiple order joint analysis benefits the optimization of the addressed objective. While the covering algorithm has been perfected recently by the iterative approaches, such as DAOmap and IMap, its application has been limited to technology mapping. The main factor preventing the covering problem's migration to other logic transformations, such as elimination and resynthesis region identification found in SIS and FBDD, is the exponential number of alternative cuts that have to be evaluated. Traditional methods of cut generation do not scale beyond a cut size of 6. In this paper, a symbolic method that can enumerate all cuts is proposed without any pruning, up to a cut size of 10. We show that it can outperform traditional methods by an order of magnitude and, as a result, scales to 100K gate benchmarks. As a practical driver, the covering problem applied to elimination is shown where it can not only produce competitive area, but also provide more than 6times average runtime reduction of the total runtime in FBDD, a BDD based logic synthesis tool with a reported order of magnitude faster runtime than SIS and commercial tools with negligible impact on area.