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A simulated annealing hyperheuristic methodology for flexible decision support
, 2007
"... One of the main motivations for investigating hyperheuristic methodologies is to provide a more general search framework than is currently available. Most of the current search techniques represent approaches that are largely adapted for specific search problems (and, in some cases, even specific ..."
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Cited by 18 (9 self)
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One of the main motivations for investigating hyperheuristic methodologies is to provide a more general search framework than is currently available. Most of the current search techniques represent approaches that are largely adapted for specific search problems (and, in some cases, even specific problem instances). There are many realworld scenarios where the development of such bespoke systems is entirely appropriate. However, there are other situations where it would be beneficial to have methodologies which are more generally applicable to more problems. One of our motivating goals is to underpin the development of more flexible search methodologies that can be easily and automatically employed on a broader range of problems than is currently possible. Almost all the heuristics that have appeared in the literature have been designed and selected by humans. In this paper, we investigate a simulated annealing hyperheuristic methodology which operates on a search space of heuristics and which employs a stochastic heuristic selection strategy and a shortterm memory. The generality and performance of the proposed algorithm is demonstrated over a large number of benchmark data sets drawn from three very different and difficult (NPhard) problems: nurse rostering, university course timetabling and onedimensional bin packing. Experimental results show that the proposed hyperheuristic is able to achieve significant performance improvements over a recently proposed tabu search hyperheuristic without lowering the level of generality. We
Bincompletion algorithms for multicontainer packing, knapsack, and covering problems
 Journal of Artificial Intelligence Research
"... Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in multiagent systems and distributed systems, and can also b ..."
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Cited by 12 (5 self)
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Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in multiagent systems and distributed systems, and can also be found as subproblems of scheduling problems. We propose bin completion, a branchandbound strategy for onedimensional, multicontainer packing problems. Bin completion combines a binoriented search space with a powerful dominance criterion that enables us to prune much of the space. The performance of the basic bin completion framework can be enhanced by using a number of extensions, including nogoodbased pruning techniques that allow further exploitation of the dominance criterion. Bin completion is applied to four problems: multiple knapsack, bin covering, mincost covering, and bin packing. We show that our bin completion algorithms yield new, stateoftheart results for the multiple knapsack, bin covering, and mincost covering problems, outperforming previous algorithms by several orders of magnitude with respect to runtime on some classes of hard, random problem instances. For the bin packing problem, we demonstrate significant improvements compared to most previous results, but show that bin completion is not competitive with current stateoftheart cuttingstock based approaches. 1.
A Simulated Annealing Enhancement of the BestFit Heuristic for the Orthogonal StockCutting Problem
, 2009
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An Evolutionary Algorithm for Column Generation in Integer Programming: an Effective . . .
 PARALLEL PROBLEM SOLVING FROM NATURE  PPSN VIII, VOLUME 3242 OF LNCS
, 2004
"... We consider the 3stage twodimensional bin packing problem, which occurs in realworld problems such as glass cutting. For it, we present a new integer linear programming formulation and a branch and price algorithm. Column generation is performed by applying either a greedy heuristic or an Evoluti ..."
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Cited by 6 (3 self)
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We consider the 3stage twodimensional bin packing problem, which occurs in realworld problems such as glass cutting. For it, we present a new integer linear programming formulation and a branch and price algorithm. Column generation is performed by applying either a greedy heuristic or an Evolutionary Algorithm (EA). Computational experiments show the benefits of the EAbased approach. The higher computational effort of the EA pays o# in terms of better final solutions; furthermore more instances can be solved to provable optimality.
Models with Variable Strip Widths for TwoDimensional TwoStage Cutting
, 2003
"... We consider several formulations of twodimensional twostage constrained cutting, where the number of variables is polynomial. Some new models with variable strip widths are developed. Symmetries in the search space are eliminated by lexicographic constraints which are already known from the li ..."
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Cited by 4 (0 self)
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We consider several formulations of twodimensional twostage constrained cutting, where the number of variables is polynomial. Some new models with variable strip widths are developed. Symmetries in the search space are eliminated by lexicographic constraints which are already known from the literature. However, previously known models with fixed strip widths are shown to be more effective. The models are solved with the branchandcut algorithm of ILOG CPLEX.
Twostage twodimensional guillotine cutting problems with usable leftovers
, 2013
"... In this study we are concerned with the nonexact twostage twodimensional guillotine cutting problem considering usable leftovers, in which stock plates remainders of the cutting patterns (nonused material or trim loss) can be used in the future, if they are large enough to fulfill future demands ..."
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Cited by 2 (0 self)
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In this study we are concerned with the nonexact twostage twodimensional guillotine cutting problem considering usable leftovers, in which stock plates remainders of the cutting patterns (nonused material or trim loss) can be used in the future, if they are large enough to fulfill future demands of items (ordered smaller plates). This cutting problem can be characterized as a residual binpacking problem because of the possibility of creating new residual pieces, as the trim loss of each cutting/packing pattern does not necessarily represent waste of material and, depending on its size, it can be put back into stock. Two bilevel mathematical programming models to represent this nonexact twostage twodimensional residual binpacking problem are presented. The models basically consist on cutting/packing the ordered items using a set of plates of minimum cost and, among all possible solutions of minimum cost, choosing one that maximizes the value of the generated usable leftovers. Because of special characteristics of these bilevel models, they can be reformulated as onelevel mixed integer programming models. Results of some numerical experiments are presented to show that the models represent appropriately the problem and to illustrate their performances.
GRASP and Path Relinking for the Twodimensional Twostaged Cutting Stock Problem
"... In this paper, we develop a greedy randomized adaptive search procedure (GRASP) for the constrained twodimensional twostaged cutting stock problem. This is a special cutting problem in which the cut is performed in two phases. In the first phase, the stock rectangle is slit down its width into dif ..."
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Cited by 1 (1 self)
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In this paper, we develop a greedy randomized adaptive search procedure (GRASP) for the constrained twodimensional twostaged cutting stock problem. This is a special cutting problem in which the cut is performed in two phases. In the first phase, the stock rectangle is slit down its width into different vertical strips and in the second phase, each of these strips is processed to obtain the final pieces. We propose two different algorithms based on GRASP methodology. One is “piece oriented ” while the other is “strip oriented”. Both procedures are fast and provide solutions of different structures to this cutting problem. We also propose a path relinking algorithm, which operates on a set of elite solutions obtained with both GRASP methods, to search for improved outcomes. We perform extensive computational experiments with wellknown instances which have been previously reported, first to study the effect of changes in critical search parameters and then to compare the efficiency of alternative solution procedures. The experiments establish the effectiveness of our procedure in relation to approaches previously identified as best, especially in largescale instances. Key Words: Cutting, Packing, Heuristics, GRASP, Path Relinking. Twostaged twodimensional cutting 2 1.
Compositional paretoalgebraic heuristic for packing problems Compositional Paretoalgebraic Heuristic for Packing Problems
"... Disclaimer This document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Student theses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the document as ..."
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Disclaimer This document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Student theses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the document as presented in the repository. The required complexity or quality of research of student theses may vary by program, and the required minimum study period may vary in duration. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profitmaking activity or commercial gain Abstract This study investigates the applicability of Compositional Paretoalgebraic Heuristic (CPH) to packing problems at Vanderlande. The two problems under study are Luggage Batch Selection (LBS) and Orderline Allocation (OA). These problems belong to the domain of multiobjective combinatorial optimization and are currently solved using Metaheuristics such as Simulated Annealing and Genetic Algorithms. We show that these problems are compatible with CPH and explain the required modifications to the heuristic for each of the problems. Two individual CPH frameworks are presented, one for each of the case studies. The implementations of the CPH frameworks obtained valid solutions for both problems with solution quality comparable to the metaheuristic methods used by Vanderlande. As other heuristics, CPH can be adjusted to favor solution quality or execution time. For Orderline Allocation (OA), the CPH framework allows a reduction of the execution time of two orders of magnitude by compromising on average 2% in solution quality. Even when adjusting CPH to aim for solution quality, the solutions provided for both problems were inferior to those obtained by metaheuristics.
ONEDIMENSIONAL CUTTING STOCK PROBLEM (1DCSP): A STUDY ON DATA DEPENDENT TRIM LOSS
"... ABSTRACT A generalized approach is introduced for getting minimal trim in onedimensional cutting stock problem (1DCSP) which occurs extensively while manufacturing of different engineering objects. Our study is especially focused on transmission tower manufacturing industry. The concept of comput ..."
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ABSTRACT A generalized approach is introduced for getting minimal trim in onedimensional cutting stock problem (1DCSP) which occurs extensively while manufacturing of different engineering objects. Our study is especially focused on transmission tower manufacturing industry. The concept of computing total trim by using the idea of predefined sustainable trim has been explored in previous work of authors. Given m stock lengths ܷ ଵ , ܷ ଶ , … , ܷ , the cutting plan consists of cutting of at most two order lengths at a time out of the demanded set of n order lengths ݈ ଵ , ݈ ଶ , … , ݈ . Considering the given data, the total trim has been computed corresponding to two different sustainable trims of order one (viz.ݐ ௦ ଵ ) and order two (viz.ݐ ௦ ଶ ). Introducing various values of sustainable trims as knots between ݐ ௦ ଵ and ݐ ௦ ଶ , the total trim has been computed corresponding to each knot, the linear approximation has been constructed which predict the total trim loss at any arbitrary point ݐ lying between ݐ ௦ ଵ and ݐ ௦ ଶ .
Gomory Cuts from a PositionIndexed Formulation of 1D Stock Cutting
"... Most integer programming problems can be formulated in several ways. Some formulations are better suited for solution by exact methods, because they have either (i) a strong LP relaxation, (ii) few symmetries in the solution space, or both. However, solving one formulation, we can often branch and/o ..."
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Most integer programming problems can be formulated in several ways. Some formulations are better suited for solution by exact methods, because they have either (i) a strong LP relaxation, (ii) few symmetries in the solution space, or both. However, solving one formulation, we can often branch and/or add cutting planes which are implicitly based on variables of other formulations, working in fact on intersection of several polytopes. Traditional examples of this approach can be found in, e.g., (capacitated) routing and network planning where decomposed models operate with paths or trees, and thus need to be solved by column generation, but original models operate on separate edges. We consider such a ‘capacityextended formulation’, the socalled arcflow model, of the 1D cutting stock problem. Its variables are known to induce effective branching constraints leading to small and stable branch&bound trees. In this work we explore ChvátalGomory cuts on its variables. The results are positive only for small instances. Moreover, we compare the results to the cuts constructed on the variables of the direct model. The latter are more involved but also more effective.