An Empirical Investigation of Meta-heuristic and Heuristic Algorithms for a 2D Packing Problem
TL;DR: This study compares the hybrid algorithms in terms of solution quality and computation time on a number of packing problems of different size and shows the effectiveness of the design of the different algorithms.
About: This article is published in European Journal of Operational Research.The article was published on 2001-01-01. It has received 487 citations till now. The article focuses on the topics: Packing problems & Set packing.
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TL;DR: An improved typology of C&P problems is presented, which is partially based on Dyckhoff’s original ideas, but introduces new categorisation criteria, which define problem categories different from those of Dykhoff.
1,359 citations
TL;DR: This paper presents a tutorial on the implementation and use of biased random-key genetic algorithms for solving combinatorial optimization problems, illustrating the ease in which sequential and parallel heuristics based on biased Random-Key genetic algorithms can be developed.
Abstract: Random-key genetic algorithms were introduced by Bean (ORSA J. Comput. 6:154---160, 1994) for solving sequencing problems in combinatorial optimization. Since then, they have been extended to handle a wide class of combinatorial optimization problems. This paper presents a tutorial on the implementation and use of biased random-key genetic algorithms for solving combinatorial optimization problems. Biased random-key genetic algorithms are a variant of random-key genetic algorithms, where one of the parents used for mating is biased to be of higher fitness than the other parent. After introducing the basics of biased random-key genetic algorithms, the paper discusses in some detail implementation issues, illustrating the ease in which sequential and parallel heuristics based on biased random-key genetic algorithms can be developed. A survey of applications that have recently appeared in the literature is also given.
432 citations
TL;DR: This paper presents a new best-fit heuristic for the two-dimensional rectangular stock-cutting problem and demonstrates its effectiveness by comparing it against other published approaches and suggesting an efficient implementation of this heuristic.
Abstract: This paper presents a new best-fit heuristic for the two-dimensional rectangular stock-cutting problem and demonstrates its effectiveness by comparing it against other published approaches. A placement algorithm usually takes a list of shapes, sorted by some property such as increasing height or decreasing area, and then applies a placement rule to each of these shapes in turn. The proposed method is not restricted to the first shape encountered but may dynamically search the list for better candidate shapes for placement. We suggest an efficient implementation of our heuristic and show that it compares favourably to other heuristic and metaheuristic approaches from the literature in terms of both solution quality and execution time. We also present data for new problem instances to encourage further research and greater comparison between this and future methods.
319 citations
Cites background or methods from "An Empirical Investigation of Meta-..."
...As an illustrative example, Figure 11 shows the solutions obtained by each placement policy with problem C2P3 from Hopper and Turton (2001)....
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...These are usually hybridised algorithms involving the generation of input sequences that are then interpreted by placement heuristics such as bottom-left or bottom-left-fill (Jakobs 1996, Ramesh Babu and Ramesh Babu 1999, Hopper and Turton 2001)....
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...The main advantage for using bottom-left is its time complexity of O(N2) (Hopper and Turton 2001)....
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...Hopper and Turton (2001) compare several metaheuristics including genetic algorithms, simulated annealing, naïve evolution, hill climbing, and random searches....
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...In Hopper and Turton (2001), the authors concluded that the methods that yielded the best results were GA+BLF and SA+BLF....
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01 Jan 2013
TL;DR: This chapter provides an overview of some of the most widely used bio-inspired algorithms, especially those based on SI such as cuckoo search, firefly algorithm, and particle swarm optimization, and analyzes the essence of algorithms and their connections to self-organization.
Abstract: Swarm intelligence (SI) and bio-inspired computing in general have attracted great interest in almost every area of science, engineering, and industry over the last two decades. In this chapter, we provide an overview of some of the most widely used bio-inspired algorithms, especially those based on SI such as cuckoo search, firefly algorithm, and particle swarm optimization. We also analyze the essence of algorithms and their connections to self-organization. Furthermore, we highlight the main challenging issues associated with these metaheuristic algorithms with in-depth discussions. Finally, we provide some key, open problems that need to be addressed in the next decade.
271 citations
TL;DR: A new relaxation is proposed that produces good lower bounds and gives information to obtain effective heuristic algorithms in orthogonally packing a given set of rectangular items into a given strip, by minimizing the overall height of the packing.
Abstract: We consider the problem of orthogonally packing a given set of rectangular items into a given strip, by minimizing the overall height of the packing. The problem is NP-hard in the strong sense, and finds several applications in cutting and packing. We propose a new relaxation that produces good lower bounds and gives information to obtain effective heuristic algorithms. These results are used in a branch-and-bound algorithm, which was able to solve test instances from the literature involving up to 200 items.
267 citations
References
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Book•
01 Sep 1988
TL;DR: In this article, the authors present the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields, including computer programming and mathematics.
Abstract: From the Publisher:
This book brings together - in an informal and tutorial fashion - the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields
Major concepts are illustrated with running examples, and major algorithms are illustrated by Pascal computer programs No prior knowledge of GAs or genetics is assumed, and only a minimum of computer programming and mathematics background is required
52,797 citations
01 Jan 1989
TL;DR: This book brings together the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields.
Abstract: From the Publisher:
This book brings together - in an informal and tutorial fashion - the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields.
Major concepts are illustrated with running examples, and major algorithms are illustrated by Pascal computer programs. No prior knowledge of GAs or genetics is assumed, and only a minimum of computer programming and mathematics background is required.
33,034 citations
"An Empirical Investigation of Meta-..." refers background or methods in this paper
...Further techniques that have been implemented include elitism and seeding (Goldberg, 1989)....
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...Partially matched crossover (PMX) (Goldberg, 1989) and order-based mutation (Syswerda, 1991) are suitable for this type of encoding and have been used in this case....
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...Further theoretical and practical details can be found in (Davis, 1991; Goldberg, 1989)....
[...]
Book•
01 Jan 1991
TL;DR: This book sets out to explain what genetic algorithms are and how they can be used to solve real-world problems, and introduces the fundamental genetic algorithm (GA), and shows how the basic technique may be applied to a very simple numerical optimisation problem.
Abstract: This book sets out to explain what genetic algorithms are and how they can be used to solve real-world problems. The first objective is tackled by the editor, Lawrence Davis. The remainder of the book is turned over to a series of short review articles by a collection of authors, each explaining how genetic algorithms have been applied to problems in their own specific area of interest. The first part of the book introduces the fundamental genetic algorithm (GA), explains how it has traditionally been designed and implemented and shows how the basic technique may be applied to a very simple numerical optimisation problem. The basic technique is then altered and refined in a number of ways, with the effects of each change being measured by comparison against the performance of the original. In this way, the reader is provided with an uncluttered introduction to the technique and learns to appreciate why certain variants of GA have become more popular than others in the scientific community. Davis stresses that the choice of a suitable representation for the problem in hand is a key step in applying the GA, as is the selection of suitable techniques for generating new solutions from old. He is refreshingly open in admitting that much of the business of adapting the GA to specific problems owes more to art than to science. It is nice to see the terminology associated with this subject explained, with the author stressing that much of the field is still an active area of research. Few assumptions are made about the reader's mathematical background. The second part of the book contains thirteen cameo descriptions of how genetic algorithmic techniques have been, or are being, applied to a diverse range of problems. Thus, one group of authors explains how the technique has been used for modelling arms races between neighbouring countries (a non- linear, dynamical system), while another group describes its use in deciding design trade-offs for military aircraft. My own favourite is a rather charming account of how the GA was applied to a series of scheduling problems. Having attempted something of this sort with Simulated Annealing, I found it refreshing to see the authors highlighting some of the problems that they had encountered, rather than sweeping them under the carpet as is so often done in the scientific literature. The editor points out that there are standard GA tools available for either play or serious development work. Two of these (GENESIS and OOGA) are described in a short, third part of the book. As is so often the case nowadays, it is possible to obtain a diskette containing both systems by sending your Visa card details (or $60) to an address in the USA.
6,758 citations
"An Empirical Investigation of Meta-..." refers background in this paper
...Further theoretical and practical details can be found in (Davis, 1991; Goldberg, 1989)....
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01 Jan 1989
TL;DR: This paper presents a list of recommended recipes for making CDRom decks and some examples of how these recipes can be modified to suit theommelier's needs.
Abstract: Keywords: informatique ; numerical recipes Note: contient un CDRom Reference Record created on 2004-09-07, modified on 2016-08-08
4,920 citations