A hybrid genetic algorithm for the container loading problem
TL;DR: A hybrid genetic algorithm for the container loading problem with boxes of different sizes and a single container for loading that uses specific genetic operators based on an integrated greedy heuristic to generate offspring.
About: This article is published in European Journal of Operational Research.The article was published on 2001-05-16. It has received 303 citations till now. The article focuses on the topics: Stowage & Greedy algorithm.
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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
Cites background from "A hybrid genetic algorithm for the ..."
...Pisinger, 2002), in which rectangular-shaped boxes have to be packed into a container (three-dimensional, rectangular SKP; also see Bischoff and Marriott, 1990; Scheithauer, 1999; Bortfeldt and Gehring, 2001)....
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...…(Single Orthogonal) Knapsack Problem (also called Knapsack Container Loading Problem; cf. Pisinger, 2002), in which rectangular-shaped boxes have to be packed into a container (three-dimensional, rectangular SKP; also see Bischoff and Marriott, 1990; Scheithauer, 1999; Bortfeldt and Gehring, 2001)....
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TL;DR: Atabu search algorithm that iteratively invokes an inner tabu search procedure for the solution of the loading subproblem is proposed, which is experimentally evaluated both on instances adapted from vehicle routing instances from the literature and on new real-world instances.
Abstract: This article considers a combination of capacitated vehicle routing and three-dimensional loading, with additional constraints frequently encountered in freight transportation. It proposes a tabu search algorithm that iteratively invokes an inner tabu search procedure for the solution of the loading subproblem. The algorithm is experimentally evaluated both on instances adapted from vehicle routing instances from the literature and on new real-world instances.
298 citations
Cites background from "A hybrid genetic algorithm for the ..."
...The loading problem is related to various threedimensional packing problems, in particular to container-loading problems, where constraints on the supporting surface or on the fragility of the items are frequently considered (e.g., Bortfeldt and Gehring 2001; Eley 2002; Pisinger 2002)....
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TL;DR: This work states that container loading problems have been dealt with frequently in the operations research literature and that the proposed approaches are of limited practical value since they do not pay enough attention to constraints encountered in practice.
296 citations
TL;DR: An exact approach is proposed, based on a branch-and-cut algorithm, for the minimization of the routing cost that iteratively calls a branch and-bound algorithm for checking the feasibility of the loadings.
Abstract: We consider a special case of the symmetric capacitated vehicle routing problem, in which a fleet of K identical vehicles must serve n customers, each with a given demand consisting in a set of rectangular two-dimensional weighted items. The vehicles have a two-dimensional loading surface and a maximum weight capacity. The aim is to find a partition of the customers into routes of minimum total cost such that, for each vehicle, the weight capacity is taken into account and a feasible two-dimensional allocation of the items into the loading surface exists.
The problem has several practical applications in freight transportation, and it is NP-hard in the strong sense. We propose an exact approach, based on a branch-and-cut algorithm, for the minimization of the routing cost that iteratively calls a branch-and-bound algorithm for checking the feasibility of the loadings. Heuristics are also used to improve the overall performance of the algorithm. The effectiveness of the approach is shown by means of computational results.
267 citations
Cites methods from "A hybrid genetic algorithm for the ..."
...For the 2CLP, heuristic approaches have been proposed by Pisinger (1998, 2002) and Bortfeldt and Gehring (2000), an analytical model was pro posed by Chen, Lee, and Shen (1995), and an LP based bound was presented by Scheithauer (1992, 1999)....
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TL;DR: A review of the use of genetic algorithms to solve operations problems and the designs of the genetic algorithms used to solve them is provided.
Abstract: Operations managers and scholars in their search for fast and good solutions to real-world problems have applied genetic algorithms to many problems. While genetic algorithms are promising tools for problem solving, future research will benefit from a review of the problems that have been solved and the designs of the genetic algorithms used to solve them. This paper provides a review of the use of genetic algorithms to solve operations problems. Reviewed papers are classified according to the problems they solve. The basic design of each genetic algorithm is described, the shortcomings of the current research are discussed and directions for future research are suggested.
251 citations
Additional excerpts
...Bortfeldt and Gehring (2001) use a hybrid GA to solve the container-loading problem (three-dimensional knapsack problem)....
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References
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Book•
01 Jan 1992
TL;DR: GAs and Evolution Programs for Various Discrete Problems, a Hierarchy of Evolution Programs and Heuristics, and Conclusions.
Abstract: 1 GAs: What Are They?.- 2 GAs: How Do They Work?.- 3 GAs: Why Do They Work?.- 4 GAs: Selected Topics.- 5 Binary or Float?.- 6 Fine Local Tuning.- 7 Handling Constraints.- 8 Evolution Strategies and Other Methods.- 9 The Transportation Problem.- 10 The Traveling Salesman Problem.- 11 Evolution Programs for Various Discrete Problems.- 12 Machine Learning.- 13 Evolutionary Programming and Genetic Programming.- 14 A Hierarchy of Evolution Programs.- 15 Evolution Programs and Heuristics.- 16 Conclusions.- Appendix A.- Appendix B.- Appendix C.- Appendix D.- References.
12,212 citations
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
Book•
01 Jan 1993TL;DR: In this paper, the Lagrangian relaxation and dual ascent tree search were used to solve the graph bisection problem and the graph partition problem, and the traveling salesman problem scheduling problems.
Abstract: Part 1 Introduction: combinatorial problems local and global optima heuristics. Part 2 Simulated annealing: the basic method enhancements and modifications applications conclusions. Part 3 Tabu search: the tabu framework broader aspects of intensification and diversification tabu search applications connections and conclusions. Part 4 Genetic algorithms: basic concepts a simple example extensions and modifications applications conclusions. Part 5 Artificial neural networks: neural networks combinatorial optimization problems the graph bisection problem the graph partition problem the travelling salesman problem scheduling problems deformable templates inequality constraints, the Knapsack problem summary. Part 6 Lagrangian relaxation: overview basic methodology Lagrangian heuristics and problem reduction determination of Lagrange multipliers dual ascent tree search applications conclusions. Part 7 Evaluation of heuristic performance: analytical methods empirical testing statistical inference conclusions.
2,571 citations
Proceedings Article•
01 Dec 1989
TL;DR: The range of scheduling mechanisms presented herein allows this type of exibility during code generation and their use on critical portions of code could create enhanced run-time performance for a wide variety of code.
Abstract: The traveling saleman and sequence scheduling quality solution using genetic edge recombination. A study of permutation crossover operators on the traveling salesman problem. example of using pseudooelds to eliminate version shuuing in horizontal code compaction. race scheduling optimization in a retargetable microcode compiler.cessing: A smart compiler and a dumb machine.man. A vliw architecture for a trace scheduling compiler. IEEE Trans-117 considered during instruction scheduling. Using methods suggested here, this complexity m a y be reduced or bounded by a c hosen amount of time. 3. The search capabilities of genetic algorithms could be used to generate better weightings on the list scheduling algorithm. As these will vary on a per-architecture basis, a suite of typical" programs could be compiled while changing the weights in the discriminating polynomial selection function. Those weights found to produce good results for the current machineeprogram combination could then be used for any program on that machine. This would also provide feedback to the machine designers as to which features have a direct bearing upon performance and which do not. Closing the loop that exists between hardware and software design will increase the speed of both. 6.4 Summary In summary, previous methods of local instruction scheduling were examined and found lacking. Several new approaches were discovered and developed to address speciic deeciencies uncovered. A wholly new method, applying genetic algorithms, was explored and found beneecial. The increasing complexity of machines mandate the strengthing of instruction scheduling; genetic algorithms are a method of achieving this. 116 6.3 Directions With the framework provided by this work, many i n teresting directions for future work exist. Three follow. 1. Software pipelining was not considered. Its ability to improve repetitive c o d e structure is impressive. Loops are important structures to optimize as more execution time will be spent in them compared to straight line code. Previous methods have used an unrolling technique combined with local compaction SDX86, MSDP86. Because of the power of the scheduling methods developed here, their use on critical portions of code could create enhanced run-time performance for a wide variety of code. Given a choice, critical sections" of code should be emphasized in the optimization process at the expense of less critical sections of code. The range of scheduling mechanisms presented herein allows this type of exibility during code generation. For example, another parameter used to decide the type of scheduling performed on a …
935 citations