## A new evolutionary approach to cutting stock problems with and without contiguity (2002)

Citations: | 15 - 6 self |

### BibTeX

@MISC{Liang02anew,

author = {Ko-hsin Liang and Xin Yao and Charles Newton and David Hoffman},

title = {A new evolutionary approach to cutting stock problems with and without contiguity},

year = {2002}

}

### Years of Citing Articles

### OpenURL

### Abstract

Evolutionary algorithms (EAs) have been applied to many optimization problems successfully in recent years. The genetic algorithm (GAs) and evolutionary programming (EP) are two different types of EAs. GAs use crossover as the primary search operator and mutation as a background operator, while EP uses mutation as the primary search operator and does not employ any crossover. This paper proposes a novel EP algorithm for cutting stock problems with and without contiguity. Two new mutation operators are proposed. Experimental studies have been carried out to examine the effectiveness of the EP algorithm. They show that EP can provide a simple yet more effective alternative to GAs in solving cutting stock problems with and without contiguity. The solutions found by EP are significantly better (in most cases) than or comparable to those found by GAs. Scope and purpose The one-dimensional cuttingstock problem (CSP) is one of the classical combinatorial optimization problems. While most previous work only considered minimizing trim loss, this paper considers CSPs with two objectives. One is the minimization of trim loss (i.e., wastage). The other is the minimization of the number of stocks with wastage, or the number of partially finished items (pattern sequencing or contiguity

### Citations

7363 |
Genetic Algorithms
- Goldberg
- 1989
(Show Context)
Citation Context ... problems. The evolutionary approach is particularly good at dealing with complex and nonlinear problems andsnding a near-optimal solution within a reasonable amount of time. Genetic algorithms (GAs) =-=[12]-=- and evolutionary programming (EP) [13] are two major classes of EAs. While GAs have been applied to the cutting and packing problems by many researchers [6, 14, 15, 16, 17, 18], EP's application in c... |

1818 | Genetic Algorithms in Search Optimization and Machine Learning - Goldberg - 1989 |

1175 | Handbook of Genetic Algorithms
- Davis
- 1991
(Show Context)
Citation Context ...maintain the feasibility of ospring, otherwise some kind of penalty or repair methods must be used in order to evolve a feasible solution. The order-based GA uses uniform order-based crossover (UOB) [=-=25]-=- that applies a template of randomly generated binary bits to exchange some items and maintain relative order information from both parents. The mutation operator uses both swap and remove and reinser... |

853 |
Evolutionary algorithms in theory and practice
- Bäck
- 1996
(Show Context)
Citation Context ...istics used. Finding good heuristics is often as dicult as solving the problem itself. In addition, most good heuristics are highly problemdependent. In the past decade, evolutionary algorithms (EAs) =-=[11]-=- have become promising methods in solving various optimization problems. The evolutionary approach is particularly good at dealing with complex and nonlinear problems andsnding a near-optimal solution... |

614 |
Evolutionary Computation: Toward a New Philosophy of Machine Learning Intelligence
- Fogel
- 1995
(Show Context)
Citation Context ... particularly good at dealing with complex and nonlinear problems andsnding a near-optimal solution within a reasonable amount of time. Genetic algorithms (GAs) [12] and evolutionary programming (EP) =-=[13]-=- are two major classes of EAs. While GAs have been applied to the cutting and packing problems by many researchers [6, 14, 15, 16, 17, 18], EP's application in combinatorial optimization is relatively... |

123 |
A linear programming approach to the cutting stock problem—Part II
- Gilmore, Gomory
- 1963
(Show Context)
Citation Context ...f requested items goes up to 600 for problems 10 and 10a. No evolutionary algorithms have ever been tests on such problems. As mentioned in Section 1, traditional OR methods such as column generation =-=[26]-=- are designed mainly for single objective optimization. Once an optimal solution is found for a single objective, it is dicult to use the optimal cutting patterns for the second objective. To deal wit... |

86 | A Hybrid Grouping Genetic Algorithm for Bin Packing
- Falkenauer
- 1996
(Show Context)
Citation Context ... amount of time. Genetic algorithms (GAs) [12] and evolutionary programming (EP) [13] are two major classes of EAs. While GAs have been applied to the cutting and packing problems by many researchers =-=[6, 14, 15, 16, 17, 18-=-], EP's application in combinatorial optimization is relatively limited [19, 20]. Crossover is the primary search operator in GAs. It combines sound building blocks from dierent parents and passes the... |

55 |
A study of reproduction in generational and steady state genetic algorithms
- Syswerda
- 1991
(Show Context)
Citation Context ...erational replacement strategy, we can use a non-generational one where only a certain percentage of the whole population will reproduce, e.g., using the idea of continuous EP [28] or steady-state GA =-=-=-[29]. This can increase the eciency of an evolutionary algorithm in many cases. Since dierent search operators introduce dierent search biases, it would be benecial to have more than two dierent mutat... |

42 | Applying evolutionary programming to selected travelling salesman problems
- Fogel
- 1993
(Show Context)
Citation Context ...major classes of EAs. While GAs have been applied to the cutting and packing problems by many researchers [6, 14, 15, 16, 17, 18], EP's application in combinatorial optimization is relatively limited =-=[19, -=-20]. Crossover is the primary search operator in GAs. It combines sound building blocks from dierent parents and passes them to their ospring. However, the eectiveness of crossover as the primary sear... |

30 | Hybrid Genetic Algorithms for Bin Packing and Related Problems
- Reeves
(Show Context)
Citation Context ... amount of time. Genetic algorithms (GAs) [12] and evolutionary programming (EP) [13] are two major classes of EAs. While GAs have been applied to the cutting and packing problems by many researchers =-=[6, 14, 15, 16, 17, 18-=-], EP's application in combinatorial optimization is relatively limited [19, 20]. Crossover is the primary search operator in GAs. It combines sound building blocks from dierent parents and passes the... |

21 | Simulated annealing with extended neighbourhood
- Yao
- 1991
(Show Context)
Citation Context ...he distance between the original list and the resulting list is thus dened as 1. Such a concept of distance between permutation lists wassrst introduced and applied to the traveling salesman problem [=-=23, 24]-=-. The rest of this paper is organized as follows. Section 2 describes CSP with and without contiguity. In both cases, two objectives have to be considered and minimized. Section 3 introduces new mutat... |

20 |
Evolutionary Computation: Theory and Applications, World Scientific
- Yao
- 1999
(Show Context)
Citation Context ...m dependent. 5 Conclusion Two critical issues in applying evolutionary algorithms to combinatorial optimization problems are problem representation and search operators used under this representation =-=[27]-=-. Over-emphasizing anyone alone can lead to inaccurate conclusions. This paper takes a more holistic view and tries to design an evolutionary algorithm for CSPs based on the best integration between p... |

19 |
Cutting stock problems and solution procedures
- Haessler, Sweeney
- 1991
(Show Context)
Citation Context .... Traditional OR approaches to one-dimensional CSPs [3] can be divided into two categories, heuristics and linear programming (LP) based methods [1]. Golden [8], Hinxman [9], and Haessler and Sweeney =-=[10]-=- gave excellent surveys on the various solution approaches. LP based methods are designed solely to minimize trim loss or cost value. They have diculties in dealing with nonlinear problems which are m... |

17 | T.: Evolutionary Algorithms in Theory and Practice - äck - 1996 |

12 |
Approaches to the cutting stock problem
- Golden
- 1976
(Show Context)
Citation Context ...cing problem [7] or CSP with contiguity [6]. Traditional OR approaches to one-dimensional CSPs [3] can be divided into two categories, heuristics and linear programming (LP) based methods [1]. Golden =-=[8]-=-, Hinxman [9], and Haessler and Sweeney [10] gave excellent surveys on the various solution approaches. LP based methods are designed solely to minimize trim loss or cost value. They have diculties in... |

12 |
The trim-loss and assortment problems: A survey
- Hinxman
- 1980
(Show Context)
Citation Context ...[7] or CSP with contiguity [6]. Traditional OR approaches to one-dimensional CSPs [3] can be divided into two categories, heuristics and linear programming (LP) based methods [1]. Golden [8], Hinxman =-=[9]-=-, and Haessler and Sweeney [10] gave excellent surveys on the various solution approaches. LP based methods are designed solely to minimize trim loss or cost value. They have diculties in dealing with... |

12 |
A comparison of evolutionary programming and genetic algorithms on selected constrained optimization problems”, Simulation
- Fogel
(Show Context)
Citation Context ...it only uses mutation. It has been applied to a number of numerical and combinatorial problems with success [13]. It has been shown to be more ecient than GAs for some numerical optimization problems =-=[21, 22]-=-. In this paper, we propose an EP algorithm with only a swap mutation operator which outperforms GAs for one-dimensional CSPs with and without contiguity. The mutation in our EP is designed using the ... |

9 |
A typology of cutting and packing problems
- Dyckho
- 1990
(Show Context)
Citation Context ...und by EP are signicantly better (in most cases) than or comparable to those found by GAs. 1 Introduction The cutting stock problem (CSP) is an important class of combinatorial optimization problems [=-=1, 2, -=-3]. The traditional goals of CSPs are to minimize the trim loss and/or the cost value. Dyckho and Finke [2] categorized seven dierent objectives according to the characteristics of CSP. Most CSP solut... |

9 | Genetic algorithms for cutting stock problems: with and without contiguity
- Hinterding, Khan
- 1994
(Show Context)
Citation Context ... a second objective. For thesrst class of CSPs, the second objective is to minimize the number of used stocks. This type of CSP with two objectives has been tackled by using some heuristic techniques =-=[4, 5, 6-=-]. For the second class of CSP, the second objective is to minimize the number of partially Accepted by Computers and Operations Research. y To whom all correspondence should be addressed. (Email: li... |

9 |
Improved heuristics for sequencing cutting patterns
- Yuen
- 1995
(Show Context)
Citation Context ... the mutation. The probability to execute the SRI mutation is 0:25. When executed, SRI will be applied 4 times in a single mutation. 4 Experimental Studies Although there is a rich literature on CSPs =-=[1, 2, 3, 4, 5, 7, 8, 9, 10]-=-, few gave the actual data for their problems. Direct comparison with them is dicult if not impossible. In our experimental studies, 20 test problems are used. The detailed description of these proble... |

7 |
The one dimensional cutting stock problem using two objectives
- Sinuany-Stern, Weiner
- 1994
(Show Context)
Citation Context ... a second objective. For thesrst class of CSPs, the second objective is to minimize the number of used stocks. This type of CSP with two objectives has been tackled by using some heuristic techniques =-=[4, 5, 6-=-]. For the second class of CSP, the second objective is to minimize the number of partially Accepted by Computers and Operations Research. y To whom all correspondence should be addressed. (Email: li... |

7 |
Continuous evolutionary programming: Analysis and experiments
- Fogel, Fogel
- 1995
(Show Context)
Citation Context ... rather than using a generational replacement strategy, we can use a non-generational one where only a certain percentage of the whole population will reproduce, e.g., using the idea of continuous EP =-=[-=-28] or steady-state GA [29]. This can increase the eciency of an evolutionary algorithm in many cases. Since dierent search operators introduce dierent search biases, it would be benecial to have more... |

6 |
Cutting and Packing in Production and Distribution. A Typology and Bibliography
- Dyckoff, Finke
- 1992
(Show Context)
Citation Context ...und by EP are signicantly better (in most cases) than or comparable to those found by GAs. 1 Introduction The cutting stock problem (CSP) is an important class of combinatorial optimization problems [=-=1, 2, -=-3]. The traditional goals of CSPs are to minimize the trim loss and/or the cost value. Dyckho and Finke [2] categorized seven dierent objectives according to the characteristics of CSP. Most CSP solut... |

6 |
A hybrid genetic algorithm for pallet loading
- Prosser
- 1988
(Show Context)
Citation Context ... amount of time. Genetic algorithms (GAs) [12] and evolutionary programming (EP) [13] are two major classes of EAs. While GAs have been applied to the cutting and packing problems by many researchers =-=[6, 14, 15, 16, 17, 18-=-], EP's application in combinatorial optimization is relatively limited [19, 20]. Crossover is the primary search operator in GAs. It combines sound building blocks from dierent parents and passes the... |

5 |
Evolutionary metaphors for the bin packing problem. In: Fogel L, Angeline P and Bäck T (eds). Evolutionary Programming V
- Bilchev
- 1996
(Show Context)
Citation Context |

4 |
Near-optimal solutions to one-dimensional cutting stock problems
- Roodman
- 1986
(Show Context)
Citation Context ... a second objective. For thesrst class of CSPs, the second objective is to minimize the number of used stocks. This type of CSP with two objectives has been tackled by using some heuristic techniques =-=[4, 5, 6-=-]. For the second class of CSP, the second objective is to minimize the number of partially Accepted by Computers and Operations Research. y To whom all correspondence should be addressed. (Email: li... |

3 |
A multi-chromosome genetic algorithm for pallet loading
- Juli
- 1993
(Show Context)
Citation Context |

2 |
One-dimensional cutting stock decision packing problems
- Sweeney, Paternoster
- 1992
(Show Context)
Citation Context ...und by EP are signicantly better (in most cases) than or comparable to those found by GAs. 1 Introduction The cutting stock problem (CSP) is an important class of combinatorial optimization problems [=-=1, 2, -=-3]. The traditional goals of CSPs are to minimize the trim loss and/or the cost value. Dyckho and Finke [2] categorized seven dierent objectives according to the characteristics of CSP. Most CSP solut... |

1 |
Exploring self-adaptive methods to improve the e$ciency of generating approximate solutions to traveling salesman problems using evolutionary programming
- Chellapilla, Fogel
- 1997
(Show Context)
Citation Context ...major classes of EAs. While GAs have been applied to the cutting and packing problems by many researchers [6, 14, 15, 16, 17, 18], EP's application in combinatorial optimization is relatively limited =-=[19, -=-20]. Crossover is the primary search operator in GAs. It combines sound building blocks from dierent parents and passes them to their ospring. However, the eectiveness of crossover as the primary sear... |

1 |
Comparison of di!erent neighbourhood sizes in simulated annealing
- Yao
- 1993
(Show Context)
Citation Context ...he distance between the original list and the resulting list is thus dened as 1. Such a concept of distance between permutation lists wassrst introduced and applied to the traveling salesman problem [=-=23, 24]-=-. The rest of this paper is organized as follows. Section 2 describes CSP with and without contiguity. In both cases, two objectives have to be considered and minimized. Section 3 introduces new mutat... |

1 | One-dimensional cuttingstock decision packingproblems - Sweeney, Paternoster - 1992 |

1 | Near-optimal solutions to one-dimensional cuttingstock problems - Roodman - 1986 |

1 | The one dimensional cuttingstock problem usingtwo objectives - SinuanyStern, Weiner - 1994 |

1 | Heuristics for sequencingcuttingpatterns. European Journal of Operational Research 1991;55:183}90. Liang et al - Yuen |

1 | Approaches to cuttingstock problem - BL - 1976 |

1 | The trim-loss and assortment problems: a survey - AI - 1980 |

1 | Cuttingstock problems and solution procedures - Haessler, Sweeney - 1991 |

1 | Simulated annealingwith extended neighbourhood - Yao - 1991 |