## An Efficient Constraint Handling Method for Genetic Algorithms (1998)

Venue: | Computer Methods in Applied Mechanics and Engineering |

Citations: | 138 - 12 self |

### BibTeX

@INPROCEEDINGS{Deb98anefficient,

author = {Kalyanmoy Deb},

title = {An Efficient Constraint Handling Method for Genetic Algorithms},

booktitle = {Computer Methods in Applied Mechanics and Engineering},

year = {1998},

pages = {311--338}

}

### Years of Citing Articles

### OpenURL

### Abstract

Many real-world search and optimization problems involve inequality and/or equality constraints and are thus posed as constrained optimization problems. In trying to solve constrained optimization problems using genetic algorithms (GAs) or classical optimization methods, penalty function methods have been the most popular approach, because of their simplicity and ease of implementation. However, since the penalty function approach is generic and applicable to any type of constraint (linear or nonlinear), their performance is not always satisfactory. Thus, researchers have developed sophisticated penalty functions specific to the problem at hand and the search algorithm used for optimization. However, the most difficult aspect of the penalty function approach is to find appropriate penalty parameters needed to guide the search towards the constrained optimum. In this paper, GA's population-based approach and ability to make pair-wise comparison in tournament selection operator are explo...

### Citations

8299 |
Genetic Algorithms
- Goldberg
- 1989
(Show Context)
Citation Context ...l allow a crossover operator to constantly find better feasible solutions. There are a number of ways diversity can be maintained in a population. Among them, niching methods [16] and use of mutation =-=[17]-=- are popular ones. In this paper, we use either or both of the above methods of maintaining diversity among the feasible solutions. A simple niching strategy is implemented in the tournament selection... |

2060 |
Genetic algorithms in search, optimization and machine learning
- Goldberg
- 1989
(Show Context)
Citation Context ...l allow a crossover operator to constantly find better feasible solutions. There are a number of ways diversity can be maintained in a population. Among them, niching methods [16] and use of mutation =-=[17]-=- are popular ones. In this paper, we use either or both of the above methods of maintaining diversity among the feasible solutions. A simple niching strategy is implemented in the tournament 11 select... |

714 |
Evolutionsstrategie: Optimierung Technischer Systeme nach Prinzipien der Biologischen Evolution. Frommann-Holzboog
- Rechenberg
- 1973
(Show Context)
Citation Context ...asible solutions can be maintained. 3.2 Evolutionary Strategies versus Real-coded GAs Evolutionary strategies (ESs) are evolutionary optimization methods which work on floating-point numbers directly =-=[18,19]-=-. The main difference in the working principles of an ES and a real-coded GA is that in ES mutation operator is the main search operator. ES also uses a block truncation selection operator, which is d... |

543 |
Numerical Optimization of Computer Models
- Schwefel
- 1981
(Show Context)
Citation Context ...asible solutions can be maintained. 3.2 Evolutionary Strategies versus Real-coded GAs Evolutionary strategies (ESs) are evolutionary optimization methods which work on floating-point numbers directly =-=[18,19]-=-. The main difference in the working principles of an ES and a real-coded GA is that in ES mutation operator is the main search operator. ES also uses a block truncation selection operator, which is d... |

279 |
An investigation of niche and species formation in genetic function optimization
- Deb, Goldberg
- 1989
(Show Context)
Citation Context ...important task, which will allow a crossover operator to constantly find better feasible solutions. There are a number of ways diversity can be maintained in a population. Among them, niching methods =-=[16]-=- and use of mutation [17] are popular ones. In this paper, we use either or both of the above methods of maintaining diversity among the feasible solutions. A simple niching strategy is implemented in... |

245 | Evolutionary algorithms for constrained parameter optimization problems
- Michalewicz, Schoenauer
- 1996
(Show Context)
Citation Context ...ations. These solutions are much closer to the true optimum solution 21 than that found by the best algorithm in [6]. 4.6 Test Problem 6 This problem has five variables and six inequality constraints =-=[23,7]-=-: Minimize f 6 (~x) = 5:3578547x 2 3 + 0:8356891x 1 x 5 + 37:293239x 1 \Gamma 40792:141; Subject to g 1 (~x) j 85:334407 + 0:0056858x 2 x 5 + 0:0006262x 1 x 4 \Gamma 0:0022053x 3 x 5s0; g 2 (~x) j 85:... |

219 | The gambler’s ruin problem, genetic algorithms, and the sizing of populations
- Harik, Goldberg, et al.
- 1997
(Show Context)
Citation Context ...s, we run GAs 50 times from different initial populations. Fixing the correct population size in a problem is an important factor for proper working of a GA. Previous population sizing considerations =-=[21,22]-=- based on schema processing suggested that the population size should increase with the problem size. Although the correct population size should also depend on the underlying signal-to-noise in a pro... |

180 |
Test Examples for Nonlinear Programming Codes, volume 187
- Hock, Schittkowski
- 1981
(Show Context)
Citation Context ...meters for obtaining better results. Appendix B. Terms and parameters used in test function 2 The following terms are required to compute the objective function and constraints for the test problem 2 =-=[23,24]-=-: 336 K. Deb / Comput. Methods Appl. Mech. Engrg. 186 (2000) 311–338 y1 ~x x1 x2 41:6; c1 ~x 0:024x4 ÿ 4:62; y2 ~x 12:5=c1 ~x 12:0; c2 ~x 0:0003535x1x1 0:5311x1 0:08705y2 ~xx1;... |

144 | Simulated binary crossover for continuous search space
- Deb, Agrawal
- 1995
(Show Context)
Citation Context ...space may be able to eliminate the above two difficulties associated with binary coding and single-point crossover. In this paper, we use real-coded GAs with simulated binary crossover (SBX) operator =-=[14]-=- and a parameter-based mutation operator [15], for this purpose. SBX operator is particularly suitable here, because the spread of children solutions around parent solutions can be controlled using a ... |

143 |
Some guidelines for genetic algorithms with penalty functions
- Richardson, Palmer, et al.
(Show Context)
Citation Context ...ng better objective function value is preferred, 7 (3) Among two infeasible solutions, the one having smaller constraint violation is preferred. Although there exist a number of other implementations =-=[6,8,12]-=- where criteria similar to the above are imposed in their constraint handling approaches, all of these implementations used different measures of constraint violations which still needed a penalty par... |

109 |
Engineering Optimization Methods and Applications
- Reklaitis, Ravindran, et al.
- 1983
(Show Context)
Citation Context ...nd (ii) specific methods that are only applicable to a special type of constraints. Generic methods, such as the penalty function method, the Lagrange multiplier method, and the complex search method =-=[1,2]-=- are popular, because each one of them can be easily applied to any problem without much change in the algorithm. But since these methods are generic, the performance of these methods in most cases is... |

109 |
Applied nonlinear programming
- Himmelblau
- 1972
(Show Context)
Citation Context ...han binary GAs. In the following, we compare these GAs to a more complicated test problem. 4.2. Test problem 2 This problem is a minimization problem with five variables and 38 inequality constraints =-=[23,24]-=-: Minimize f2 ~x 0:1365ÿ 5:843 10ÿ7y17 1:17 10ÿ4y14 2:358 10ÿ5y13 1:502 10ÿ6y16 0:0321y12 0:004324y5 1:0 10ÿ4c15=c16 37:48y2=c12 Subject to g1 ~x 1:5x2 ÿ x3 P 0; g2 ~x y1 ~x... |

108 | On the use of nonstationary penalty functions to solve non-linear constrained optimization problems with GAs
- Joines, Houck
- 1994
(Show Context)
Citation Context ... This dependency of GA's performance on penalty parameters has led researchers to devise sophisticated penalty function approaches such as multi-level penalty functions [3], dynamic penalty functions =-=[4]-=-, and penalty functions involving temperaturebased evolution of penalty parameters with repair operators [5]. All these approaches require extensive experimentation for setting up appropriate paramete... |

91 |
Optimization for Engineering Design: Algorithms and Examples
- Deb
- 1995
(Show Context)
Citation Context ...nd (ii) specific methods that are only applicable to a special type of constraints. Generic methods, such as the penalty function method, the Lagrange multiplier method, and the complex search method =-=[1,2]-=- are popular, because each one of them can be easily applied to any problem without much change in the algorithm. But since these methods are generic, the performance of these methods in most cases is... |

90 |
Using genetic algorithms in engineering design optimization with non-linear constraints
- Powell, Skolnick
- 1993
(Show Context)
Citation Context ... to population-based search methods such as GAs or other evolutionary computation methods. Although at least one other constraint handling method satisfying above three criteria was suggested earlier =-=[8]-=- it involved penalty parameters which again must be set right for proper working of the algorithm. In the remainder of the paper, we first show that the performance of a binary-coded GA using the stat... |

70 | Real-coded genetic algorithms with simulated binary crossover: Studies on multimodal and multiobjective problems
- Deb, Kumar
- 1995
(Show Context)
Citation Context ...ork in general. Moreover, there exists a plethora of other implementations of GAs such as multimodal GAs, multi-objective GAs, and others, which have been successfully implemented with real-coded GAs =-=[20]-=-. We believe that the constraint handling strategy suggested in this study can also be easily incorporated along with various other kinds of existing real-coded GAs. Thus, for the sake of simplicity i... |

65 |
Constrained optimization via genetic algorithms. Simulation 62(4
- Homaifar, Qi, et al.
- 1994
(Show Context)
Citation Context ...m to obtain feasible solutions. This dependency of GA's performance on penalty parameters has led researchers to devise sophisticated penalty function approaches such as multi-level penalty functions =-=[3]-=-, dynamic penalty functions [4], and penalty functions involving temperaturebased evolution of penalty parameters with repair operators [5]. All these approaches require extensive experimentation for ... |

65 | Genetic algorithms, numerical optimization, and constraints
- Michalewicz
(Show Context)
Citation Context ...lution of penalty parameters with repair operators [5]. All these approaches require extensive experimentation for setting up appropriate parameters needed to define the penalty function. Michalewicz =-=[6]-=- describes the difficulties in each method and compares the performance of these algorithms on a number of test problems. In a similar study, Michalewicz and Schoenauer [7] concluded that the static p... |

56 |
Evolutionary optimization of constrained problems
- Michalewicz, Attia
- 1994
(Show Context)
Citation Context ...ty function approaches such as multi-level penalty functions [3], dynamic penalty functions [4], and penalty functions involving temperaturebased evolution of penalty parameters with repair operators =-=[5]-=-. All these approaches require extensive experimentation for setting up appropriate parameters needed to define the penalty function. Michalewicz [6] describes the difficulties in each method and comp... |

32 |
Evolutionary programming techniques for constrained optimization problems” in
- Kim, Myung
- 1997
(Show Context)
Citation Context ...erformance of different methods, they suggested to use the static penalty function method, similar to that given in equation 2. Recently, a two-phase evolutionary programming (EP) method is developed =-=[10]-=-. In the first phase, a standard EP technique with a number of strategy parameters which were evolved during the optimization process was used. With the solution obtained in the first phase, a neural ... |

28 | A combined genetic adaptive search (GeneAS) for engineering design
- Deb, Goyal
- 1996
(Show Context)
Citation Context ...difficulties associated with binary coding and single-point crossover. In this paper, we use real-coded GAs with simulated binary crossover (SBX) operator [14] and a parameter-based mutation operator =-=[15]-=-, for this purpose. SBX operator is particularly suitable here, because the spread of children solutions around parent solutions can be controlled using a distribution index j c (see Appendix A). With... |

10 |
Applied nonlinear programming, Mc-Graw Hill book-Company
- Himmelblau
- 1972
(Show Context)
Citation Context ...llowing, we compare these GAs to a more complicated test problem. ----- Figure 8 here ----- 4.2 Test Problem 2 This problem is a minimization problem with five variables and 38 inequality constraints =-=[23,24]-=-: Minimize f 2 (~x) = 0:1365 \Gamma 5:843(10 \Gamma7 )y 17 + 1:17(10 \Gamma4 )y 14 + 2:358(10 \Gamma5 )y 13 +1:502(10 \Gamma6 )y 16 + 0:0321y 12 + 0:004324y 5 +1:0(10 \Gamma4 )c 15 =c 16 + 37:48y 2 =c... |

8 |
Engineering Optimization—Methods and Applications
- Reklaitis, Ravindran, et al.
- 1983
(Show Context)
Citation Context ...nd (ii) specific methods that are only applicable to a special type of constraints. Generic methods, such as the penalty function method, the Lagrange multiplier method, and the complex search method =-=[1,2]-=- are popular, because each one of them can be easily applied to any problem without much change in the algorithm. But since these methods are generic, the performance of these methods in most cases is... |

8 |
Genetic algorithms, noise, and the sizing of populations, Complex Systems 6
- Goldberg, Deb, et al.
- 1992
(Show Context)
Citation Context ...s, we run GAs 50 times from different initial populations. Fixing the correct population size in a problem is an important factor for proper working of a GA. Previous population sizing considerations =-=[21,22]-=- based on schema processing suggested that the population size should increase with the problem size. Although the correct population size should also depend on the underlying signal-to-noise in a pro... |

3 |
Optimal design of a welded beam structure via genetic algorithms
- Deb
- 1991
(Show Context)
Citation Context ...ed solution reported in the literature [2] is h = 0:2444, ` = 6:2187, t = 8:2915, and b = 0:2444 with a function value equal to f = 2:38116. Binary GAs are applied on this problem in an earlier study =-=[9]-=- and the solution ~x = (0:2489; 6:1730; 8:1789; 0:2533) with f = 2:43 (within 2% of the above best solution) was obtained with a population size of 100. However, it was observed that the performance o... |