## An Adaptive Penalty Approach for Constrained Genetic-Algorithm Optimization (1998)

Venue: | Proceedings of the Third Annual Genetic Programming Conference |

Citations: | 8 - 2 self |

### BibTeX

@INPROCEEDINGS{Rasheed98anadaptive,

author = {Khaled Rasheed},

title = {An Adaptive Penalty Approach for Constrained Genetic-Algorithm Optimization},

booktitle = {Proceedings of the Third Annual Genetic Programming Conference},

year = {1998},

pages = {584--590},

publisher = {Morgan Kaufmann Publishers}

}

### OpenURL

### Abstract

In this paper we describe a new adaptive penalty approach for handling constraints in genetic algorithm optimization problems. The idea is to start with a relatively small penalty coefficient and then increase it or decrease it on demand as the optimization progresses. Empirical results in several engineering design domains demonstrate the merit of the proposed approach. 1 Introduction Genetic Algorithms (GAs) (Goldberg 1989) are search algorithms that mimic the behavior of natural selection. GAs attempt to find the best solution to some problem (e.g., the maximum of a function) by generating a collection ("population ") of potential solutions ("individuals") to the problem. Through mutation and recombination (crossover) operations, better solutions are hopefully generated out of the current set of potential solutions. This process continues until an acceptably good solution is found. GAs have many advantages over other search techniques, including the ability to deal with qualitativ...

### Citations

7782 |
Genetic Algorithms
- Goldberg
- 1989
(Show Context)
Citation Context ... decrease it on demand as the optimization progresses. Empirical results in several engineering design domains demonstrate the merit of the proposed approach. 1 Introduction Genetic Algorithms (GAs) (=-=Goldberg 1989) are sear-=-ch algorithms that mimic the behavior of natural selection. GAs attempt to find the best solution to some problem (e.g., the maximum of a function) by generating a collection ("population ")... |

2063 |
Genetic Algorithms + Data Structures = Evolutionary Programs
- Michalewicz
- 1992
(Show Context)
Citation Context ...ill map this problem to: minimize f(x) + p(x) where p(x) is called the penalty function. Several forms of penalty functions have been proposed in the GA literature. A thorough survey can be found in (=-=Michalewicz 1996-=-). These include: 1. Rejection of infeasible solutions (the death penalty). 2. Using a mapping function so that all feasible solutions will have fitness values that are better than the fitness value o... |

87 |
Using genetic algorithms in engineering design optimization with nonlinear constraints, in: S. Forrest (Ed
- Powell, Skolnick
- 1993
(Show Context)
Citation Context ...ion of infeasible solutions (the death penalty). 2. Using a mapping function so that all feasible solutions will have fitness values that are better than the fitness value of any infeasible solution (=-=Powell and Skolnick 1993-=-). 3. Using one or more multiplicative coefficients (as will be discussed shortly). The first two approaches can make the search extremely difficult in non-convex feasible regions especially if the op... |

51 |
Genetic optimization using a penalty function
- Smith, Tate
- 1993
(Show Context)
Citation Context ...gn (Lienig and Thulasiraman 1993), mechanical design (Chapman and Jakiela 1996, Deb 1997) and aircraft design (Obayashi et al. 1997). The idea of using a dynamic penalty coefficient was discussed in (=-=Smith and Tate 1993-=-). A dynamic approach was proposed and tested in a combinatorial optimization problem (the unequal area facility layout problem). The approach is similar to the one proposed in this paper in the sense... |

29 | GADO: A genetic algorithm for continuous design optimization
- Rasheed
- 1988
(Show Context)
Citation Context ...tic engineering tasks. We conclude the paper with a discussion of related efforts and future work. 2 GA Architecture GADO, the GA used in this research is described in detail in (Rasheed et al. 1997, =-=Rasheed 1998-=-). Each individual in the GA population represents a parametric description of an artifact, such as an aircraft, or a process, with each parameter taking on a value in some continuous interval. The fi... |

25 | Using modeling knowledge to guide design space search
- Gelsey, Schwabacher, et al.
- 1998
(Show Context)
Citation Context ...se domains. 4.1 Supersonic Transport Aircraft Design Our first domain concerns the conceptual design of supersonic transport aircraft. We summarize it briefly here; it is described in more detail in (=-=Gelsey et al. 1996-=-). Figure 1 shows a diagram of a typical airplane automatically designed by our software system. The GA attempts to find a good design for a particular mission by varying the aircraft conceptual desig... |

23 |
GeneAS: a robust optimal design technique for mechanical component design
- Deb
- 1997
(Show Context)
Citation Context ... design (Kundu and Kawata 1996), architectural and civil engineering design (Gero et al. 1997, Rosenman 1997), VLSI design (Lienig and Thulasiraman 1993), mechanical design (Chapman and Jakiela 1996, =-=Deb 1997-=-) and aircraft design (Obayashi et al. 1997). The idea of using a dynamic penalty coefficient was discussed in (Smith and Tate 1993). A dynamic approach was proposed and tested in a combinatorial opti... |

23 | The generation of form using an evolutionary approach
- Rosenman
- 1997
(Show Context)
Citation Context ... algorithms to engineering design optimization problems in a variety of domains, including control system design (Kundu and Kawata 1996), architectural and civil engineering design (Gero et al. 1997, =-=Rosenman 1997-=-), VLSI design (Lienig and Thulasiraman 1993), mechanical design (Chapman and Jakiela 1996, Deb 1997) and aircraft design (Obayashi et al. 1997). The idea of using a dynamic penalty coefficient was di... |

18 | A genetic algorithm for channel routing in VLSI circuits
- Lienig, Thulasiraman
- 1993
(Show Context)
Citation Context ...sign optimization problems in a variety of domains, including control system design (Kundu and Kawata 1996), architectural and civil engineering design (Gero et al. 1997, Rosenman 1997), VLSI design (=-=Lienig and Thulasiraman 1993-=-), mechanical design (Chapman and Jakiela 1996, Deb 1997) and aircraft design (Obayashi et al. 1997). The idea of using a dynamic penalty coefficient was discussed in (Smith and Tate 1993). A dynamic ... |

17 |
Genetic algorithm-based structural topology design with compliance and topology simplification considerations
- Chapman, Jakiela
- 1994
(Show Context)
Citation Context ..., including control system design (Kundu and Kawata 1996), architectural and civil engineering design (Gero et al. 1997, Rosenman 1997), VLSI design (Lienig and Thulasiraman 1993), mechanical design (=-=Chapman and Jakiela 1996-=-, Deb 1997) and aircraft design (Obayashi et al. 1997). The idea of using a dynamic penalty coefficient was discussed in (Smith and Tate 1993). A dynamic approach was proposed and tested in a combinat... |

15 |
Multiobjective Genetic Algorithm for Multidisciplinary Design of Transonic Wing Planform
- Obayashi, Yamaguchi, et al.
- 1997
(Show Context)
Citation Context ..., architectural and civil engineering design (Gero et al. 1997, Rosenman 1997), VLSI design (Lienig and Thulasiraman 1993), mechanical design (Chapman and Jakiela 1996, Deb 1997) and aircraft design (=-=Obayashi et al. 1997-=-). The idea of using a dynamic penalty coefficient was discussed in (Smith and Tate 1993). A dynamic approach was proposed and tested in a combinatorial optimization problem (the unequal area facility... |

15 |
The Utility of Nonlinear Programming Algorithms
- Sandgren
- 1977
(Show Context)
Citation Context ...tions 'GADO_Benchmark' 'GADO_Benchmark_fixed_penalty' Figure 4 Effect of adaptive penalty in the benchmark domain All points are evaluable. A more detailed description of this domain can be found in (=-=Sandgren 1977-=-). Optimization in this domain proved to be very difficult for conventional numerical optimizers and traditional GAs (Powell and Skolnick 1993). The main reason for this difficulty was the fact that 1... |

8 | Using Case-Based Learning to Improve GeneticAlgorithm-Based Design Optimization
- Rasheed, Hirsh
- 1997
(Show Context)
Citation Context ...ulation completely loses diversity and practically converges to a single point in the search space. The GA architecture also includes a screening module (SM) and a diversity maintenance module (DMM) (=-=Rasheed and Hirsh 1997-=-) which can both be turned on or off. The SM saves time by preventing the GA from evaluating points that are close to previously encountered bad points. It uses a case based learning technique to do t... |

7 |
AI in control system design using a new paradigm for design representation
- Kundu
- 1996
(Show Context)
Citation Context ...design of a membrane separation process. Several research efforts have applied genetic algorithms to engineering design optimization problems in a variety of domains, including control system design (=-=Kundu and Kawata 1996-=-), architectural and civil engineering design (Gero et al. 1997, Rosenman 1997), VLSI design (Lienig and Thulasiraman 1993), mechanical design (Chapman and Jakiela 1996, Deb 1997) and aircraft design ... |

1 | Kazakov and Thorsten Schinier - Gero, Vladimir - 1997 |

1 | Haym Hirsh and Andrew Gelsey - Rasheed - 1997 |