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## Navigation on a Pareto-optimal front utilizing gradient information in interactive multiobjective optimization

### Citations

464 |
Multiple objective optimization with vector evaluated genetic algorithms. In Genetic algorithms and their applications
- Schaffer
- 1985
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Citation Context ...reto-optimal point Pareto-optimal front p = 0 p = 1 p = 2 p = 3 Figure 1: Approximations of a Pareto-optimal front based on Taylor’s polynomial for a multiobjective optimization problem formulated in =-=[17]-=-. If we have derivative information of degree p, we can find a good Taylor’s polynomial approximation to a Pareto-optimal front. Nevertheless, in practice (in the real world problems), we usually have... |

456 |
Nonlinear Multiobjective Optimization
- Miettinen
- 1999
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Citation Context ...ple having three conflicting targets. The final section is devoted for conclusions. 4. Multiobjective optimization approach In general, a multiobjective optimization problem can be defined as follows =-=[16]-=- minimize {f1(x ), f2(x ), . . . , fk(x )} subject to x ∈ S, (1) where x is a vector of decision variables from the feasible set S ⊂ Rn defined by box, linear and nonlinear constraints. We can denote ... |

17 | Interactive multiobjective optimization procedure. Accepted for publication
- Tappeta, Renaud
- 2007
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Citation Context ...timal solutions can be predicted in a certain area, which can be useful information in decision making. Similar ideas of approximating Pareto-optimal fronts have been presented also in the literature =-=[1, 2, 3, 4]-=-. Second, gradient information can be employed during an interactive solution process to generate so-called trade-off information. Here, a decision maker (a person who is supposed to have better insig... |

17 | Interactive Multiobjective Optimization Design Strategy for Decision Based Design
- Tappeta, Renaud
- 2001
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Citation Context ...timal solutions can be predicted in a certain area, which can be useful information in decision making. Similar ideas of approximating Pareto-optimal fronts have been presented also in the literature =-=[1, 2, 3, 4]-=-. Second, gradient information can be employed during an interactive solution process to generate so-called trade-off information. Here, a decision maker (a person who is supposed to have better insig... |

14 |
Synchronous approach in interactive multiobjective optimization
- Miettinen, Mäkelä
- 2006
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Citation Context ... Therefore, we tested these ideas with a classification based method. In these examples (one academic and one real world), a classification-based interactive multiobjective optimization method NIMBUS =-=[18]-=- was used. 6.1. Example 1: An academic example Here, we used an example presented in [17] in which there were two conflicting objective functions (f1 : R → R and f2 : R → R) to be minimized at the sam... |

9 | Integrating approximation and interactive decision making in multicriteria optimization
- Klamroth, Miettinen
- 2008
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Citation Context ...timal solutions can be predicted in a certain area, which can be useful information in decision making. Similar ideas of approximating Pareto-optimal fronts have been presented also in the literature =-=[1, 2, 3, 4]-=-. Second, gradient information can be employed during an interactive solution process to generate so-called trade-off information. Here, a decision maker (a person who is supposed to have better insig... |

6 | Interactive Physical Programming: Tradeoff Analysis and Decision Making in Multidisciplinary Optimization
- Tappeta, Renaud
- 2000
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6 |
Efficient solutions and bounds on trade-offs
- KALISZEWSKI, MICHALOWSKI
- 1997
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Citation Context ...as clearly as possible so that interpreting and utilizing it becomes easier and the desired solution is easy to choose. The concept of trade-off have been widely discussed in the literature, see e.g. =-=[5, 6, 7, 8, 9, 10, 11, 12, 13]-=-, but here we concentrate on supporting the decision making process with the trade-off information such as in [14]. Results from the numerical examples indicate that presenting an approximation of a P... |

5 |
Trade-off analysis using parametric optimisation techniques
- Nakayama
- 1992
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Citation Context ...as clearly as possible so that interpreting and utilizing it becomes easier and the desired solution is easy to choose. The concept of trade-off have been widely discussed in the literature, see e.g. =-=[5, 6, 7, 8, 9, 10, 11, 12, 13]-=-, but here we concentrate on supporting the decision making process with the trade-off information such as in [14]. Results from the numerical examples indicate that presenting an approximation of a P... |

4 |
Generation of outcomes with selectively bounded trade-offs
- KALISZEWSKI, MICHALOWSKI
- 1995
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Citation Context ...as clearly as possible so that interpreting and utilizing it becomes easier and the desired solution is easy to choose. The concept of trade-off have been widely discussed in the literature, see e.g. =-=[5, 6, 7, 8, 9, 10, 11, 12, 13]-=-, but here we concentrate on supporting the decision making process with the trade-off information such as in [14]. Results from the numerical examples indicate that presenting an approximation of a P... |

4 |
Normal Vector Identification and Interactive Tradeoff Analysis Using Minimax Formulation in Multiobejctive Optimization
- Yang, Li
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2 |
Kuhn-Tucker Multipliers as Trade-Offs in Multiobjective DecisionMaking Analysis, Automatica
- Haimes, Chankong
- 1979
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2 |
Trade-off Analysis for Vector Optimization Problems via Scalarization
- Kuk, Tanino, et al.
- 1997
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Objective trade-off rate information in interactive multiobjective optimization methods – A survey of theory and applications
- Eskelinen
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1 |
Ideas of using trade-off information in supporting the decision maker in reference point based interactive multiobjective optimization
- Hakanen, Eskelinen
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Citation Context ...off have been widely discussed in the literature, see e.g. [5, 6, 7, 8, 9, 10, 11, 12, 13], but here we concentrate on supporting the decision making process with the trade-off information such as in =-=[14]-=-. Results from the numerical examples indicate that presenting an approximation of a Pareto-optimal 1 front and the trade-off information to the decision maker makes the optimization process more intu... |

1 | Madetoja E and Ruotsalainen H. CFD-based optimization for a complete industrial process: papermaking. Optimization and computational fluid dynamics - Hämäläinen, Hämäläinen - 2008 |