The normalized normal constraint method for generating the Pareto frontier

@article{Messac2003TheNN,
  title={The normalized normal constraint method for generating the Pareto frontier},
  author={Achille Messac and Amir Ismail-Yahaya and Christopher A. Mattson},
  journal={Structural and Multidisciplinary Optimization},
  year={2003},
  volume={25},
  pages={86-98}
}
Abstract The authors recently proposed the normal constraint (NC) method for generating a set of evenly spaced solutions on a Pareto frontier – for multiobjective optimization problems. Since few methods offer this desirable characteristic, the new method can be of significant practical use in the choice of an optimal solution in a multiobjective setting. This paper’s specific contribution is two-fold. First, it presents a new formulation of the NC method that incorporates a critical linear… 

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References

SHOWING 1-10 OF 19 REFERENCES

Effective generation of the Pareto frontier using the Normal Constraint method

A new and simple method to generate an evenly spaced set of Pareto solutions in the design space and this method bears some similarities to the Normal Boundary Intersection and to the e-Constraint methods, and it works for an arbitrary number of objectives.

A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems

A standard technique for generating the Pareto set in multicriteria optimization problems is to minimize (convex) weighted sums of the different objectives for various different settings of the

Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems

This paper proposes an alternate method for finding several Pareto optimal points for a general nonlinear multicriteria optimization problem that can handle more than two objectives while retaining the computational efficiency of continuation-type algorithms.

Genetic Algorithm Development for Multiobjective Optimization of Structures

Genetic algorithms (GAs) have the characteristic of maintaining a population of solutions and can search in a parallel manner for many nondominated solutions. These features coincide with the

Generating Well-Distributed Sets of Pareto Points for Engineering Design Using Physical Programming

This paper examines the effectiveness of physical programming (PP) with respect to the latter, yielding favorable conclusions, and presents a comparative study featuring PP and other popular methods, where PP is shown to perform favorably.

Quality utility : a Compromise Programming approach to robust design

In robust design, associated with each quality characteristic, the design objective often involves multiple aspects such as bringing the mean of performance on target and minimizing the variations.

A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm

A new method of transformation of the multiple criteria problem into a single-criterion problem is presented and preliminary computer generated results show that this approach produces better, and far more Pareto solutions, than plain stochastic optimization methods.

Multiobjective Optimization of Large-Scale Structures

A multiobjective optimization algorithm based on generalized compound scaling techniques that generates a partial Pareto set while solving the optimization problem, similar to handling behavior constraints.

Heuristics-guided evolutionary approach to multiobjective generation scheduling

A novel approach for multiobjective generation scheduling is presented. The work reported employs a simple heuristics-guided evolutionary algorithm to generate solutions to this nonlinear constrained

Physical programming - Effective optimization for computational design

Physical programming is a new approach to realistic design optimization that may be appealing to the design engineer in an industrial setting that provides the means to reliably employ optimization with minimal prior knowledge thereof.