Structural and Multidisciplinary Optimization

, Volume 46, Issue 6, pp 839–852 | Cite as

On improving normal boundary intersection method for generation of Pareto frontier

Research Paper

Abstract

Gradient-based methods, including Normal Boundary Intersection (NBI), for solving multi-objective optimization problems require solving at least one optimization problem for each solution point. These methods can be computationally expensive with an increase in the number of variables and/or constraints of the optimization problem. This paper provides a modification to the original NBI algorithm so that continuous Pareto frontiers are obtained “in one go,” i.e., by solving only a single optimization problem. Discontinuous Pareto frontiers require solving a significantly fewer number of optimization problems than the original NBI algorithm. In the proposed method, the optimization problem is solved using a quasi-Newton method whose history of iterates is used to obtain points on the Pareto frontier. The proposed and the original NBI methods have been applied to a collection of 16 test problems, including a welded beam design and a heat exchanger design problem. The results show that the proposed approach significantly reduces the number of function calls when compared to the original NBI algorithm.

Keywords

Normal Boundary Intersection (NBI) Multi-objective optimization Continuous nonlinear optimization Pareto solutions Quasi-Newton methods 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.ICF InternationalFairfaxUSA
  2. 2.Department of Mechanical EngineeringUniversity of MarylandCollege ParkUSA
  3. 3.Department of Civil and Environmental EngineeringUniversity of MarylandCollege ParkUSA

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