On improving normal boundary intersection method for generation of Pareto frontier

  • Authors:

  • S. Siddiqui;S. Azarm;S. A. Gabriel

  • Affiliations:

  • ICF International, Fairfax, USA 22031;Department of Mechanical Engineering, University of Maryland, College Park, USA 20742;Department of Civil and Environmental Engineering, University of Maryland, College Park, USA 20742

  • Venue:
  • Structural and Multidisciplinary Optimization
  • Year:
  • 2012

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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.