Abstract
This paper is concerned with the problem of finding a representative sample of Pareto-optimal points in multi-objective optimization. The Normal Boundary Intersection algorithm is a scalarization scheme for generating a set of evenly spaced Efficient solutions. A drawback of this algorithm is that Pareto-optimality of solutions is not guaranteed. The contributions of this paper are two-fold. First, it presents alternate formulation of this algorithms, such that (weak) Pareto-optimality of solutions is guaranteed. This improvement makes these algorithm theoretically equivalent to other classical algorithms (like weighted-sum or ε-constraint methods), without losing its ability to generate a set of evenly spaced Efficient solutions. Second, an algorithm is presented so as to know beforehand about certain sub-problems whose solutions are not Pareto-optimal and thus not wasting computational effort to solve them. The relationship of the new algorithm with weighted-sum and goal programming method is also presented.
Chapter PDF
Similar content being viewed by others
References
Das, I., Dennis, J.E.: A closer look at drawbacks of minimizing weighted sum of objecties for Pareto set generation in multicriteria optimization problems. Structural Optimization 14(1), 63–69 (1997)
Das, I., Dennis, J.E.: Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM Journal of Optimization 8(3), 631–657 (1998)
Deb, K.: Multi-objective optimization using evolutionary algorithms. Wiley, Chichester (2001)
Ehrgott, M.: Multicriteria Optimization. Springer, Berlin (2000)
Eschenauer, H., Koski, J., Osyczka, A.: Multicriteria Design Optimization. Springer, Berlin (1990)
Gembicki, F.W.: Performance and Sensitivity Optimization: A Vector Index Approach. PhD thesis, Case Western Reserve University, Cleveland, OH (1974)
Kim, I.Y., de Weck, O.: Multiobjective optimization via the adaptive weighted sum method. In: 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference (2004)
Kim, I.Y., de Weck, O.: Adaptive weighted sum method for multiobjective optimization: a new method for Pareto front generation. Structural and Multidisciplinary Optimization 31(2), 105–116 (2005)
Messac, A., Mattson, C.A.: Normal constraint method with guarantee of even representation of complete pareto frontier. AIAA Journal 42(10), 2101–2111 (2004)
Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer, Boston (1999)
Osyczka, A.: Evolutionary Algorithms for Single and Multicriteria Design Optimization. Physica Verlag, Heidelberg (2002)
Sandgren, E.: Multicriteria design optimization by goal programming. In: Adeli, H. (ed.) Advances in Design Optimization, pp. 225–265. Chapman & Hall, London (1994)
Stanikov, R.B., Matusov, J.B.: Multicriteria Optimization and Engineering. Chapman and Hall, New York (1995)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Shukla, P.K. (2007). On the Normal Boundary Intersection Method for Generation of Efficient Front. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds) Computational Science – ICCS 2007. ICCS 2007. Lecture Notes in Computer Science, vol 4487. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72584-8_40
Download citation
DOI: https://doi.org/10.1007/978-3-540-72584-8_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72583-1
Online ISBN: 978-3-540-72584-8
eBook Packages: Computer ScienceComputer Science (R0)