Optimization methods
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Date |
15/09/2006 |
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Author |
T.
V. Tran, S. Brisset, P. Brochet |
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Affiliation |
L2EP
– EC Lille – France |
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Email |
tran.tuan-vu@ec-lille.fr, stephane.brisset@ec-lille.fr, pascal.brochet@ec-lille.fr |
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Method |
Weighted Sum method |
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References |
[1]
Koski, J (1985), “Defectiveness of weighting method in multicriterion
optimization of structures”, Communication in Applied Numerical Methods, Vol.
1, Issue 6, pp. 333-337. [2] P. Venkataraman, Applied
Optimization with MatlabÒ Programming, A Wiley - Interscience publication,
John Wiley & Sons, New York, 2001. [3] Das I, Dennis IE (1998), Normal
Boundary Intersection: a new method for generating Pareto optimal points in
multicriteria optimization problems, [4] Kim IY, de Weck OL (2005),
Adaptive weighted sum method for bi-objective optimization: Pareto front
generation, Struct MUltidiscipl Optim 29: 149-158 |
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Description of the method |
The determinist algorithm is the weighted sum (WS)
method in Koski (1985). This is the most widely used method for
multi-objective optimization. This optimization is performed with the SQP
method. The stochastic algorithm is Non-Dominated Sorting Genetic Algorithm
II (NSGA II) in Deb et al. (2002). The weighted sum method transforms biobjectives into an aggregated
scalar objective function by multiplying both objective functions by a
weighting factor α Î[0,1].
Thus, the suboptimization problem is stated as:
where nf1 and nf2 are normalization factors for Mtot(x) and (1-η(x)), respectively (nf1
= 6 and nf2 = 0.05). By changing the weighting factor
systematically, the several suboptimization problems are solved that obtain
optimal solutions in the objective space. The optimum solution points then
represent the Pareto front. The distribution of Pareto-optimal front found by WS
method generally is non uniform. This is a first drawback of this method.
Furthermore, WS method can not reach the solution that lie in the non-convex
regions of the Pareto-optimal front. Therefore, the Normal Boundary
Intersection (NBI) [3] method and the Adaptive Weighted Sum (AWS) [4] method
can handle these problems. |
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Publication of the method |
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