An Information-Theoretic Entropy Metric for Assessing Multi-Objective Optimization Solution Set Quality

[+] Author and Article Information
Ali Farhang-Mehr, Shapour Azarm

Department of Mechanical Engineering, University of Maryland, College Park, MD 20742

J. Mech. Des 125(4), 655-663 (Jan 22, 2004) (9 pages) doi:10.1115/1.1623186 History: Received November 01, 2001; Revised March 01, 2003; Online January 22, 2004
Copyright © 2003 by ASME
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Two different feasible solution sets with the same number of points: (a) grouped into clusters; (b) evenly distributed
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Visual assessment of solution sets from: (a) Fig. 1(a); (b) Fig. 1(b)
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A set of solution points in a one-dimensional feasible space with the corresponding influence and density functions
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(a) Density hyper-surface of the solution set in Fig. 1(a); (b) density hyper-surface of the solution set in Fig. 1(b)
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The feasible region as divided into a grid of cells
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(a) A population of points; (b) a non-dominated hypersurface with good and bad points
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The origin of the cartesian coordinate system as transferred to the good point
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The projection mapping of solution points: (a) projection plane and direction in three dimensions, (b) projection plane with projected points in two dimensions
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Solutions that influence the density function values at points A and B
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Compensation of a boundary effect
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The density surface of Fig. 4(b) after the boundary effect correction
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Virtual image of a solution point located close to a boundary
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The density surface of non-dominated solution sets for different generations




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