Compromise solutions and estimation of the noninferior set

Gearhart, W. B.

doi:10.1007/bf00933599

Cited by 60 publications

(16 citation statements)

References 9 publications

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“…Proposition 1. If 2 E X satisfies the Kuhn-Tucker (KT) conditions for problem (9) and p,(Z) > 0, it also satisfies the K T conditions for P(w) with d,,, as in (8a) and some w E W, provided that T o test the validity of Proposition I it suffices to show that at Z for some C > 0 and some w E W, since the constraint set is the same in both problems. Since p,(Z) > 0, it is possible to write …”

Section: Multiple Intersection Problemmentioning

confidence: 99%

Goal Aggregation in Design Optimization

Diaz

1988

Engineering Optimization

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Criteria for design evaluation in an optimization environment may be combined in diRerenl forms to produce a more accurate representation of the overall merit of a design. A rational and systematic procedure for aggregating peaormance criteria based on fuzzy set theory is presented. Optimal solutions obtained from this orocedure are formallv related to solutions to traditional formulations in multiobiective optimization. The procedure is illustrated with an example.

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Section: Multiple Intersection Problemmentioning

confidence: 99%

Goal Aggregation in Design Optimization

Diaz

1988

Engineering Optimization

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“…Considering that the geometric contour varies during shape optimization, structured and unstructured meshes are jointly used to suit the geometric variation. The material parameters used here are material density = 7800 kg=m (1) c 1 =0.1, c 2 =0.9 (2) c 1 =0.3, c 2 =0.7 (3) c 1 =0.4, c 2 =0.6 (4) c 1 =0.5, c 2 =0.5 (5) c 1 =0.6, c 2 =0.4 (6) c 1 =0.9, c 2 =0.1 Figure 13. Pareto optimum solutions versus weightings.…”

Section: Shape Optimization Of a Rotating Diskmentioning

confidence: 99%

“…It was intensively studied later by Gearhart [2], Yu and Leitmann [3] and others. Chen et al [4] applied the degenerated version of the CP method, i.e.…”

Section: Introductionmentioning

confidence: 98%

A compromise programming method using multibounds formulation and dual approach for multicriteria structural optimization

Zhang

2003

Numerical Meth Engineering

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SUMMARYTo enhance the reliability and e ciency of the multicriteria optimization procedure, a compromise programming method using multibounds formulation (MBF) is proposed in this paper. This method can be used either to obtain the Pareto optimum set or to ÿnd the 'best' Pareto optimum solution in the sense of having the minimum distance to the utopia point. By introducing a set of artiÿcial design variables, it is shown that a simpliÿed and easy-to-use formulation can be established for practical applications. Particularly, this formulation is well adapted to the e cient dual solution approach due to the convexity of objective function. Theoretically, based on the Kuhn-Tucker optimality conditions, demonstrations show that the new formulation is equivalent to its original form and thus retains the basic properties of the latter. Numerical examples will be solved to show the capacity of this method.

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“…The optimal solution, found from the feasible set, is the highest possible value for the objective function based upon the preferences of the decision maker (Romero and Rehman, 1989), whereas the corresponding distance functions are introduced through a family of p-metrics (Yu, 1973;Zeleny, 1973;Gearhart, 1979;Wierzbizki, 1980;Steuer, 1986 …”

Section: Compromise Programming (Cp)mentioning

confidence: 99%

A compromise programming model for site selection of borrow pits

Pantouvakis

Manoliadis

2008

Construction Management and Economics

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Road fill construction requires soil for filling low areas; this soil is obtained from temporary mineral workings known as 'borrow pits' (BP). Between a number of possible BPs, the appropriate site should be selected based upon conflicting econo-technical and environmental criteria aiming at achieving optimal BP performance while minimizing the adverse impacts to human and natural resources. For solving this problem a model for BP selection has been developed by this research using compromise programming (CP). The model incorporates a hierarchical structure integrating criteria and sub-criteria whose relative importance is set by the decision makers. Possible alternative BP sites are subsequently assessed on all these sub-criteria. Based upon this analysis, the model determines the distance of each of the possible alternatives from the utopia (ideal) point; the option with the minimum distance is considered the best compromise. The relevant concepts are exemplified through the presentation of a case study concerning the BP site selection for an Egnatia Motorway section in northwest Greece. The main conclusion that can be drawn from this work is that the CP approach is appropriate and valid for BP selection and, furthermore, it may also be used for other multiple objective construction-related site selection problems.Multiple objectives, decision making, compromise programming, borrow pits,

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Compromise solutions and estimation of the noninferior set

Cited by 60 publications

References 9 publications

Goal Aggregation in Design Optimization

Goal Aggregation in Design Optimization

A compromise programming method using multibounds formulation and dual approach for multicriteria structural optimization

A compromise programming model for site selection of borrow pits

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