Note on combinatorial optimization with max-linear objective functions

Chung, Sung-Jin; Hamacher, Horst W.; Maffioli, Francesco; Murty, Katta G.

doi:10.1016/0166-218x(93)90043-n

Cited by 15 publications

(8 citation statements)

References 12 publications

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“…Here this includes the max-ordering scalarization of the unconstrained 0-1 problem (Chung et al, 1993) min x∈{0,1} n p max k=1 c k x, i.e., a problem that is trivial in the single objective case, and the max-ordering scalarization of the shortest path problem (Warburton, 1987).…”

Section: The Augmented Weighted Chebychev Methodsmentioning

confidence: 99%

A discussion of scalarization techniques for multiple objective integer programming

Ehrgott

2006

Ann Oper Res

160

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In this paper we consider solution methods for multiobjective integer programming (MOIP) problems based on scalarization. We define the MOIP, discuss some common scalarizations, and provide a general formulation that encompasses most scalarizations that have been applied in the MOIP context as special cases. We show that these methods suffer some drawbacks by either only being able to find supported efficient solutions or introducing constraints that can make the computational effort to solve the scalarization prohibitive. We show that Lagrangian duality applied to the general scalarization does not remedy the situation. We also introduce a new scalarization technique, the method of elastic constraints, which is shown to be able to find all efficient solutions and overcome the computational burden of the scalarizations that use constraints on objective values. Finally, we present some results from an application in airline crew scheduling as evidence.

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Section: The Augmented Weighted Chebychev Methodsmentioning

confidence: 99%

A discussion of scalarization techniques for multiple objective integer programming

Ehrgott

2006

Ann Oper Res

160

View full text Add to dashboard Cite

show abstract

“…Bishop, E. and Phelps, R.R. (1981) [39] [40] [41] [42] Borwein, J.M. The support functionals of a convex set.…”

Section: Referencesmentioning

confidence: 99%

“…Blum, E. and Oettli, W. (1994). Vector Variational Inequalities and Vector Equilibria,[39][40][41][42][43][44][45][46][47][48][49][50][51][52][53] Optimization and its Applications 38. The Mathematics Student, 63: 123-145.…”

Section: Referencesmentioning

confidence: 99%

“…Recently, a problem of optimizing another objective function over the (weakly) efficient set of a multiobjective programming problem has been discussed by several authors [40,56,85,112,457,493,494]. This problem requires a combination of global optimization and multiobjective optimization.…”

Section: Efficiency and Weak Efficiencymentioning

confidence: 99%

“…Engineering (all types) [73,227] Environmental and Waste Management [42,43,44,45] Health Planning [106] Natural Resource Management [115,188] 140 MULTIPLE CRITERIA OPTIMIZATION Theoretical [49,51,109,138,148,149,151,181,182,201,202,246] Transportation and Distribution [22,23,40] Again, the high percentage of theoretical papers is an indication of the newness of this extension.…”

Section: Fuzzy Goal Programming Modelsmentioning

confidence: 99%

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