An Augmented Lagrangian Scalarization for Multiple Objective Programming

TenHuisen, Matthew L.; Wiecek, Margaret M.

doi:10.1007/978-3-642-46854-4_16

Cited by 3 publications

(2 citation statements)

References 9 publications

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“…All the globally efficient solutions can be found by means of the lexicographic weighted Tchebycheff approach (see Steuer 1986), while the locally efficient solutions can be generated using the augmented Lagrangian approach (see TenHuisen and Wiecek 1996). In order to avoid treating (4) in this general methodological framework and to obtain specific and more effective approaches, we focus on the special case of line barriers with passages but still consider Downloaded from informs.org by [129.93.16.3] on 11 June 2016, at 04:43 .…”

Section: Introductionmentioning

confidence: 99%

A Bi-Objective Median Location Problem With a Line Barrier

Klamroth

Wiecek

2002

Operations Research

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The multiple objective median problem (MOMP) involves locating a new facility with respect to a given set of existing facilities so that a vector of performance criteria is optimized. A variation of this problem is obtained if the existing facilities are situated on two sides of a linear barrier. Such barriers, like rivers, highways, borders, or mountain ranges, are frequently encountered in practice. In this paper, theory of an MOMP with line barriers is developed. As this problem is nonconvex but specially structured, a reduction to a series of convex optimization problems is proposed. The general results lead to a polynomial algorithm for finding the set of efficient solutions. The algorithm is proposed for bicriteria problems with different measures of distance.

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Section: Introductionmentioning

confidence: 99%

A Bi-Objective Median Location Problem With a Line Barrier

Klamroth

Wiecek

2002

Operations Research

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“…In general, non-convex problems with even just two criteria may have a very complex structure: the set of outcomes in the objective space may not be W$-convex, the nondominated set may be disconnected and nondominated solutions may include local and global solutions. The recent study of TenHuisen (1993), motivated by the complexity of non-convex cases, provides a special treatment of non-linear multiple-objective problems that are not required to satisfy rigid convexity assumptions. This paper, as an extension of the aforementioned research, introduces and discusses some new concepts that could be further employed in analysing the structure of the non-dominated set.…”

Section: Introductionmentioning

confidence: 99%

On the Structure of the Non-dominated Set for Bicriteria Programmes

TenHuisen

Wiecek

1996

J. Multi-Crit. Decis. Anal.

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In multiple-objective programming, a knowledge of the structure of the non-dominated set can aid in generating efficient solutions. We present new concepts which allow for a better understanding of the structure of the set of nondominated solutions for non-convex bicriteria programming problems. In particular, a means of determining whether or not this set is connected is examined. Both supersets and newly defined subsets of the non-dominated set are utilized in this investigation. Of additional value is the use of the lower envelope of the set of outcomes in classifying feasible points as (properly) non-dominated solutions.

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Tind

Wiecek

1999

Journal of Global Optimization

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An Augmented Lagrangian Scalarization for Multiple Objective Programming

Cited by 3 publications

References 9 publications

A Bi-Objective Median Location Problem With a Line Barrier

A Bi-Objective Median Location Problem With a Line Barrier

On the Structure of the Non-dominated Set for Bicriteria Programmes

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