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  • vector maximization  (3)
  • Springer  (3)
  • American Association for the Advancement of Science (AAAS)
  • 1
    Electronic Resource
    Electronic Resource
    Outcome Space Partition of the Weight Set in Multiobjective Linear Programming (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 17-36 
    Details
    ISSN: 1573-2878
    Keywords: multiple-objective linear programming ; vector maximization ; efficient points ; weight set
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Approaches for generating the set of efficient extreme points of the decision set of a multiple-objective linear program (P) that are based upon decompositions of the weight set W0 suffer from one of two special drawbacks. Either the required computations are redundant, or not all of the efficient extreme point set is found. This article shows that the weight set for problem (P) can be decomposed into a partition based upon the outcome set Y of the problem, where the elements of the partition are in one-to-one correspondence with the efficient extreme points of Y. As a result, the drawbacks of the decompositions of W0 based upon the decision set of problem (P) disappear. The article explains also how this new partition offers the potential to construct algorithms for solving large-scale applications of problem (P) in the outcome space, rather than in the decision space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004605810296
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  • 2
    Electronic Resource
    Electronic Resource
    Admissible points of a convex polyhedron (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 341-361 
    Details
    ISSN: 1573-2878
    Keywords: Admissible points ; multiple-objective decision making ; efficient points ; vector maximization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we present several new properties of the admissible points of a convex polyhedron. These properties can be classified into two categories. One category concerns the characterization and generation of these points. The other category concerns the circumstances under which these points are efficient solutions for linear multiple-objective programs with nonnegative criteria matrices. To illustrate some of the potential utility of these properties, we describe their application to two practical problems. These problems are the linear multiple-objective problem with interval coefficients and the problem of optimizing over the efficient set.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935343
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  • 3
    Electronic Resource
    Electronic Resource
    Hybrid Approach for Solving Multiple-Objective Linear Programs in Outcome Space (1998)
    Springer
    Journal of optimization theory and applications 98 (1998), S. 17-35 
    Details
    ISSN: 1573-2878
    Keywords: Multiple-objective linear programming ; vector maximization ; efficient set ; outcome set ; global optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Various difficulties arise in using decision set-based vector maximization methods to solve a multiple-objective linear programming problem (MOLP). Motivated by these difficulties, some researchers in recent years have begun to develop tools for analyzing and solving problem (MOLP) in outcome space, rather than in decision space. In this article, we present and validate a new hybrid vector maximization approach for solving problem (MOLP) in outcome space. The approach systematically integrates a simplicial partitioning technique into an outer approximation procedure to yield an algorithm that generates the set of all efficient extreme points in the outcome set of problem (MOLP) in a finite number of iterations. Some key potential practical and computational advantages of the approach are indicated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022628612489
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