Multiple‐objective weighting factor auxiliary optimization problems

White, D. J.

doi:10.1002/mcda.4020040205

Cited by 2 publications

(2 citation statements)

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“…This approach poses several problems, however. For example, for the case of optimisation of convex combinations of the objective functions (see [35,37]), if there are no preconditions, we may not be able to generate enough solutions to obtain a good approximation of the nondominated set. Moreover, unless appropriate convexity conditions for the objective functions and the set of alternatives hold, current methods cannot solve the corresponding optimisation problem.…”

Section: Introductionmentioning

confidence: 98%

“…Therefore, a good idea would be to convert the problem into a form where relevant algorithms do exist which may benefit from the problem structure. In that sense, White [37] proposes convex combinations of finite powers of the objective functions to generate all efficient solutions. This method can be considered as a means of generating solutions additional to those generated from convex combinations of the objective functions.…”

Section: Introductionmentioning

confidence: 99%

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Approximating nondominated sets in continuous multiobjective optimization problems

Jd¹,

Bielza²,

Insua³

2005

Naval Research Logistics

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Many important problems in Operations Research and Statistics require the computation of nondominated (or Pareto or efficient) sets. This task may be currently undertaken efficiently for discrete sets of alternatives or for continuous sets under special and fairly tight structural conditions. Under more general continuous settings, parametric characterisations of the nondominated set, for example through convex combinations of the objective functions or -constrained problems, or discretizations-based approaches, pose several problems. In this paper, the lack of a general approach to approximate the nondominated set in continuous multiobjective problems is addressed. Our simulation-based procedure only requires to sample from the set of alternatives and check whether an alternative dominates another. Stopping rules, efficient sampling schemes, and procedures to check for dominance are proposed. A continuous approximation to the nondominated set is obtained by fitting a surface through the points of a discrete approximation, using a local (robust) regression method. Other actions like clustering and projecting points onto the frontier are required in nonconvex feasible regions and nonconnected Pareto sets. In a sense, our method may be seen as an evolutionary algorithm with a variable population size.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%