Analysis of the objective space in multiple objective linear programming

Dauer, Jerald P.

doi:10.1016/0022-247x(87)90065-5

Cited by 51 publications

(24 citation statements)

References 5 publications

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“…Also, for decision-makers, it is easier to choose a solution to the outcome space than on the feasible set. These and other arguments may be seen in [10,11,12].…”

Section: Examplementioning

confidence: 84%

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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“…Also, for decision-makers, it is easier to choose a solution to the outcome space than on the feasible set. These and other arguments may be seen in [10,11,12].…”

Section: Examplementioning

confidence: 84%

Approximating nondominated sets in continuous multiobjective optimization problems

Jd¹,

Bielza²,

Insua³

2005

Naval Research Logistics

View full text Add to dashboard Cite

show abstract

“…6 To illustrate the main aspects of the approach proposed, representatives of two classes of multiobjective methods, namely the Geoffrion, Dyer, Feinberg (GDF) method (Ref. 9) and a fuzzy method of Baptistella and Ollero (Ref.…”

Section: F(x)=(ft(x)f2(x) F(x)) M>_2mentioning

confidence: 99%

Solving multiple-objective problems in the objective space

Ferreira

Machado

1996

J Optim Theory Appl

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Abstract. Projection and relaxation techniques are employed to decompose a multiobjective problem into a two-level structure. The basic manipulation consists in projecting the decision variables onto the space of the implicit tradeoffs, allowing the definition of a relaxed multiobjective master problem directly in the objective space. An additional subproblem tests the feasibility of the solution encountered by the relaxed problem. Some properties of the relaxed problem (linearity, small number of variables, etc.) render its solution efficient by a number of methods. Representatives of two different classes of multiobjective methods [the Geoffrion, Dyer, Feinberg (GDF) method and the fuzzy method of Baptistella and OUero] are implemented and applied within this context to a water resources allocation problem. The results attest the computational viability of the overall procedure and its usefulness for the solution of multiobjective problems.

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“…Therefore, further severe computational burdens are expected for such problems. Moreover, in recent works it was mentioned that the solution polyhedron in objective space often has much simpler structure than in decision space [8,9]. This phenomenon is due to the fact that in most practical problems, the decision space dimension is much greater than the objective space dimension.…”

Section: Introductionmentioning

confidence: 96%

Efficient solution generation for multiple objective linear programming based on extreme ray generation method

Ida

2005

European Journal of Operational Research

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Analysis of the objective space in multiple objective linear programming

Cited by 51 publications

References 5 publications

Approximating nondominated sets in continuous multiobjective optimization problems

Approximating nondominated sets in continuous multiobjective optimization problems

Solving multiple-objective problems in the objective space

Efficient solution generation for multiple objective linear programming based on extreme ray generation method

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