Approximation Methods in Multiobjective Programming

@article{Ruzika2005ApproximationMI,
  title={Approximation Methods in Multiobjective Programming},
  author={Stefan Ruzika and Margaret M. Wiecek},
  journal={Journal of Optimization Theory and Applications},
  year={2005},
  volume={126},
  pages={473-501}
}
  • S. RuzikaM. Wiecek
  • Published 1 September 2005
  • Economics
  • Journal of Optimization Theory and Applications
Approaches to approximate the efficient set and Pareto set of multiobjective programs are reviewed. Special attention is given to approximating structures, methods generating Pareto points, and approximation quality. The survey covers more than 50 articles published since 1975. 

A literature review of multi-objective programming

This paper provides a survey of methods that have been developed to solve multiobjective problems. We focus only on non-interactive exact methods that generate the entire set of optimal solutions.

Constructing a Pareto front approximation for decision making

An approach to constructing a Pareto front approximation to computationally expensive multiobjective optimization problems is developed as a sub-complex of a Delaunay triangulation of a finite set of Pare to optimal outcomes to the problem.

Decision Making on Pareto Front Approximations with Inherent Nondominance

It is shown that an approximation having the above property can be explored by interactively solving a multiobjective optimization problem related to it, and this exploration can be performed with available interactive multiobjectives optimization methods.

Generating the weakly efficient set of nonconvex multiobjective problems

The convergence of the method is proven and the set of weakly efficient solutions of a nonconvex multiobjective optimization problem is generated.

Visualizing the Pareto Frontier

Visualization techniques for visualizing the Pareto optimal set that can be used if the multiobjective optimization problem considered has more than two objective functions are described.

Covers and approximations in multiobjective optimization

The concept of tolerance function is proposed as a tool for modeling representation quality and leads to the extension of the traditional dominance relation to $$t\hbox {-}$$t-dominance.

A Filled Function Algorithm for Multiobjective Optimization

In this paper a filled function algorithm is applied to compute one of the nonisolated Pareto optimal points of an unconstrained multiobjective optimization problem to solve the corresponding global optimization problem.

An approximation to the nondominated set of a multiobjective linear fractional programming problem

A method for approximating the nondominated set of a multiobjective linear fractional programming (MOLFP) problem is presented, where is the tolerance vector and the method controls the cardinality of the resulting approximation set.

A Computationally Inexpensive Approach in Multiobjective Heat Exchanger Network Synthesis

The Pareto front of a heat exchanger network synthesis problem is approximated with a new approximation approach and the preferred point on the approximation is found with the interactive multiobjective optimization method NIMBUS.

A computationally efficient algorithm to approximate the pareto front of multi-objective linear fractional programming problem

The procedure is constructed that constructs a good approximation to the non-dominated set of multiple objective linear fractional programming problem using the solutions to certain linear optimization problems to generate a discrete set of feasible solutions that are further used as starting points in any procedure for deriving efficient solutions.
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