Approximation Methods in Multiobjective Programming

  title={Approximation Methods in Multiobjective Programming},
  author={Stefan Ruzika and Margaret M. Wiecek},
  journal={Journal of Optimization Theory and Applications},
  • 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.



An approximation method for the efficiency set of multiobjective programming problems

A general generating algorithm for E-approximations for the efficiency set of vector minimization problems is given which will be modified for linear continuous problems by means of the Dual Simplex Method.

Solving multiobjective programming problems by discrete representation

In the paper two theorems are given concerning the relationship between the conflict among the objectives and the nature of the Pareto-set in vector optimization. Taking this into consideration, a

Multiobjective optimization using evolutionary algorithms

The results of the automated optimization cycle show shapes previously obtained by physical understanding as well as novel shapes of even higher eciency.

Quantitative Pareto Analysis by Cone Separation Technique

Preface. Notation. 1. Introduction. 2. Basic Elements. 3. Cones, Efficiency and Proper Efficiency -- a General Setting. 4. Proper Efficiency with Respect to k+. 5. Quantitative Pareto Analysis. 6.

Approximation of Multiobjective Optimization Problems

It turns out that, under general conditions, there is a polynomially succinct curve that approximates the Pareto curve within any desired accuracy.

Efficient Pareto Frontier Exploration using Surrogate Approximations

The results indicate that the proposed method is effective at capturing convex and concave Pareto frontiers even when discontinuities are present.

Minimum Effort Approximation of the Pareto Space of Convex Bi-Criteria Problems

One of the major issues facing design practitioners using multiple-criteria optimization problems is how to decide on the trade-off between the various objectives. Since the Pareto set of those