# Approximation with a Fixed Number of Solutions of Some Biobjective Maximization Problems

@inproceedings{Bazgan2011ApproximationWA, title={Approximation with a Fixed Number of Solutions of Some Biobjective Maximization Problems}, author={Cristina Bazgan and Laurent Gourv{\`e}s and J{\'e}r{\^o}me Monnot}, booktitle={WAOA}, year={2011} }

We investigate the problem of approximating the Pareto set of biobjective optimization problems with a given number of solutions. This task is relevant for two reasons: (i) Pareto sets are often computationally hard so approximation is a necessary tradeoff to allow polynomial time algorithms; (ii) limiting explicitly the size of the approximation allows the decision maker to control the expected accuracy of approximation and prevents him to be overwhelmed with too many alternatives. Our purpose…

## 2 Citations

Online Resource Management

- Computer Science
- 2015

A novel and consistent framework for the analysis of multi-objective online problems is achieved and a real-world optimization problem, namely a cutting problem arising in the veneer industry, featuring uncertainty in the input data is presented.

Competitive Analysis for Multi-objective Online Algorithms

- Computer Science, BusinessWALCOM
- 2015

This work analyzes the multi-objective time series search problem and presents deterministic algorithms with best possible competitive ratios.

## References

SHOWING 1-10 OF 24 REFERENCES

Approximation of Pareto Optima in Multiple-Objective, Shortest-Path Problems

- Computer Science, MathematicsOper. Res.
- 1987

It is shown how approximation methods may be applied to yield fully polynomial approximation schemes for a variety of NP-complete, single-objective problems.

Approximating Multiobjective Knapsack Problems

- Computer ScienceManag. Sci.
- 2002

The first known polynomial-time approximation scheme (PTAS), based on linear programming, is presented and is based on a new approach to the single-objective knapsack problem using a partition of the profit space into intervals of exponentially increasing length.

On the approximate tradeoff for bicriteria batching and parallel machine scheduling problems

- Computer ScienceTheor. Comput. Sci.
- 2003

On the approximability of trade-offs and optimal access of Web sources

- Economics, Computer ScienceProceedings 41st Annual Symposium on Foundations of Computer Science
- 2000

These concepts and techniques are applied to formulate and solve approximately a cost-time-quality trade-off for optimizing access to the World-Wide Web, in a model first studied by Etzioni et al. (1996).

(Non)-Approximability for the Multi-criteria TSP(1, 2)

- Computer ScienceFCT
- 2005

A new way of proving non-approximability results which relies on the existence of a small size good approximating set, which holds even in the unlikely event of P=NP is provided.

Implementing an efficient fptas for the 0-1 multi-objective knapsack problem

- Computer ScienceEur. J. Oper. Res.
- 2009

Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming

- Computer ScienceJACM
- 1995

This algorithm gives the first substantial progress in approximating MAX CUT in nearly twenty years, and represents the first use of semidefinite programming in the design of approximation algorithms.

Multiobjective Optimization: Improved FPTAS for Shortest Paths and Non-Linear Objectives with Applications

- Computer ScienceTheory of Computing Systems
- 2007

A new generic method for obtaining FPTAS to any multiobjective optimization problem with non-linear objectives and how these results can be used to obtain better approximate solutions to three related problems, multiobjectives constrained [optimal] path and non-additive shortest path.

On Approximating Multi-Criteria TSP

- Computer ScienceSTACS
- 2009

We present approximation algorithms for almost all variants of the multi-criteria traveling salesman problem (TSP), whose performances are independent of the number $k$ of criteria and come close to…

Some Considerations about Computational Complexity for Multi Objective Combinatorial Problems

- Mathematics
- 1987

In the field of vector (or multi objective) optimization there has been a relatively little interest in solving combinatorial or discrete problems. During the 70’s just a few papers have been…