# A decision-theoretic approach to robust optimization in multivalued graphs

@article{Perny2006ADA, title={A decision-theoretic approach to robust optimization in multivalued graphs}, author={Patrice Perny and Olivier Spanjaard and Louis-Xavier Storme}, journal={Annals of Operations Research}, year={2006}, volume={147}, pages={317-341} }

This paper is devoted to the search of robust solutions in finite graphs when costs depend on scenarios. We first point out similarities between robust optimization and multiobjective optimization. Then, we present axiomatic requirements for preference compatibility with the intuitive idea of robustness in a multiple scenarios decision context. This leads us to propose the Lorenz dominance rule as a basis for robustness analysis. Then, after presenting complexity results about the determination…

## 54 Citations

### Anytime Algorithms for Adaptive Robust Optimization with OWA and WOWA

- Computer ScienceADT
- 2017

This approach consists in interleaving adaptive preference elicitation methods aiming to assess the attitude of the Decision Maker towards robustness or risk with combinatorial optimization algorithms aiming to determine a robust solution.

### Choquet-based optimisation in multiobjective shortest path and spanning tree problems

- Computer Science, BusinessEur. J. Oper. Res.
- 2010

### Lexicographic α-robustness: an application to the 1-median problem

- Mathematics, EconomicsRAIRO Oper. Res.
- 2010

A new robustness approach is presented, called lexicographic α-robustness, which compensates for the drawbacks of criteria based on the worst case, which is applied to the 1-median location problem under uncertainty on node weights and can be extended to the case of a general network.

### Exact algorithms for OWA-optimization in multiobjective spanning tree problems

- Computer ScienceComput. Oper. Res.
- 2012

### Decision making with multiple objectives using GAI networks

- Computer Science, EconomicsArtif. Intell.
- 2011

### Lorenz dominance based algorithms to solve a practical multiobjective problem

- EconomicsComput. Oper. Res.
- 2019

### Multiagent Fair Optimization with Lorenz Dominance

- Economics, Computer ScienceAAMAS
- 2015

This work considers the adaptation of the well-known two-phase method proposed in biobjective optimization to the bi-agent optimization case, where one wants to directly compute the Lorenz efficient solutions.

### Multiagent Fair Optimization with Lorenz Dominance (Extended Abstract)

- Computer Science, Economics
- 2015

The adaptation of the well-known two-phase method proposed in biobjective optimization to the bi-agent optimization case, where one wants to directly compute the Lorenz ecient solutions, is considered.

### Lorenz versus Pareto Dominance in a Single Machine Scheduling Problem with Rejection

- BusinessEMO
- 2011

This paper addresses the problem of single machine scheduling in which due to some constraints like capacity, rejection of a set of jobs is accepted, and suggests the application of Lorenz-dominance to an adapted bi-objective simulated annealing algorithm.

### Exact Methods for Computing All Lorenz Optimal Solutions to Biobjective Problems

- Computer Science, EconomicsADT
- 2015

It is shown that some properties of the Lorenz dominance can provide a more efficient variant of the two-phase method and is compared to state-of-the-art methods on various biobjective combinatorial optimization problems and shows that the new method is more efficient in a majority of cases.

## References

SHOWING 1-10 OF 52 REFERENCES

### An Axiomatic Approach to Robustness in Search Problems with Multiple Scenarios

- Computer Science, EconomicsUAI
- 2003

The Lorenz dominance rule is proposed as a basis for robustness analysis and a new sophistication of A* specially designed to determine the set of robust paths in a state space graph is proposed.

### Robustness and Efficiency : A Study of the Relationship and an Algorithm for the Bicriteria Discrete Optimization Problem

- Computer Science, Mathematics
- 2002

An algorithm that relies on a parametric search to identify all of the efficient solutions of a bicriteria discrete optimization problem and a modification of the algorithm that generates a sample of efficient solutions within the coverage error specified by the Decision Maker are proposed.

### Selecting preferred solutions in the minimax approach to dynamic programming problems under flexible constraints

- Computer ScienceEur. J. Oper. Res.
- 2005

### Multiobjective A*

- Computer ScienceJACM
- 1991

A multiobjective generalization of the heuristic search algorithm A* is presented and it is shown that &fOA * is complete and, when used with a suitably defined set of admissible heuristic functions, admissible.

### Solving min‐max shortest‐path problems on a network

- Computer Science, Mathematics
- 1992

This article presents a label-correcting procedure for determining a path between two nodes in a network that minimizes the maximum of r path length values associated with it and develops two pruning techniques, which are able to speed up the label-Correcting procedure by many orders of magnitude.

### On spanning tree problems with multiple objectives

- Mathematics, Computer ScienceAnn. Oper. Res.
- 1994

This work investigates two versions of multiple objective minimum spanning tree problems defined on a network with vectorial weights and uses neighbourhood search to determine a sequence of solutions with the property that the distance between two consecutive solutions is less than a given accuracy.

### An exact algorithm for the robust shortest path problem with interval data

- Computer ScienceComput. Oper. Res.
- 2004