On the properties of lexicographic tolerable robust solution sets for uncertain multi-objective optimization problems

This study provides the important properties of the lexicographic tolerable robust solution for uncertain multi-objective optimization problems which was introduced by Boriwan et al. [Boriwan, P.; Ehrgott, M.; Kuroiwa, D.; Petrot, N. The lexicographic tolerable robustness concept for uncertain multi-objective optimization problems: a study on water resources management. Sustainability. 12 (2020), no. 18, article number 7582.]. Also, the relationship between the lexicographic tolerable solution concept and the well-known robust solution, as the set-based robust efficiency [Ehrgott, M.; Ide, J.; Schöbel, A. Minmax robustness for multi-objective optimization problems. European Journal of Operational Research. 239 (2014), no. 1, 17-31.], are provided.

Download Full-text

On the properties of lexicographic tolerable robust solution sets for uncertain multi-objective optimization problems

Carpathian Journal of Mathematics ◽

10.37193/cjm.2021.03.05 ◽

2021 ◽

Vol 37 (3) ◽

pp. 417-426

Author(s):

PORNPIMON BORIWAN ◽

◽

DAISHI KUROIWA ◽

NARIN PETROT ◽

◽

...

Keyword(s):

Water Resources ◽

Water Resources Management ◽

Optimization Problems ◽

Solution Concept ◽

Multi Objective Optimization ◽

Robust Solution ◽

Solution Sets ◽

Resources Management ◽

Multi Objective ◽

The Relationship

This study provides the important properties of the lexicographic tolerable robust solution for uncertain multi-objective optimization problems which was introduced by Boriwan et al. [Boriwan, P.; Ehrgott, M.; Kuroiwa, D.; Petrot, N. The lexicographic tolerable robustness concept for uncertain multi-objective optimization problems: a study on water resources management. Sustainability. 12 (2020), no. 18, article number 7582.]. Also, the relationship between the lexicographic tolerable solution concept and the well-known robust solution, as the set-based robust efficiency [Ehrgott, M.; Ide, J.; Schöbel, A. Minmax robustness for multi-objective optimization problems. Eur. J. Oper. Res. 239 (2014), no. 1, 17–31.], are provided.

Download Full-text

The Lexicographic Tolerable Robustness Concept for Uncertain Multi-Objective Optimization Problems: A Study on Water Resources Management

Sustainability ◽

10.3390/su12187582 ◽

2020 ◽

Vol 12 (18) ◽

pp. 7582

Author(s):

Pornpimon Boriwan ◽

Matthias Ehrgott ◽

Daishi Kuroiwa ◽

Narin Petrot

Keyword(s):

Water Resources ◽

Optimization Problems ◽

Solution Concept ◽

Decision Makers ◽

Practical Implementation ◽

Multi Objective Optimization ◽

Robust Solution ◽

Resources Management ◽

Multi Objective ◽

Priority Levels

In this study, we introduce a robust solution concept for uncertain multi-objective optimization problems called the lexicographic tolerable robust solution. This approach is advantageous for the practical implementation of problems in which the solution should satisfy priority levels in the objective function and the worst performance vector of the solution obtained by the proposed concept is close to a reference point of the considered problem, within an acceptable tolerance threshold. Important properties of the solution sets of this introduced concept as well as an algorithm for finding such solutions are presented and discussed. We provide the implementation of the proposed lexicographic tolerable robust solution to improve understanding for practitioners by relying on the data of the water resources master plan for Serbia from Simonovic, 2009. Moreover, we are also concerned with the method of updating a desirable solution for fitting with the preferences when compromising of the multiple groups of decision makers is needed.

Download Full-text

A Study on Multi-level Robust Solution Search for Noisy Multi-objective Optimization Problems

Proceedings in Adaptation, Learning and Optimization - Proceedings of the 18th Asia Pacific Symposium on Intelligent and Evolutionary Systems - Volume 2 ◽

10.1007/978-3-319-13356-0_20 ◽

2015 ◽

pp. 239-253

Author(s):

Tomohisa Hashimoto ◽

Hiroyuki Sato

Keyword(s):

Optimization Problems ◽

Multi Objective Optimization ◽

Robust Solution ◽

Multi Objective ◽

Multi Level

Download Full-text

Pareto Set as a Model for Dispatching Resources in Emergency Centres (Preprint)

10.2196/preprints.10298 ◽

2018 ◽

Author(s):

Ricardo Guedes ◽

Vasco Furtado ◽

Tarcísio Pequeno ◽

Joel Rodrigues

Keyword(s):

Operational Research ◽

Real Data ◽

Pareto Set ◽

Multi Objective Optimization ◽

Pareto Dominance ◽

Four Dimensions ◽

Multi Objective ◽

The Best Approximation ◽

One Year ◽

The Cost

UNSTRUCTURED The article investigates policies for helping emergency-centre authorities for dispatching resources aimed at reducing goals such as response time, the number of unattended calls, the attending of priority calls, and the cost of displacement of vehicles. Pareto Set is shown to be the appropriated way to support the representation of policies of dispatch since it naturally fits the challenges of multi-objective optimization. By means of the concept of Pareto dominance a set with objectives may be ordered in a way that guides the dispatch of resources. Instead of manually trying to identify the best dispatching strategy, a multi-objective evolutionary algorithm coupled with an Emergency Call Simulator uncovers automatically the best approximation of the optimal Pareto Set that would be the responsible for indicating the importance of each objective and consequently the order of attendance of the calls. The scenario of validation is a big metropolis in Brazil using one-year of real data from 911 calls. Comparisons with traditional policies proposed in the literature are done as well as other innovative policies inspired from different domains as computer science and operational research. The results show that strategy of ranking the calls from a Pareto Set discovered by the evolutionary method is a good option because it has the second best (lowest) waiting time, serves almost 100% of priority calls, is the second most economical, and is the second in attendance of calls. That is to say, it is a strategy in which the four dimensions are considered without major impairment to any of them.

Download Full-text