A robust augmented ε-constraint method (AUGMECON-R) for finding exact solutions of multi-objective linear programming problems

Systems can be unstructured, uncertain and complex, and their optimisation often requires operational research techniques. In this study, we introduce AUGMECON-R, a robust variant of the augmented ε-constraint algorithm, for solving multi-objective linear programming problems, by drawing from the we...

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Vydané v:Operational research Ročník 22; číslo 2; s. 1291 - 1332
Hlavní autori: Nikas, Alexandros, Fountoulakis, Angelos, Forouli, Aikaterini, Doukas, Haris
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2022
Springer Nature B.V
Predmet:
Algorithms
Business and Management
Computational Intelligence
Exact solutions
Linear programming
Lower bounds
Management Science
Operations Research
Operations Research/Decision Theory
Optimization
Original Paper
Robustness
Pareto
ε-constraint
Multi-objective programming
Optimisation
Augmecon
ISSN:1109-2858, 1866-1505
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Shrnutí:Systems can be unstructured, uncertain and complex, and their optimisation often requires operational research techniques. In this study, we introduce AUGMECON-R, a robust variant of the augmented ε-constraint algorithm, for solving multi-objective linear programming problems, by drawing from the weaknesses of AUGMECON 2, one of the most widely used improvements of the ε-constraint method. These weaknesses can be summarised in the ineffective handling of the true nadir points of the objective functions and, most notably, in the significant amount of time required to apply it as more objective functions are added to a problem. We subsequently apply AUGMECON-R in comparison with its predecessor, in both a set of reference problems from the literature and a series of significantly more complex problems of four to six objective functions. Our findings suggest that the proposed method greatly outperforms its predecessor, by solving significantly less models in emphatically less time and allowing easy and timely solution of hard or practically impossible, in terms of time and processing requirements, problems of numerous objective functions. AUGMECON-R, furthermore, solves the limitation of unknown nadir points, by using very low or zero-value lower bounds without surging the time and resources required.
Bibliografia:ObjectType-Article-1
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ISSN:1109-2858
1866-1505
DOI:10.1007/s12351-020-00574-6