Efficient solution concepts and their application in uncertain multiobjective programming

[Display omitted] •The model of uncertain multiobjective programming based on uncertainty theory is originally presented, and six concepts of efficient solutions are defined.•The relations among the efficiency concepts are established under the assumed conditions.•We apply the uncertain multiobjecti...

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Bibliographic Details
Published in:Applied soft computing Vol. 56; pp. 557 - 569
Main Authors: Zheng, Mingfa, Yi, Yuan, Wang, Zutong, Liao, Tianjun
Format: Journal Article
Language:English
Published: Elsevier B.V 01.07.2017
Subjects:
Pareto efficiency
Redundancy allocation problem
Uncertain multiobjective programming
Uncertainty theory
Redundancy allocation problem
Uncertain multiobjective programming
Pareto efficiency
Uncertainty theory
ISSN:1568-4946, 1872-9681
Online Access:Get full text
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Summary:[Display omitted] •The model of uncertain multiobjective programming based on uncertainty theory is originally presented, and six concepts of efficient solutions are defined.•The relations among the efficiency concepts are established under the assumed conditions.•We apply the uncertain multiobjective optimization methods to a real-life problem, i.e., the uncertain multiobjective redundancy allocation problem.•A modified multiobjective artificial bee colony (MOABC) algorithm is designed to generate Pareto efficient set to the UMRA problem. Based on uncertainty theory, we investigate the relations among efficiency concepts of the multiobjective programming (MOP) with uncertain vectors. We first propose the uncertain MOP model, and study its convexity. Then, we define different efficiency concepts such as expected-value efficiency, expected-value proper efficiency, and establish their relations under the assumed conditions, which are illustrated through two numerical examples. Finally, in the uncertain environment, we apply the theoretical results to a redundancy allocation problem with two objectives in reparable parallel-series systems, and discuss how to obtain different types of efficient solutions according to the decision-maker's preferences.
ISSN:1568-4946
1872-9681
DOI:10.1016/j.asoc.2016.07.021