Fuzzy bilevel programming with multiple objectives and cooperative multiple followers

• Published in: Journal of global optimization Vol. 47; no. 3; pp. 403 - 419
• Main Authors: Zhang, Guangquan, Lu, Jie
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.07.2010; Springer Nature B.V
• Subjects: Algorithms; Approximation; Computer Science; Decision making; Fuzzy sets; Mathematics; Mathematics and Statistics; Objectives; Operations Research/Decision Theory; Optimization; Real Functions; Studies; Fuzzy sets; Bilevel programming; Multi-follower bilevel programming; Multi-objective decision making; th-best algorithm; Optimization
• ISSN: 0925-5001; 1573-2916
• DOI: 10.1007/s10898-008-9365-z

Classic bilevel programming deals with two level hierarchical optimization problems in which the leader attempts to optimize his/her objective, subject to a set of constraints and his/her follower’s solution. In modelling a real-world bilevel decision problem, some uncertain coefficients often appear in the objective functions and/or constraints of the leader and/or the follower. Also, the leader and the follower may have multiple conflicting objectives that should be optimized simultaneously. Furthermore, multiple followers may be involved in a decision problem and work cooperatively according to each of the possible decisions made by the leader, but with different objectives and/or constraints. Following our previous work, this study proposes a set of models to describe such fuzzy multi-objective, multi-follower (cooperative) bilevel programming problems. We then develop an approximation K th-best algorithm to solve the problems.