Fuzzy Bi-level Decision-Making Techniques: A Survey

© 2016 the authors. Bi-level decision-making techniques aim to deal with decentralized management problems that feature interactive decision entities distributed throughout a bi-level hierarchy. A challenge in handling bi-level decision problems is that various uncertainties naturally appear in decision-making process. Significant efforts have been devoted that fuzzy set techniques can be used to effectively deal with uncertain issues in bi-level decision-making, known as fuzzy bi-level decision-making techniques, and researchers have successfully gained experience in this area. It is thus vital that an instructive review of current trends in this area should be conducted, not only of the theoretical research but also the practical developments. This paper systematically reviews up-to-date fuzzy bi-level decisionmaking techniques, including models, approaches, algorithms and systems. It also clusters related technique developments into four main categories: basic fuzzy bi-level decision-making, fuzzy bi-level decision-making with multiple optima, fuzzy random bi-level decision-making, and the applications of bi-level decision-making techniques in different domains. By providing state-of-the-art knowledge, this survey paper will directly support researchers and practitioners in their understanding of developments in theoretical research results and applications in relation to fuzzy bi-level decision-making techniques

An Evolutionary Algorithm Using Duality-Base-Enumerating Scheme for Interval Linear Bilevel Programming Problems

Interval bilevel programming problem is hard to solve due to its hierarchical structure as well as the uncertainty of coefficients. This paper is focused on a class of interval linear bilevel programming problems, and an evolutionary algorithm based on duality bases is proposed. Firstly, the objective coefficients of the lower level and the right-hand-side vector are uniformly encoded as individuals, and the relative intervals are taken as the search space. Secondly, for each encoded individual, based on the duality theorem, the original problem is transformed into a single level program simply involving one nonlinear equality constraint. Further, by enumerating duality bases, this nonlinear equality is deleted, and the single level program is converted into several linear programs. Finally, each individual can be evaluated by solving these linear programs. The computational results of 7 examples show that the algorithm is feasible and robust

An algorithm for solving rule sets-based bilevel decision problems

Bilevel decision addresses the problem in which two levels of decision makers each tries to optimize their individual objectives under certain constraints, and to act and react in an uncooperative and sequential manner. Given the difficulty of formulating a bilevel decision problem by mathematical functions, a rule sets-based bilevel decision (RSBLD) model was proposed. This article presents an algorithm to solve a RSBLD problem. A case-based example is given to illustrate the functions of the proposed algorithm. Finally, a set of experiments is analyzed to further show the functions and the effectiveness of the proposed algorithm. © 2011 Wiley Periodicals, Inc

Fuzzy Random Noncooperative Two-level Linear Programming through Absolute Deviation Minimization Using Possibility and Necessity

This paper considers fuzzy random two-level linear programming problems under noncooperative behaviorof the decision makers. Having introduced fuzzy goals of decision makers together with the possibiliy and necessity measure, following absolute deviation minimization, fuzzy random two-level programin problems are transformed into deterministic ones. Extended Stackelberg solutions are introduced andcomputational methods are also presented

A compromise-based particle swarm optimization algorithm for solving Bi-level programming problems with fuzzy parameters

© 2015 IEEE. Bi-level programming has arisen to handle decentralized decision-making problems that feature interactive decision entities distributed throughout a bi-level hierarchy. Fuzzy parameters often appear in such a problem in applications and this is called a fuzzy bi-level programming problem. Since the existing approaches lack universality in solving such problems, this study aims to develop a particle swarm optimization (PSO) algorithm to solve fuzzy bi-level programming problems in the linear and nonlinear versions. In this paper, we first present a general fuzzy bi-level programming problem and discuss related theoretical properties based on a fuzzy number ranking method commonly used. A PSO algorithm is then developed to solve the fuzzy bi-level programming problem based on different compromised selections by decision entities on the feasible degree for constraint conditions under fuzziness. Lastly, an illustrative numerical example and two benchmark examples are adopted to state the effectiveness of the compromise-based PSO algorithm

On SOCP-based disjunctive cuts for solving a class of integer bilevel nonlinear programs

We study a class of integer bilevel programs with second-order cone constraints at the upper-level and a convex-quadratic objective function and linear constraints at the lower-level. We develop disjunctive cuts (DCs) to separate bilevel-infeasible solutions using a second-order-cone-based cut-generating procedure. We propose DC separation strategies and consider several approaches for removing redundant disjunctions and normalization. Using these DCs, we propose a branch-and-cut algorithm for the problem class we study, and a cutting-plane method for the problem variant with only binary variables. We present an extensive computational study on a diverse set of instances, including instances with binary and with integer variables, and instances with a single and with multiple linking constraints. Our computational study demonstrates that the proposed enhancements of our solution approaches are effective for improving the performance. Moreover, both of our approaches outperform a state-of-the-art generic solver for mixed-integer bilevel linear programs that is able to solve a linearized version of our binary instances.Comment: arXiv admin note: substantial text overlap with arXiv:2111.0682

Fuzzy multi-objective bilevel decision making by an approximation Kth-best approach

Many industrial decisions problems are decentralized in which decision makers are arranged at two levels, called bilevel decision problems. Bilevel decision making may involve uncertain parameters which appear either in the objective functions or constraints of the leader or the follower or both. Furthermore, the leader and the follower may have multiple conflict decision objectives that should be optimized simultaneously. This study proposes an approximation K th-best approach to solve the fuzzy multi-objective bilevel problem. Two case based examples further illustrate how to use the approach to solve industrial decision problems