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

Stochastic Multilevel Programming with a Hybrid Intelligent Algorithm

A framework of stochastic multilevel programming is proposed for modelling decentralized decision-making problem in stochastic environment. According to different decision criteria, the stochastic decentralized decision-making problem is formulated as expected value multilevel programming, and chanceconstrained multilevel programming. In order to solve the proposed stochastic multilevel programming models for the Stackelberg-Nash equilibriums, genetic algorithms, neural networks and stochastic simulation are integrated to produce a hybrid intelligent algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the hybrid intelligent algorithm

A solution to bi/tri-level programming problems using particle swarm optimization

© 2016 Elsevier Inc. Multilevel (including bi-level and tri-level) programming aims to solve decentralized decision-making problems that feature interactive decision entities distributed throughout a hierarchical organization. Since the multilevel programming problem is strongly NP-hard and traditional exact algorithmic approaches lack efficiency, heuristics-based particle swarm optimization (PSO) algorithms have been used to generate an alternative for solving such problems. However, the existing PSO algorithms are limited to solving linear or small-scale bi-level programming problems. This paper first develops a novel bi-level PSO algorithm to solve general bi-level programs involving nonlinear and large-scale problems. It then proposes a tri-level PSO algorithm for handling tri-level programming problems that are more challenging than bi-level programs and have not been well solved by existing algorithms. For the sake of exploring the algorithms' performance, the proposed bi/tri-level PSO algorithms are applied to solve 62 benchmark problems and 810 large-scale problems which are randomly constructed. The computational results and comparison with other algorithms clearly illustrate the effectiveness of the proposed PSO algorithms in solving bi-level and tri-level programming problems

Fuzzy multilevel programming with a hybrid intelligent algorithm

AbstractIn order to model fuzzy decentralized decision-making problem, fuzzy expected value multilevel programming and chance-constrained multilevel programming are introduced. Furthermore, fuzzy simulation, neural network, and genetic algorithm are integrated to produce a hybrid intelligent algorithm for finding the Stackelberg-Nash equilibrium. Finally, two numerical examples are provided to illustrate the effectiveness of the hybrid intelligent algorithm

Toward an estimation of nadir objective vector using a hybrid of evolutionary and local search approaches

A nadir objective vector is constructed from the worst Pareto-optimal objective values in a multiobjective optimization problem and is an important entity to compute because of its significance in estimating the range of objective values in the Pareto-optimal front and also in executing a number of interactive multiobjective optimization techniques. Along with the ideal objective vector, it is also needed for the purpose of normalizing different objectives, so as to facilitate a comparison and agglomeration of the objectives. However, the task of estimating the nadir objective vector necessitates information about the complete Pareto-optimal front and has been reported to be a difficult task, and importantly an unsolved and open research issue. In this paper, we propose certain modifications to an existing evolutionary multiobjective optimization procedure to focus its search toward the extreme objective values and combine it with a reference-point based local search approach to constitute a couple of hybrid procedures for a reliable estimation of the nadir objective vector. With up to 20-objective optimization test problems and on a three-objective engineering design optimization problem, one of the proposed procedures is found to be capable of finding the nadir objective vector reliably. The study clearly shows the significance of an evolutionary computing based search procedure in assisting to solve an age-old important task in the field of multiobjective optimization