Solving tri-level programming problems using a particle swarm optimization algorithm

© 2015 IEEE. Tri-level programming, a special case of multilevel programming, arises to deal with decentralized decision-making problems that feature interacting decision entities distributed throughout three hierarchical levels. As tri-level programming problems are strongly NP-hard and the existing solution approaches lack universality in solving such problems, the purpose of this study is to propose an intelligence-based heuristic algorithm to solve tri-level programming problems involving linear and nonlinear versions. In this paper, we first propose a general tri-level programming problem and discuss related theoretical properties. A particle swarm optimization (PSO) algorithm is then developed to solve the tri-level programming problem. Lastly, a numerical example is adopted to illustrate the effectiveness of the proposed PSO algorithm

Particle Swarm Optimized Autonomous Learning Fuzzy System

The antecedent and consequent parts of a first-order evolving intelligent system (EIS) determine the validity of the learning results and overall system performance. Nonetheless, the state-of-the-art techniques mostly stress on the novelty from the system identification point of view but pay less attention to the optimality of the learned parameters. Using the recently introduced autonomous learning multiple model (ALMMo) system as the implementation basis, this paper introduces a particles warm-based approach for EIS optimization. The proposed approach is able to simultaneously optimize the antecedent and consequent parameters of ALMMo and effectively enhance the system performance by iteratively searching for optimal solutions in the problem spaces. In addition, the proposed optimization approach does not adversely influence the “one pass” learning ability of ALMMo. Once the optimization process is complete, ALMMo can continue to learn from new data to incorporate unseen data patterns recursively without a full retraining. Experimental studies with a number of real-world benchmark problems validate the proposed concept and general principles. It is also verified that the proposed optimization approach can be applied to other types of EISs with similar operating mechanisms