A hybrid system for multiobjective problems  A case study in NP-hard problems
In attempt to solve multiobjective problems, various mathematical and stochastic methods have been developed. The methods operate based on mathematical models while in most cases these models are drastically simplified imagine of real world problems. In this study, a hybrid intelligent system is used instead of mathematical models. The main core of the system is fuzzy rule base which maps decision space (Z) to solution space (X). The system is designed on noninferior region and gives a big picture of this region in the pattern of fuzzy rules. Since some solutions may be infeasible; then specified feedforward neural network is used to obtain noninferior solutions in an exterior movement. In addition, numerical examples of well-known NP-hard problems (i.e. multiobjective traveling salesman problem and multiobjective knapsack problem) are provided to clarify the accuracy of developed system.
hybrid systems np-hard problems neural networks multiobjective decision making fuzzy inferencing methods