A hybrid system for multiobjective problems – A case study in NP-hard problems |
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| Affiliation: | 1. Department of Finance and Management Science, Edwards School of Business, University of Saskatchewan, Saskatoon, Saskatchewan, S7N 5A7, Canada;2. Department of Mechanical and Industrial Engineering, Northeastern University, 334 Snell Engineering Center, 360 Huntington Avenue, Boston, MA 02115, United States;1. Department of Mathematics, Khalifa University, Abu Dhabi Campus, PO Box 127788, Abu Dhabi, United Arab Emirates;2. Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, United Kingdom;3. Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, and Center for Light-Matter Interaction, Tel Aviv University, Tel Aviv 69978, Israel;4. Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile |
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| Abstract: | 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. |
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