Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers by Lotfi A. Zadeh
Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers by Lotfi A. Zadeh
Muiltiobjective optimization using nondominated sorting in genetic algorithms
Evolutionary Computation
GA-based solutions comparison for warehouse storage optimization
International Journal of Hybrid Intelligent Systems - Advances in Intelligent Agent Systems
Fuzzy linear multi-objective programming
ECCE'10/ECCIE'10/ECME'10/ECC'10 Proceedings of the European conference of chemical engineering, and European conference of civil engineering, and European conference of mechanical engineering, and European conference on Control
The use of possibility theory in the definition of fuzzy Pareto-optimality
Fuzzy Optimization and Decision Making
Fuzzy-Pareto-Dominance and its application in evolutionary multi-objective optimization
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
Genetic algorithms for estimating longest path from inherently fuzzy data acquired with GPS
IDEAL'06 Proceedings of the 7th international conference on Intelligent Data Engineering and Automated Learning
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Pareto optimality is someway ineffective for optimization problems with several (more than three) objectives. In fact the Pareto optimal set tends to become a wide portion of the whole design domain search space with the increasing of the numbers of objectives. Consequently, little or no help is given to the human decision maker. Here we use fuzzy logic to give two new definitions of optimality that extend the notion of Pareto optimality. Our aim is to identify, inside the set of Pareto optimal solutions, different "degrees of optimality" such that only a few solutions have the highest degree of optimality; even in problems with a big number of objectives. Then we demonstrate (on simple analytical test cases) the coherence of these definitions and their reduction to Pareto optimality in some special subcases. At last we introduce a first extension of (1+1)ES mutation operator able to approximate the set of solutions with a given degree of optimality, and test it on analytical test cases.