Unified representation of proper efficiency by means of dilating cones
Journal of Optimization Theory and Applications
Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Constrained Test Problems for Multi-objective Evolutionary Optimization
EMO '01 Proceedings of the First International Conference on Evolutionary Multi-Criterion Optimization
In Search of Proper Pareto-optimal Solutions Using Multi-objective Evolutionary Algorithms
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part IV: ICCS 2007
Consideration of Partial User Preferences in Evolutionary Multiobjective Optimization
Multiobjective Optimization
On the Effect of the Steady-State Selection Scheme in Multi-Objective Genetic Algorithms
EMO '09 Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization
Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II
IEEE Transactions on Evolutionary Computation
A framework for incorporating trade-off information using multi-objective evolutionary algorithms
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part II
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
A review of multiobjective test problems and a scalable test problem toolkit
IEEE Transactions on Evolutionary Computation
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In recent years, multi-objective evolutionary algorithms have diversified their goal from finding an approximation of the complete efficient front of a multi-objective optimization problem, to integration of user preferences. These user preferences can be used to focus on a preferred region of the efficient front. Many such user preferences come from so called proper Pareto-optimality notions. Although, starting with the seminal work of Kuhn and Tucker in 1951, proper Pareto-optimal solutions have been around in the multi-criteria decision making literature, there are (surprisingly) very few studies in the evolutionary domain on this. In this paper, we introduce new ranking schemes of various state-of-the-art multi-objective evolutionary algorithms to focus on a preferred region corresponding to proper Pareto-optimal solutions. The algorithms based on these new ranking schemes are successfully tested on extensive benchmark test problems of varying complexity, with the aim to find the preferred region of the efficient front. This comprehensive study adequately demonstrates the efficiency of the developed multi-objective evolutionary algorithms in finding the complete preferred region for a large class of complex problems.