Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Evolutionary Algorithms for Solving Multi-Objective Problems
Evolutionary Algorithms for Solving Multi-Objective Problems
Multiple Objective Optimization with Vector Evaluated Genetic Algorithms
Proceedings of the 1st International Conference on Genetic Algorithms
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
Reference point based multi-objective optimization using evolutionary algorithms
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Epsilon-constraint with an efficient cultured differential evolution
Proceedings of the 9th annual conference companion on Genetic and evolutionary computation
Alternative techniques to solve hard multi-objective optimization problems
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Proceedings of the 9th annual conference on Genetic and evolutionary computation
A robust evolutionary framework for multi-objective optimization
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Introduction to Multiobjective Optimization: Noninteractive Approaches
Multiobjective Optimization
An Evolutionary Algorithm to Estimate the Nadir Point in MOLP
EMO '09 Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization
A Hybrid Integrated Multi-Objective Optimization Procedure for Estimating Nadir Point
EMO '09 Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization
Robust multi-objective optimization in high dimensional spaces
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
On set-based multiobjective optimization
IEEE Transactions on Evolutionary Computation
IEEE Transactions on Evolutionary Computation
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Nadir point plays an important role in multi-objective optimization because of its importance in estimating the range of objective values corresponding to desired Pareto-optimal solutions and also in using many classical interactive optimization techniques. Since this point corresponds to the worst Pareto-optimal solution of each objective, the task of estimating the nadir point necessitates information about the whole Pareto optimal frontier and is reported to be a difficult task using classical means. In this paper, for the first time, we have proposed a couple of modifications to an existing evolutionary multi-objective optimization procedure to focus its search towards the extreme objective values front-wise. On up to 20-objective optimization problems, both proposed procedures are found to be capable of finding a near nadir point quickly and reliably. Simulation results are interesting and should encourage further studies and applications in estimating the nadir point, a process which should lead to a better interactive procedure of finding and arriving at a desired Pareto-optimal solution.