Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Combining convergence and diversity in evolutionary multiobjective optimization
Evolutionary Computation
An Investigation of Niche and Species Formation in Genetic Function Optimization
Proceedings of the 3rd International Conference on Genetic Algorithms
The Pareto Envelope-Based Selection Algorithm for Multi-objective Optimisation
PPSN VI Proceedings of the 6th International Conference on Parallel Problem Solving from Nature
Towards estimating nadir objective vector using evolutionary approaches
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation)
Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation)
Techniques for highly multiobjective optimisation: some nondominated points are better than others
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Multi-objective genetic algorithms: Problem difficulties and construction of test problems
Evolutionary Computation
Objective reduction using a feature selection technique
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
Multiobjective Optimization: Interactive and Evolutionary Approaches
Multiobjective Optimization: Interactive and Evolutionary Approaches
A Hybrid Integrated Multi-Objective Optimization Procedure for Estimating Nadir Point
EMO '09 Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization
A preference-based evolutionary algorithm for multi-objective optimization
Evolutionary Computation
Performance scaling of multi-objective evolutionary algorithms
EMO'03 Proceedings of the 2nd international conference on Evolutionary multi-criterion optimization
I-MODE: an interactive multi-objective optimization and decision-making using evolutionary methods
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
A taxonomy of online stopping criteria for multi-objective evolutionary algorithms
EMO'11 Proceedings of the 6th international conference on Evolutionary multi-criterion optimization
A preference based interactive evolutionary algorithm for multi-objective optimization: PIE
EMO'11 Proceedings of the 6th international conference on Evolutionary multi-criterion optimization
ADT'11 Proceedings of the Second international conference on Algorithmic decision theory
Advances in differential evolution for solving multiobjective optimization problems
ICSI'12 Proceedings of the Third international conference on Advances in Swarm Intelligence - Volume Part I
On finding well-spread pareto optimal solutions by preference-inspired co-evolutionary algorithm
Proceedings of the 15th annual conference on Genetic and evolutionary computation
Comprehensive Survey of the Hybrid Evolutionary Algorithms
International Journal of Applied Evolutionary Computation
General framework for localised multi-objective evolutionary algorithms
Information Sciences: an International Journal
Expert Systems with Applications: An International Journal
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A nadir objective vector is constructed from the worst Pareto-optimal objective values in a multiobjective optimization problem and is an important entity to compute because of its significance in estimating the range of objective values in the Pareto-optimal front and also in executing a number of interactive multiobjective optimization techniques. Along with the ideal objective vector, it is also needed for the purpose of normalizing different objectives, so as to facilitate a comparison and agglomeration of the objectives. However, the task of estimating the nadir objective vector necessitates information about the complete Pareto-optimal front and has been reported to be a difficult task, and importantly an unsolved and open research issue. In this paper, we propose certain modifications to an existing evolutionary multiobjective optimization procedure to focus its search toward the extreme objective values and combine it with a reference-point based local search approach to constitute a couple of hybrid procedures for a reliable estimation of the nadir objective vector. With up to 20-objective optimization test problems and on a three-objective engineering design optimization problem, one of the proposed procedures is found to be capable of finding the nadir objective vector reliably. The study clearly shows the significance of an evolutionary computing based search procedure in assisting to solve an age-old important task in the field of multiobjective optimization.