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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
Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study
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Evolutionary Multiobjective Optimization: Theoretical Advances and Applications (Advanced Information and Knowledge Processing)
Multiobjective Evolutionary Algorithms and Applications (Advanced Information and Knowledge Processing)
Reference point based multi-objective optimization using evolutionary algorithms
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Computers and Operations Research
Techniques for highly multiobjective optimisation: some nondominated points are better than others
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Behavior of Evolutionary Many-Objective Optimization
UKSIM '08 Proceedings of the Tenth International Conference on Computer Modeling and Simulation
A preference-based evolutionary algorithm for multi-objective optimization
Evolutionary Computation
Performance scaling of multi-objective evolutionary algorithms
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Controlling dominance area of solutions and its impact on the performance of MOEAs
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Robust multi-objective optimization in high dimensional spaces
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
Substitute distance assignments in NSGA-II for handling many-objective optimization problems
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
Pareto-, aggregation-, and indicator-based methods in many-objective optimization
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
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
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An EMO algorithm using the hypervolume measure as selection criterion
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
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A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
Performance assessment of multiobjective optimizers: an analysis and review
IEEE Transactions on Evolutionary Computation
MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition
IEEE Transactions on Evolutionary Computation
A New Evolutionary Algorithm for Solving Many-Objective Optimization Problems
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Proceedings of the 13th annual conference on Genetic and evolutionary computation
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This paper proposes an idea of approximating the hypervolume of a non-dominated solution set using a number of achievement scalarizing functions with uniformly distributed weight vectors. Each achievement scalarizing function with a different weight vector is used to measure the distance from the reference point of the hypervolume to the attainment surface of the non-dominated solution set along its own search direction specified by its weight vector. Our idea is to approximate the hypervolume by the average distance from the reference point to the attainment surface over a large number of uniformly distributed weight vectors (i.e., over various search directions). We examine the effect of the number of weight vectors (i.e., the number of search directions) on the approximation accuracy and the computation time of the proposed approach. As expected, experimental results show that the approximation accuracy is improved by increasing the number of weight vectors. It is also shown that the proposed approach needs much less computation time than the exact hypervolume calculation for a six-objective knapsack problem even when we use about 100,000 weight vectors.