Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study
PPSN V Proceedings of the 5th International Conference on Parallel Problem Solving from Nature
Comparison of Multiobjective Evolutionary Algorithms: Empirical Results
Evolutionary Computation
Covariance Matrix Adaptation for Multi-objective Optimization
Evolutionary Computation
Approximating the Volume of Unions and Intersections of High-Dimensional Geometric Objects
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Theory of the hypervolume indicator: optimal μ-distributions and the choice of the reference point
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
Investigating and exploiting the bias of the weighted hypervolume to articulate user preferences
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
The measure of Pareto optima applications to multi-objective metaheuristics
EMO'03 Proceedings of the 2nd international conference on Evolutionary multi-criterion optimization
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
A two-level evolutionary approach to multi-criterion optimization of water supply systems
EMO'05 Proceedings of the Third international conference on Evolutionary Multi-Criterion Optimization
Investigating and exploiting the bias of the weighted hypervolume to articulate user preferences
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Weighted preferences in evolutionary multi-objective optimization
AI'11 Proceedings of the 24th international conference on Advances in Artificial Intelligence
Expert Systems with Applications: An International Journal
GECCO 2012 tutorial on evolutionary multiobjective optimization
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
GECCO 2013 tutorial on evolutionary multiobjective optimization
Proceedings of the 15th annual conference companion on Genetic and evolutionary computation
Variable space diversity, crossover and mutation in MOEA solving many-objective knapsack problems
Annals of Mathematics and Artificial Intelligence
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The hypervolume indicator has become popular in recent years both for performance assessment and to guide the search of evolutionary multiobjective optimizers. Two critical research topics can be emphasized with respect to hypervolume-based search: (i) the hypervolume indicator inherently introduces a specific preference and the question is how arbitrary user preferences can be incorporated; (ii) the exact calculation of the hypervolume indicator is expensive and efficient approaches to tackle many-objective problems are needed. In two previous studies, we addressed both issues independently: a study proposed the weighted hypervolume indicator with which user-defined preferences can be articulated; other studies exist that propose to estimate the hypervolume indicator by Monte-Carlo sampling. Here, we combine these two approaches for the first time and extend them, i.e., we present an approach of sampling the weighted hypervolume to incorporate user-defined preferences into the search for problems with many objectives. In particular, we propose weight distribution functions to stress extreme solutions and to define preferred regions of the objective space in terms of so-called preference points; sampling them allows to tackle problems with many objectives. Experiments on several test functions with up to 25 objectives show the usefulness of the approach in terms of decision making and search.