New upper bounds in Klee's measure problem
SIAM Journal on Computing
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
Genetic diversity as an objective in multi-objective evolutionary algorithms
Evolutionary Computation
Muiltiobjective optimization using nondominated sorting in genetic algorithms
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
IEEE Transactions on Evolutionary Computation
Hype: An algorithm for fast hypervolume-based many-objective optimization
Evolutionary Computation
A faster algorithm for calculating hypervolume
IEEE Transactions on Evolutionary Computation
A review of multiobjective test problems and a scalable test problem toolkit
IEEE Transactions on Evolutionary Computation
Defining and optimizing indicator-based diversity measures in multiobjective search
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
Effects of the existence of highly correlated objectives on the behavior of MOEA/D
EMO'11 Proceedings of the 6th international conference on Evolutionary multi-criterion optimization
A concentration-based artificial immune network for multi-objective optimization
EMO'11 Proceedings of the 6th international conference on Evolutionary multi-criterion optimization
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Engineering Applications of Artificial Intelligence
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Multiobjective optimization in general aims at learning about the problem at hand. Usually the focus lies on objective space properties such as the front shape and the distribution of optimal solutions. However, structural characteristics in the decision space can also provide valuable insights. In certain applications, it may even be more important to find a structurally diverse set of close-to-optimal solutions than to identify a set of optimal but structurally similar solutions. Accordingly, multiobjective optimizers are required that are capable of considering both the objective space quality of a Pareto-set approximation and its diversity in the decision space. Although NSGA, one of the first multiobjective evolutionary algorithms, explicitly considered decision space diversity, only a few other studies address that issue. It therefore is an open research question how modern multiobjective evolutionary algorithms can be adapted to search for structurally diverse high-quality Pareto-set approximations. To this end we propose an approach to integrate decision space diversity into hypervolume-based multiobjective search. We present a modified hypervolume indicator and integrate it into an evolutionary algorithm. The proof-of-principle results show the potential of the approach and indicate further research directions for structure-oriented multiobjective search.