Finite Markov chain results in evolutionary computation: a tour d'horizon
Fundamenta Informaticae
Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Combining convergence and diversity in evolutionary multiobjective optimization
Evolutionary Computation
Fuzzy Recombination for the Breeder Genetic Algorithm
Proceedings of the 6th International Conference on Genetic Algorithms
Exploiting gradient information in numerical multi--objective evolutionary optimization
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy
Evolutionary Computation
Multicriteria Optimization
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Convergence of stochastic search algorithms to gap-free pareto front approximations
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Convergence of stochastic search algorithms to finite size pareto set approximations
Journal of Global Optimization
A new approach for online multiobjective optimization of mechatronic systems
International Journal on Software Tools for Technology Transfer (STTT)
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Capabilities of EMOA to detect and preserve equivalent pareto subsets
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
Approximating the Ɛ-efficient set of an MOP with stochastic search algorithms
MICAI'07 Proceedings of the artificial intelligence 6th Mexican international conference on Advances in artificial intelligence
Local convergence rates of simple evolutionary algorithms withCauchy mutations
IEEE Transactions on Evolutionary Computation
Properties of an adaptive archiving algorithm for storing nondominated vectors
IEEE Transactions on Evolutionary Computation
Performance assessment of multiobjective optimizers: an analysis and review
IEEE Transactions on Evolutionary Computation
New challenges for memetic algorithms on continuous multi-objective problems
Proceedings of the 12th annual conference companion on Genetic and evolutionary computation
Some comments on GD and IGD and relations to the Hausdorff distance
Proceedings of the 12th annual conference companion on Genetic and evolutionary computation
Using gradient information for multi-objective problems in the evolutionary context
Proceedings of the 12th annual conference companion on Genetic and evolutionary computation
Convergence of set-based multi-objective optimization, indicators and deteriorative cycles
Theoretical Computer Science
A fast approximation-guided evolutionary multi-objective algorithm
Proceedings of the 15th annual conference on Genetic and evolutionary computation
Multi Agent Collaborative Search based on Tchebycheff decomposition
Computational Optimization and Applications
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Recently, a convergence proof of stochastic search algorithms toward finite size Pareto set approximations of continuous multi-objective optimization problems has been given. The focus was on obtaining a finite approximation that captures the entire solution set in some suitable sense, which was defined by the concept of ε-dominance. Though bounds on the quality of the limit approximation---which are entirely determined by the archiving strategy and the value of ε---have been obtained, the strategies do not guarantee to obtain a gap free approximation of the Pareto front. That is, such approximations A can reveal gaps in the sense that points f in the Pareto front can exist such that the distance of f to any image point F(a), a ∈ A, is “large.” Since such gap free approximations are desirable in certain applications, and the related archiving strategies can be advantageous when memetic strategies are included in the search process, we are aiming in this work for such methods. We present two novel strategies that accomplish this task in the probabilistic sense and under mild assumptions on the stochastic search algorithm. In addition to the convergence proofs, we give some numerical results to visualize the behavior of the different archiving strategies. Finally, we demonstrate the potential for a possible hybridization of a given stochastic search algorithm with a particular local search strategy---multi-objective continuation methods---by showing that the concept of ε-dominance can be integrated into this approach in a suitable way.