Randomized algorithms
Combining convergence and diversity in evolutionary multiobjective optimization
Evolutionary Computation
Evolutionary Search for Minimal Elements in Partially Ordered Finite Sets
EP '98 Proceedings of the 7th International Conference on Evolutionary Programming VII
Monotonic solution concepts in coevolution
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
Covariance Matrix Adaptation for Multi-objective Optimization
Evolutionary Computation
Convergence of stochastic search algorithms to finite size pareto set approximations
Journal of Global Optimization
Monotonicity versus performance in co-optimization
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
On the effects of adding objectives to plateau functions
IEEE Transactions on Evolutionary Computation
Computing gap free pareto front approximations with stochastic search algorithms
Evolutionary Computation
EMO'07 Proceedings of the 4th international conference on Evolutionary multi-criterion optimization
Approximating the volume of unions and intersections of high-dimensional geometric objects
Computational Geometry: Theory and Applications
On set-based multiobjective optimization
IEEE Transactions on Evolutionary Computation
Set-based multi-objective optimization, indicators, and deteriorative cycles
Proceedings of the 12th annual conference on Genetic and evolutionary computation
The maximum hypervolume set yields near-optimal approximation
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Convergence rates of (1+1) evolutionary multiobjective optimization algorithms
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
Tight bounds for the approximation ratio of the hypervolume indicator
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
Bioinspired Computation in Combinatorial Optimization: Algorithms and Their Computational Complexity
Bioinspired Computation in Combinatorial Optimization: Algorithms and Their Computational Complexity
On the effect of populations in evolutionary multi-objective optimisation**
Evolutionary Computation
Theory of Randomized Search Heuristics: Foundations and Recent Developments
Theory of Randomized Search Heuristics: Foundations and Recent Developments
Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach
IEEE Transactions on Evolutionary Computation
IEEE Transactions on Evolutionary Computation
A fast and elitist multiobjective genetic algorithm: NSGA-II
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
Population size matters: rigorous runtime results for maximizing the hypervolume indicator
Proceedings of the 15th annual conference on Genetic and evolutionary computation
A note on the ε-indicator subset selection
Theoretical Computer Science
Information Sciences: an International Journal
Hi-index | 5.23 |
Multi-objective optimization deals with the task of computing a set of solutions that represents possible trade-offs with respect to a given set of objective functions. Set-based approaches such as evolutionary algorithms are very popular for solving multi-objective optimization problems. Convergence of set-based approaches for multi-objective optimization is essential for their success. We take an order-theoretic view on the convergence of set-based multi-objective optimization and examine how the use of indicator functions can help to direct the search towards Pareto optimal sets. In doing so, we point out that set-based multi-objective optimization working on the dominance relation of search points has to deal with a cyclic behavior that may lead to worsening with respect to the Pareto-dominance relation defined on sets. Later on, we show in which situations well-known binary and unary indicators can help to avoid this cyclic behavior and therefore guarantee convergence of the algorithm. We also study the impact of deteriorative cycles on the runtime behavior and give an example in which they provably slow down the optimization process.