On the Average Number of Maxima in a Set of Vectors and Applications
Journal of the ACM (JACM)
An updated survey of GA-based multiobjective optimization techniques
ACM Computing Surveys (CSUR)
Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
On the Performance Assessment and Comparison of Stochastic Multiobjective Optimizers
PPSN IV Proceedings of the 4th International Conference on Parallel Problem Solving from Nature
Algorithms to identify pareto points in multi-dimensional data sets
Algorithms to identify pareto points in multi-dimensional data sets
Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy
Evolutionary Computation
Random Structures & Algorithms
Compressed-objective genetic algorithm
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
Performance assessment of multiobjective optimizers: an analysis and review
IEEE Transactions on Evolutionary Computation
A review of multiobjective test problems and a scalable test problem toolkit
IEEE Transactions on Evolutionary Computation
Distance Based Ranking in Many-Objective Particle Swarm Optimization
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
Online Objective Reduction to Deal with Many-Objective Problems
EMO '09 Proceedings of the 5th International Conference on Evolutionary Multi-Criterion Optimization
Study of preference relations in many-objective optimization
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
PEPPA: a project for evolutionary predator prey algorithms
Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers
Some techniques to deal with many-objective problems
Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers
A grid-based fitness strategy for evolutionary many-objective optimization
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Alternative fitness assignment methods for many-objective optimization problems
EA'09 Proceedings of the 9th international conference on Artificial evolution
IEEE Transactions on Evolutionary Computation - Special issue on preference-based multiobjective evolutionary algorithms
An interactive evolutionary multi-objective optimization method based on polyhedral cones
LION'10 Proceedings of the 4th international conference on Learning and intelligent optimization
Adaptive objective space partitioning using conflict information for many-objective optimization
EMO'11 Proceedings of the 6th international conference on Evolutionary multi-criterion optimization
Framework for many-objective test problems with both simple and complicated pareto-set shapes
EMO'11 Proceedings of the 6th international conference on Evolutionary multi-criterion optimization
A preference based interactive evolutionary algorithm for multi-objective optimization: PIE
EMO'11 Proceedings of the 6th international conference on Evolutionary multi-criterion optimization
A new multi-objective evolutionary algorithm based on a performance assessment indicator
Proceedings of the 14th annual conference on Genetic and evolutionary computation
A multi-objective artificial immune system based on hypervolume
ICARIS'12 Proceedings of the 11th international conference on Artificial Immune Systems
Advances in evolutionary multi-objective optimization
SSBSE'12 Proceedings of the 4th international conference on Search Based Software Engineering
Computers and Operations Research
Behavioral repertoire learning in robotics
Proceedings of the 15th annual conference on Genetic and evolutionary computation
Multi-criteria scheduling: an agent-based approach for expert knowledge integration
Journal of Scheduling
Objective space partitioning using conflict information for solving many-objective problems
Information Sciences: an International Journal
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The scalability of EMO algorithms is an issue of significant concern for both algorithm developers and users. A key aspect of the issue is scalability to objective space dimension, other things being equal. Here, we make some observations about the efficiency of search in discrete spaces as a function of the number of objectives, considering both uncorrelated and correlated objective values. Efficiency is expressed in terms of a cardinality-based (scaling-independent) performance indicator. Considering random sampling of the search space, we measure, empirically, the fraction of the true PF covered after p iterations, as the number of objectives grows, and for different correlations. A general analytical expression for the expected performance of random search is derived, and is shown to agree with the empirical results. We postulate that for even moderately large numbers of objectives, random search will be competitive with an EMO algorithm and show that this is the case empirically: on a function where each objective is relatively easy for an EA to optimize (an NK-landscape with K=2), random search compares favourably to a well-known EMO algorithm when objective space dimension is ten, for a range of inter-objective correlation values. The analytical methods presented here may be useful for benchmarking of other EMO algorithms.