Mathematical Programming: Series A and B
Fitness landscapes and memetic algorithm design
New ideas in optimization
Foundations of genetic programming
Foundations of genetic programming
Representations for Genetic and Evolutionary Algorithms
Representations for Genetic and Evolutionary Algorithms
SIAM Review
Group properties of crossover and mutation
Evolutionary Computation
Formal Algorithms + Formal Representations = Search Strategies
PPSN IV Proceedings of the 4th International Conference on Parallel Problem Solving from Nature
Convex Optimization
Evolutionary Computation
EC theory: a unified viewpoint
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartII
No free lunch theorems for optimization
IEEE Transactions on Evolutionary Computation
How crossover helps in pseudo-boolean optimization
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Geometry of evolutionary algorithms
Proceedings of the 13th annual conference companion on Genetic and evolutionary computation
Runtime analysis of convex evolutionary search
Proceedings of the 14th annual conference on Genetic and evolutionary computation
Geometry of evolutionary algorithms
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
Geometric semantic genetic programming
PPSN'12 Proceedings of the 12th international conference on Parallel Problem Solving from Nature - Volume Part I
More effective crossover operators for the all-pairs shortest path problem
Theoretical Computer Science
Genetic Programming and Evolvable Machines
Runtime analysis of mutation-based geometric semantic genetic programming on boolean functions
Proceedings of the twelfth workshop on Foundations of genetic algorithms XII
Approximating geometric crossover by semantic backpropagation
Proceedings of the 15th annual conference on Genetic and evolutionary computation
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Geometric crossover is a formal class of crossovers which includes many well-known recombination operators across representations. In this paper, we present a general result showing that all evolutionary algorithms using geometric crossover with no mutation perform the same form of convex search regardless of the underlying representation, the specific selection mechanism, the specific offspring distribution, the specific search space, and the problem at hand. We then start investigating a few representation/space-independent geometric conditions on the fitness landscape - various forms of generalized concavity - that when matched with the convex evolutionary search guarantee, to different extents, improvement of offspring over parents for any choice of parents. This is a first step towards showing that the convexity relation between search and landscape may play an important role towards explaining the performance of evolutionary algorithms in a general setting across representations.