Genetic programming: on the programming of computers by means of natural selection
Genetic programming: on the programming of computers by means of natural selection
Foundations of genetic programming
Foundations of genetic programming
A Metric for Genetic Programs and Fitness Sharing
Proceedings of the European Conference on Genetic Programming
Empirical Study of Hybrid Particle Swarm Optimizers with the Simplex Method Operator
ISDA '05 Proceedings of the 5th International Conference on Intelligent Systems Design and Applications
Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)
Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)
Geometric particle swarm optimization for the sudoku puzzle
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Low Dimensional Simplex Evolution--A Hybrid Heuristic for Global Optimization
SNPD '07 Proceedings of the Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing - Volume 02
Geometric particle swarm optimization
Journal of Artificial Evolution and Applications - Particle Swarms: The Second Decade
Geometric differential evolution
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Inbreeding properties of geometric crossover and non-geometric recombinations
FOGA'07 Proceedings of the 9th international conference on Foundations of genetic algorithms
Geometric particle swarm optimisation
EuroGP'07 Proceedings of the 10th European conference on Genetic programming
Geometric differential evolution on the space of genetic programs
EuroGP'10 Proceedings of the 13th European conference on Genetic Programming
Geometric generalization of the nelder-mead algorithm
EvoCOP'10 Proceedings of the 10th European conference on Evolutionary Computation in Combinatorial Optimization
IEEE Transactions on Evolutionary Computation
Geometry of evolutionary algorithms
Proceedings of the 13th annual conference companion on Genetic and evolutionary computation
Geometry of evolutionary algorithms
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
Genetic Programming and Evolvable Machines
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The Nelder-Mead Algorithm (NMA) is a close relative of Particle Swarm Optimization (PSO) and Differential Evolution (DE). In recent work, PSO, DE and NMA have been generalized using a formal geometric framework that treats solution representations in a uniform way. These formal algorithms can be used as templates to derive rigorously specific PSO, DE and NMA for both continuous and combinatorial spaces retaining the same geometric interpretation of the search dynamics of the original algorithms across representations. In previous work, a geometric NMA has been derived for the binary string representation and permutation representation. Furthermore, PSO and DE have already been derived for the space of genetic programs. In this paper, we continue this line of research and derive formally a specific NMA for the space of genetic programs. The result is a Nelder-Mead Algorithm searching the space of genetic programs by acting directly on their tree representation. We present initial experimental results for the new algorithm. The challenge tackled in the present work compared with earlier work is that the pair NMA and genetic programs is the most complex considered so far. This combination raises a number of issues and casts light on how algorithmic features can interact with representation features to give rise to a highly peculiar search behaviour.