Abstract
Forma analysis is applied to the task of optimising the connectivity of a feed- forward neural network with a single layer of hidden units. This problem is reformulated as a multiset optimisation problem, and techniques are developed to allow principled genetic search over fixed- and variable-size sets and multisets. These techniques require a further generalisation of the notion of gene, which is presented. The result is a non-redundant representation of the neural network topology optimisation problem, together with recombination operators which have carefully designed and well-understood properties. The techniques developed have relevance to the application of genetic algorithms to constrained optimisation problems.
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Radcliffe NJ. Equivalence class analysis of genetic algorithms. Complex Syst 1991; 5(2): 183–205
Radcliffe NJ. Forma analysis and random respectful recombination. In: Proceedings of the Fourth International Conference on Genetic Algorithms. San Mateo (CA): Morgan Kaufmann, 1991: 222–229
Rudnick M. A bibliography of the intersection of genetic search and neural networks. Oregon (OR): Oregon Graduate Centre, Technical Report CS/E 90-001, 1990
Weiss G. Combining neural and evolutionary learning: Aspects and approaches. Technical Report FKI-132-90, Forschungsberichte Künstliche Intelligenz, 1990
Rumelhart DE, Hinton GE, Williams RJ. Learning representations by back-propagating errors. Nature 1986: 323
Miller GF, Todd PM, Hegde SU. Designing neural networks using genetic algorithms. In: Proceedings of the Third International Conference on Genetic Algorithms. San Mateo, Morgan Kaufmann, 1989
Harp SA, Samad T, Guha A. Towards the genetic synthesis of neural networks. In: Proceedings of the Third International Conference on Genetic Algorithms. San Mateo (CA): Morgan Kaufmann, 1989
Harp SA, Samad T, Guha A. The genetic synthesis of neural networks. Technical Report CSDD-89-I4852-2, Honeywell, 1989
Whitley D, Starkweather T, Bogart C. Genetic algorithms and neural networks: Optimising connections and connectivity. Colorado (CO): Colorado State University, Technical Report CS-89-117, 1989
Mülenbein H, Kindermann J. The dynamics of evolution and learning — Towards genetic neural networks. In Pfiefer P, Schreter Z, Fogelman-Soulié F, Steels L, editors. Connectionism in perspective. Amsterdam: North-Holland, 1989
Hancock PJB. GANNET: Design of a neral net for face recognition by a genetic algorithm. Stirling (UK): University of Stirling, Technical report, 1990
Whitley D. Applying genetic algorithms to neural network problems: A preliminary report. (Unpublished manuscript)
Whitley D, Hanson T. The Genitor algorithm: Using genetic algorithms to optimise neural networks. Colorado (CO): Colorado State University, Technical Report CS-89-107, 1989
Montana DJ, Davis L. Training feedforward neural networks using genetic algorithms. In: Proceedings of the Eleventh International Joint Conference on Artificial Intelligence, New York: AAAI, 1989: 762–767
Radcliffe NJ. Genetic neural networks on MIMD computers [dissertation]. Edinburgh (UK): Univ of Edinburgh, 1990
Belew RK, McInerny J, Schraudolph NN. Evolving networks: Using the genetic algorithm with connectionist learning. San Diego (CA): UCSD (La Jolla), Technical Report CS90-174, 1990
Radcliffe NJ. The permutation problem (unpublished manuscript), 1988
Whitley D, Dominic S, Das R. Genetic reinforcement learning with multilayer neural networks. In: Proceedings of the Fourth International Conference on Genetic Algorithms. San Mateo (CA): Morgan Kaufmann, 1991
Holland JH. Adaptation in natural and artificial systems. Ann Arbor (MI): University of Michigan Press, 1975
Goldberg DE, Lingle Jr R. Alleles, loci and the traveling salesman problem. In: Proceedings of an International Conference on Genetic Algorithms. Hillsdale: Lawrence Erlbaum Associates, 1985
Goldberg DE. Genetic algorithms in search, optimization & machine learning. Reading (MA): Addison-Wesley, 1989
Vose MD. Generalizing the notion of schema in genetic algorithms. Artif. Intell. (in press)
Vose MD, Liepins GE. Schema disruption. In: Proceedings of the Fourth International Conference on Genetic Algorithms. San Mateo (CA): Morgan Kaufmann, 1991: 237–243
Norman M. A genetic approach to topology optimisation for multiprocessor architectures. Edinburgh (UK): University of Edinburgh, Technical Report, 1988
Mühlenbein H. Parallel genetic algorithms, population genetics and combinatorial optimization. In: Proceedings of the Third International Conference on Genetic Algorithms. San Mateo (CA): Morgan Kaufmann, 1989
Seitsma J, Dow RJF. Neural net pruning — Why and how. In: Proceedings of the IEEE Conference on Neural Networks, vol II. New York: IEEE Press, 1988
Burkitt AN. Optimisation of the architecture of feed-forward neural networks with hidden layers by unit elimination. Complex Syst 1991; 5(4): 371–380
Whitley D. Using reproductive evaluation to improve genetic search and heuristic discovery. In: Proceedings of the Second International Conference on Genetic Algorithms. Hillsdale (NJ): Lawrence Erlbaum Associates, 1987
Goldberg DE. Genetic algorithms and Walsh functions: Part I, A gentle introduction. Complex Syst 1990; 3: 129–152
Syswerda G. Uniform crossover in genetic algorithms. In: Proceedings of the Third International Conference on Genetic Algorithms. San Mateo (CA): Morgan Kaufmann, 1989
Koza JR. Genetic programming: A paradigm for genetically breeding populations of computer programs to solve problems. Stanford (EA): Stanford University, Technical Report STAN-CS-90-1314, 1990
Koza JR. Evolving a computer to generate random numbers using the genetic programming paradigm. In: Proceedings of the Fourth International Conference on Genetic Algorithms, San Mateo (CA): Morgan Kaufmann, 1991, 37–44
Schaffer JD, Eshelman LJ. On crossover as an evolutionary viable strategy: In Proceedings of the Fourth International Conference on Genetic Algorithms, San Mateo (CA): Morgan Kaufmann, 1991: 61–68
Davis L. Bit-climbing, representational bias, and test suite design. In: Proceedings of the Fourth International Conference on Genetic Algorithms. San Mateo: Morgan Kaufmann, 1991
Whitley D, Starkweather T, Fuquay D. Scheduling problems and traveling salesmen: The genetic edge recombination operator In: Proceedings of the Third International Conference on Genetic Algorithms. San Mateo (CA): Morgan Kaufmann, 1989
Vose MD. Personal communication, 1991
Whitley D, Starkweather T, Shaner D. The traveling salesman and sequence sheduling: Quality solutions using genetic edge recombination. In: Davis L, editor. Handbook of genetic algorithms. New York (NY): Van Nostrand Reinhold, 1991
Davis L. Handbook of genetic algorithms. New York: Van Nostrand Reinhold, 1991
Goldberg DE. Real-coded genetic algorithms, virtual alphabets, and blocking. Urbana-Champaign (IL): University of Illinois at Urbana-Champaign, Technical Report IlliGAL Report No. 90001, 1990
Booker L. Improving search in genetic algorithms. In: Davis L, editor. Genetic algorithms and simulated annealing. London: Pitman, 1987
Schaffer JD, Caruna RA, Eshelman LJ, Das R. A study of the control parameters affecting online performance of genetic algorithms for function optimisation. In: Proceedings of the Third International Conference on Genetic Algorithms. San Mateo (CA): Morgan Kaufmann, 1989
Spears WM, De Jong KA. On the virtues of parameterised uniform crossover. In: Proceedings of the Fourth International Conference on Genetic Algorithms. San Mateo (CA): Morgan Kaufmann, 1991: 230–236
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Radcliffe, N.J. Genetic set recombination and its application to neural network topology optimisation. Neural Comput & Applic 1, 67–90 (1993). https://doi.org/10.1007/BF01411376
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DOI: https://doi.org/10.1007/BF01411376