Preserving the Diversity of a Genetically Evolving Population of Nets Using the Functional Behavior of Neurons

Popul at ion diversity loss is a major obstacle in applying genetic algorithms to optimizat ion problems, which often results in population degeneration and pr emature convergence . The diversity changes caused by t hree nat ural-select ion strategies-comparing new offspring to the leastfit spec imen in t he population , to one of t he parents, and to the most similar specimen in t he pop ulat ion-are analyzed theoret ically and demonstrated experimentally. Using Hamming distances, the changes in diversity induced by these strategies are analyzed for an evolving population of bin ary st rings. The resu lts of the analysis show that the st rategy of comparing new offspring to the most similar specimen (select ing the fit ter of the two) causes the smallest diversity loss. To demonstrat e the efficiency of the various methods we exa mine the populat ion diversity of neural nets trained to perfor m certain tasks using a genetic algorithm. The funct ional behavior of neur ons, represent ed by the intern al repr esent ations of each neuron for the ent ire t ra ining set, is used to derive the functional similari ty of every pair of neuro ns and to evaluate the similarity of every pair of nets in a populati on of neur al networks. Using a meas ure of the functional behavior of neurons, the changes in diversity are demonst rated for evolving populat ions of nets trained on t he Parity dat a set. The experiment al result s demonst rate the success of the third strat egy in preserving popu lation diversity throughout generat ions: overcoming obstacles in the course of t raining and preventing pop ulation degeneration, and thus provi ding more successful and reliable learn ing. *Current address: Department of Electrical Engineering, Technion-I srael Institute of Technology, Technion City, Haifa 32000, Israel. tCurrent address: Department of Physics, University of Edinburgh, J . C. Maxwell Building, Mayfield Road, Edinburgh EH9 3JZ, UK. 328 Nachum Shamir, David Saad, and Em anuel Marom