1. Coevolutionary Models A/Prof. Xiaodong Li School of Computer Science and IT, RMIT University Melbourne, Australia Email: xiaodong.li@rmit.edu.au April 2015

2. Coevolution In biology, coevolution is "the change of a biological object triggered by the change of a related object”. In other words, when changes in at least two species’ genetic compositions reciprocally affect each other’s evolution, coevolution has occurred. There is evidence for coevolution at the level of populations and species. The above is cited from wikipedia. 12/10/20152

3. Predators and preys 12/10/20153

4. Predator-prey population dynamics 12/10/20154

5. The Red Queen Effect The Red Queen Effect, is an evolutionary hypothesis which proposes that organisms must constantly adapt, evolve, and proliferate not merely to gain reproductive advantage, but also simply to survive while pitted against ever-evolving opposing organisms in an ever-changing environment. The Red Queen hypothesis intends to explain two different phenomena: the constant extinction rates as observed in the paleontological record caused by co-evolution between competing species, and the advantage of sexual reproduction (as opposed to asexual reproduction) at the level of individuals (from Wikipedia). 12/10/20155

6. Competitive coevolution In competitive coevolution, individual fitness is evaluated through competition with other individuals in the population, rather than through an absolute fitness measure. In other words, fitness signifies only the relative strengths of solutions; an increased fitness in one solution leads to a decreased fitness for another. Ideally, competing solutions will continually outdo one another, leading to an “arms race” of increasingly better solutions. 12/10/20156

7. Coevolving sorting networks A model of hosts and parasites to the evolution of sorting networks using a GA (Hillis, 1991). One species (the hosts) represents sorting networks, and the other species (the parasites) represents test cases in the form of sequences of numbers to be sorted. The interaction between the two species takes the form of complementary fitness functions. More specifically, a sorting network is evaluated on how well it sorts test cases, while the test cases are evaluated on how poorly they are sorted. 12/10/20157

8. Cooperative coevolution 12/10/20158 Modelling an ecosystem consisting of two or more species, collaborating cooperatively with one and another. Fitness of an individual is evaluated based on how well it “cooperates” with the best-fit individuals from other species.

9. Cooperative coevolutionary GA 1) A species represents a subcomponent of a potential solution; 2) Complete solutions are obtained by assembling representative members of each of the species present; 3) Credit assignment at the species level is defined in terms of the fitness of the complete solutions in which the species members participate; 4) When required, the number of species (subpopulations) should itself evolve; and 5) The evolution of each species (subpopulation) is handled by a standard GA. 12/10/20159

10. CCGA-1 12/10/201510

11. CCGA-1 CCGA-1 begins by initializing a separate population of individuals for each function variable. The initial fitness of each subpopulation member is computed by combining it with a random individual from each of the other species and applying the resulting vector of variable values to the target function. After the startup phase, each of the individual subpopulations in CCGA-1 is coevolved in a round-robin fashion using a traditional GA. The fitness of a subpopulation member is obtained by combining it with the current best subcomponents of the remaining (temporarily frozen) subpopulations. 12/10/201511

12. CCGA-1 results on test functions 12/10/201512

13. CCGA-2 Interacting variable (e.g., product terms) may present difficulties. To overcome this, the simple credit assignment scheme can be modified as follows: each individual in a subpopulation is evaluated by combining it with the best known individual from each of the other species and with a random selection of individuals from each of the other species. The two resulting vectors are then applied to the target function and then the better of the two values is returned as the offspring’s fitness. 12/10/201513

14. CCGA-1 and CCGA-2 results 12/10/201514

15. Evolving cascade networks 12/10/201515 In cascade networks, all input units have direct connections to all hidden units and to all output units, the hidden units are ordered, and each hidden unit sends its output to all downstream hidden units and to all output units.

16. Evolving cascade networks The network shown in Figure 8 (shown in the previous slide) is constructed incrementally as follows: 1) When the evolution of the network begins, there is only one species in the ecosystem, and its individuals represent alternatives for the output connection weights denoted by the three black boxes. 2) Later in the network’s evolution, the first hidden unit is added, and a second species is created to represent the new unit’s input connection weights. In addition, a new connection weight is added to each individual of the first species. All of these new weights are denoted by gray boxes in the figure. 3) The species creation event is triggered by evolutionary stagnation as described earlier. Later still, evolution again stagnates and the second hidden unit is added, a third species is created to represent the unit’s connection weights, and the individuals of the first species are further lengthened. Further information refer to (Potter and De Jong, 2000). 12/10/201516

17. Further readings Mitchell A. Potter and Kenneth De Jong. A cooperative coevolutionary approach to function optimization. In Yuval Davidor, Hans-Paul Schwefel, and Reinhard Manner, editors, Parallel Problem Solving from Nature - PPSN III, pages 249-257, Berlin, 1994. Springer. Mitchell A. Potter and Kenneth De Jong. Cooperative Coevolution: An Architecture for Evolving Coadapted Subcomponents. Evolutionary Computation, 8(1): 1-29. MIT Press. 12/10/201517