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Table 1:
Asymptotic bounds on expected parallel (Tpar, number of generations) and sequential (Tseq, number of function evaluations) runtimes and expected communication efforts (Tcom, total number of migrated individuals) for various n-bit functions and island models with islands running the (1+1) EA and using migration probability p=1. The number of islands was always chosen to give the best possible upper bound on the parallel runtime, while not increasing the upper bound on the sequential runtime by more than a constant factor. For unimodal functions d+1 denotes the number of function values. See Droste et al. (2002) for bounds for the (1+1) EA. Results for Jumpk were restricted to for simplicity. All upper bounds for OneMax and LO stated here are asymptotically tight, as follows from general results in Sudholt (2013).
(1+1) EARingGrid/torusHypercubeComplete
OneMax      
 best       
      
      
     
LO      
 best       
      
      
     
Unimodal      
 best       
 O(dn    
 O(dn    
     
Jumpk      
 best       
      
      
     
(1+1) EARingGrid/torusHypercubeComplete
OneMax      
 best       
      
      
     
LO      
 best       
      
      
     
Unimodal      
 best       
 O(dn    
 O(dn    
     
Jumpk      
 best       
      
      
     
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