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Under Frequency Fitness Assignment (FFA), the fitness corresponding to anobjective value is its encounter frequency in fitness assignment steps and issubject to minimization. FFA renders optimization processes invariant underbijective transformations of the objective function value. On TwoMax, Jump, andTrap functions of dimension s, the classical (1+1)-EA with standard mutation atrate 1/s can have expected runtimes exponential in s. In our experiments, a(1+1)-FEA, the same algorithm but using FFA, exhibits mean runtimes that seemto scale as $s^2\ln{s}$. Since Jump and Trap are bijective transformations ofOneMax, it behaves identical on all three. On OneMax, LeadingOnes, and Plateauproblems, it seems to be slower than the (1+1)-EA by a factor linear in s. The(1+1)-FEA performs much better than the (1+1)-EA on W-Model and MaxSatinstances. We further verify the bijection invariance by applying the Md5checksum computation as transformation to some of the above problems and yieldthe same behaviors. Finally, we show that FFA can improve the performance of amemetic algorithm for job shop scheduling.

Frequency Fitness Assignment: Making Optimization Algorithms Invariant under Bijective Transformations of the Objective Function Value