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Frequency Fitness Assignment: Making Optimization Algorithms Invariant under Bijective Transformations of the Objective Function Value
IEEE Transactions on Evolutionary Computation ( IF 14.3 ) Pub Date : 2020-01-01 , DOI: 10.1109/tevc.2020.3032090
Thomas Weise , Zhize Wu , Xinlu Li , Yan Chen

Under Frequency Fitness Assignment (FFA), the fitness corresponding to an objective value is its encounter frequency in fitness assignment steps and is subject to minimization. FFA renders optimization processes invariant under bijective transformations of the objective function value. On TwoMax, Jump, and Trap functions of dimension s, the classical (1+1)-EA with standard mutation at rate 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 seem to scale as $s^2\ln{s}$. Since Jump and Trap are bijective transformations of OneMax, it behaves identical on all three. On OneMax, LeadingOnes, and Plateau problems, 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 MaxSat instances. We further verify the bijection invariance by applying the Md5 checksum computation as transformation to some of the above problems and yield the same behaviors. Finally, we show that FFA can improve the performance of a memetic algorithm for job shop scheduling.

中文翻译:

频率适应度分配:使优化算法在目标函数值的双射变换下保持不变

在频率适应度分配 (FFA) 下,与目标值对应的适应度是其在适应度分配步骤中的遇到频率,并进行最小化。FFA 使优化过程在目标函数值的双射变换下保持不变。在维度为 s 的 TwoMax、Jump 和 Trap 函数上,具有标准变异速率 1/s 的经典 (1+1)-EA 可以具有以 s 为指数的预期运行时间。在我们的实验中,(1+1)-FEA,相同的算法但使用 FFA,表现出的平均运行时间似乎按 $s^2\ln{s}$ 缩放。由于 Jump 和 Trap 是 OneMax 的双射变换,因此它在所有三个上的行为都相同。在 OneMax、LeadingOnes 和 Plateau 问题上,它似乎比 (1+1)-EA 慢了一个以 s 为线性的因子。(1+1)-FEA 在 W-Model 和 MaxSat 实例上的性能比 (1+1)-EA 好得多。我们通过将 Md5 校验和计算作为对上述一些问题的转换应用来进一步验证双射不变性,并产生相同的行为。最后,我们表明 FFA 可以提高用于作业车间调度的模因算法的性能。
更新日期:2020-01-01
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