Frequency Fitness Assignment: Optimization Without Bias for Good Solutions Can Be Efficient

A fitness assignment process transforms the features (such as the objective value) of a candidate solution to a scalar fitness, which then is the basis for selection. Under frequency fitness assignment (FFA), the fitness corresponding to an objective value is its encounter frequency in selection steps and is subject to minimization. FFA creates algorithms that are not biased toward better solutions and are invariant under all injective transformations of the objective function value. We investigate the impact of FFA on the performance of two theory inspired, state-of-the-art evolutionary algorithms, the Greedy (2+1) GA and the self-adjusting $(1+(\lambda,\lambda))$ GA. FFA improves their performance significantly on some problems that are hard for them. In our experiments, one FFA-based algorithm exhibited mean runtimes that appear to be polynomial on the theory-based benchmark problems in our study, including traps, jumps, and plateaus. We propose two hybrid approaches that use both direct and FFA-based optimization and find that they perform well. All FFA-based algorithms also perform better on satisfiability problems than any of the pure algorithm variants.