Basic, Dual, Adaptive, and Directed Mutation Operators in the Fly Algorithm

Our work is based on a Cooperative Co-evolution Algorithm -- the Fly algorithm -- in which individuals correspond to 3-D points. The Fly algorithm uses two levels of fitness function: i) a local fitness computed to evaluate a given individual (usually during the selection process) and ii) a global fitness to assess the performance of the population as a whole. This global fitness is the metrics that is minimised (or maximised depending on the problem) by the optimiser. Here the solution of the optimisation problem corresponds to a set of individuals instead of a single individual (the best individual) as in classical evolutionary algorithms. The Fly algorithm heavily relies on mutation operators and a new blood operator to insure diversity in the population. To lead to accurate results, a large mutation variance is often initially used to avoid local minima (or maxima). It is then progressively reduced to refine the results. Another approach is the use of adaptive operators. However, very little research on adaptive operators in Fly algorithm has been conducted. We address this deficiency and propose 4 different fully adaptive mutation operators in the Fly algorithm: Basic Mutation, Adaptive Mutation Variance, Dual Mutation, and Directed Mutation. Due to the complex nature of the search space, ($kN$-dimensions, with $k$ the number of genes per individuals and $N$ the number of individuals in the population), we favour operators with a low maintenance cost in terms of computations. Their impact on the algorithm efficiency is analysed and validated on positron emission tomography (PET) reconstruction.