Iterative Optimization RCO: A “Ruler & Compass” Deterministic Method

We present a basic version of a deterministic iterative optimization algorithm that requires only one parameter and is often capable of finding a good solution after very few evaluations of the fitness function. We demonstrate its principles using a multimodal one-dimensional problem. For such problems, the algorithm could be applied with just a ruler and a compass, which is how it got its name. We also provide classical examples and compare its performance with six well-known stochastic optimizers. These comparisons highlight the strengths and weaknesses of RCO. Since this version does not address potential stagnation, it is best suited for low-dimensional problems (typically no more than ten), where each evaluation of a position in the search space is computationally expensive.