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The domain of an optimization problem is seen as one of its most importantcharacteristics. In particular, the distinction between continuous and discreteoptimization is rather impactful. Based on this, the optimizing algorithm,analyzing method, and more are specified. However, in practice, no problem isever truly continuous. Whether this is caused by computing limits or moretangible properties of the problem, most variables have a finite resolution.  In this work, we use the notion of the resolution of continuous variables todiscretize problems from the continuous domain. We explore how the resolutionimpacts the performance of continuous optimization algorithms. Through amapping to integer space, we are able to compare these continuous optimizers todiscrete algorithms on the exact same problems. We show that the standard$(\mu_W, \lambda)$-CMA-ES fails when discretization is added to the problem.

When to be Discrete: Analyzing Algorithm Performance on Discretized Continuous Problems