We introduce the Spacing Memetic Algorithm (SMA), a formal evolutionary model devoted to a systematic control of spacing (distances) among individuals. SMA uses search space distance information to decide what individuals are acceptable in the population, what individuals need to be replaced and when to apply mutations. By ensuring a "healthy" spacing (and thus diversity), SMA substantially reduces the risk of premature convergence and helps the search process to continuously discover new high-quality search areas. Generally speaking, the number of distance calculations represents a limited computational overhead compared to the number of local search iterations. Most existing memetic algorithms can be "upgraded" to a spacing memetic algorithm, provided that a suitable distance measure can be specified. The impact of the main SMA components is assessed within several case studies on different problems.