This report documents the activities of Dagstuhl Seminar 19431 on "Theory of Randomized Optimization Heuristics". 46 researchers from Europe, Australia, Asia, and North America have come together to discuss ongoing research. This tenth edition of the seminar series had three focus topics: (1) relation between optimal control and heuristic optimization, (2) benchmarking optimization heuristics, and (3) the interfaces between continuous and discrete optimization. Several breakout sessions have provided ample opportunity to brainstorm on recent developments in the research landscape, to discuss and solve open problems, and to kick-start new research initiatives. Seminar October 20-25, 2019-http://www.dagstuhl.de/19431 2012 ACM Subject Classification Theory of computation → Bio-inspired optimization, Theory of computation → Evolutionary algorithms, Theory of computation → Optimization with randomized search heuristics License Creative Commons BY 3.0 Unported license © Efficient optimization techniques affect our personal, industrial, and academic environments through the supply of well-designed processes that enable a best-possible use of our limited resources. Despite significant research efforts, most real-world problems remain too complex to admit exact analytical or computational solutions. Therefore, heuristic approaches that trade the accuracy of a solution for a simple algorithmic structure, fast running times, or an otherwise efficient use of computational resources are required. Randomized optimization heuristics form a highly successful and thus frequently applied class of such problem solvers. Among the best-known representatives of this class are stochastic local search methods, Monte Carlo techniques, genetic and evolutionary algorithms, and swarm intelligence techniques.