The optimization of physical processes in engineering applications poses different challenges to the optimization engineer such as: Which optimization algorithm do I choose for a particular application? How do I choose optimization parameters and functions in a practical problem? How do I optimize highly dynamical, noisy, or expensive problems?This thesis answers these questions in the context of stochastic optimization methods and applications. It provides new developments of bio-inspired optimization algorithms with an emphasis on evolutionary algorithms and their applications to a wide rΓ€nge of problems in the areas turbomachinery, aeronautics, and micro- and nanotechnology.The development of bio-inspired algorithms includes the coupling of evolutionary algorithms with machine learning techniques for generalization purposes, the enhancement of convergence speed of evolutionary algorithms for parallel Computer architectures, and a novel optimization algorithm in-spired by the food-searching behavior of bacteria.In the application part. we discuss the optimal design of airfoil prohles, the cooling of turbine blades, jet mixing, and aircraft trailing vortex destruction, as well as micromixers, design of microchannels, and molecular dynamics applications.