The evolutionary computation is a collective name of methods that belong to the metaheuristics of the artificial intelligence. Various problem-solving methods are in this group that were developed first by the inspiration of the biological evolution. The book consists of two main parts. The first part after a review of basic techniques shows groups of methods, which are inspired by the biological evolution, the swarm intelligence, the human immune system, the application of mathematical models, or by the building of probabilistic models. The second part shows the application of the evolutionary computations in the optimization. From the optimization problems we selected the scalar and multi-objective non-linear programming and several difficult combinatorial optimization problems. These problems are the binary quadratic, the Boolean satisfiability, the quadratic assignment, the p-median, the scheduling, the routing, the timetabling, the cutting and packing, as well as the dynamic optimization problems. The book can be used in higher education of informatics, mathematics and engineering, and it can be useful for computer scientists, engineers and economists.