This book introduces readers to the ¿Jayä algorithm, an advanced optimization technique that can be applied to many physical and engineering systems. It describes the algorithm, discusses its differences with other advanced optimization techniques, and examines the applications of versions of the algorithm in mechanical, thermal, manufacturing, electrical, computer, civil and structural engineering. In real complex optimization problems, the number of parameters to be optimized can be very large and their influence on the goal function can be very complicated and nonlinear in character. Such problems cannot be solved using classical methods and advanced optimization methods need to be applied. The Jaya algorithm is an algorithm-specific parameter-less algorithm that builds on other advanced optimization techniques. The application of Jaya in several engineering disciplines is critically assessed and its success compared with other complex optimization techniquessuch as Genetic Algorithms (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), Artificial Bee Colony (ABC), and other recently developed algorithms.