Deterministic and Stochastic Models in Optimization Theory. Optimization, Optical Designing, Stability Analysis, Log-scaled Mutation, Genetic Algorithm

      Аннотация: Optimization theory emerges as an integral part of applied mathematics in order to address complex scientific and engineering problems. Optical optimization is formulated mathematically by considering the corresponding focal length of the lens/ mirror as the objective function subject to object distance and lateral magnification. The stability domains of objective function are examined by multivariable calculus and eigenvalue analysis. Qualitative depictions of stability components are provided to enhance the comprehension of optical systems. This book gives criteria for the domains in searching the global optima. We discuss the notion of the intrinsic optical length, zoom-in, zoom-out, power, constrained and multicomponent optimizations. We propose an Enhanced Selection and Log-scaled Mutation Genetic Algorithm as a metaheuristic optimizer, which arises via the simulated annealing selection and adaptive log-scaled mutation schemes. A hybridization of deterministic and metaheuristic optimization emerges as a novel tool towards industrial applications. Validation on various objective functions reveals that our proposal offers improved convergence in realism of the Genetic Algorithm.

Ключевые слова: genetic algorithm, Optimization, stability analysis, Optical designing, Log scaled mutation