Handbook of Optimization: From Classical to Modern Approach

Book Preface

Optimization problems have belonged to the mathematical and technical publications with myriad applications for a considerable period of time. The relatively long optimization problem was solved by the now classical mathematical apparatus, which is based on infinitesimal calculus, methods of variations applied in functional areas or numerical methods. This apparatus enables and allows finding
of the optimal solution for the simpler nature of the problems and solving complex problems usually sub-optimally. Computational and algorithmic complexity increases not only the complexity of the problem, but also by whether the subject of arguments optimized functions of one type or not. In the domain of current engineering problems, it is quite frequent to meet optimization problems in which the objective function arguments are defined in different domains (real, integer, logical, linguistic), but also with the fact that an argument may change in certain parts of the interval allowed values not only within its own field, and with various restrictions resulting from physical or economic feasibility. The same is true of the field values of objective function.

The fact that the classical optimization methods are not usually suitable for a certain class of problems, beyond a certain degree of difficulty or complexity, implies the fact that we need more powerful methods to access the wider engineering community, which facilitated the solution of complex optimization tasks. The term “not appropriate“ here does not mean that classical methods cannot solve it, but implies
that with increasing difficulty and complexity of the problem, it usually require a migration from analytical to numerical methods and also the increasing complexity of the problem does not automatically require only longer time to get a solution, but also participation of a suitable expert.