The Nested Genetic Algorithms for Distributed Optimization Problems

In the first part, we review basic principles of the distributed modeling approach in optimization and present introduction to the formal framework based on the concept of a distributed optimization program. The framework is a general one and may be utilized for various classes of decision problems. The DOPs (distributed optimization programs) are introduced as syntactical entities containing certain optimization elements and based on composition rules. They may describe both basic and advanced mathematical programs (e.g., dynamic, stochastic, multistage, and hierarchical) and also game theory models. In addition, more complicated models can be derived from these building stones and further transformed in the syntactical correct way. Although the introduced descriptions are particularly designed for manipulations of programs' structures, semantics for certain DOPs can also be defined. Hence, the next challenge is to search promising solutions in the feasible sets of optimization elements of DOPs. Therefore, several genetic algorithms (GAs) are chosen to search in separate feasible sets and they may also exchange information about different populations for achieved solutions of DOP elements in various ways. The general inspiration comes from decomposition techniques in scenario based multistage programs, so the name nested GAs is used in our case. The computational results and implementation description are presented for the specific min-max problems that are chosen as elementary prototype instances.