A hybrid approach based on genetic algorithms and (max, +) algebra for network applications

The following work addresses the problem of scheduling operations on a flow network, as well as alignment (path) allocation. This is a multi-objective problem, and this paper proposes a solution method through a hybrid approach based on a genetic algorithm in conjunction with (max, +) algebra. A concise system abstraction is proposed through a non-linear (max, +) model. This model describes the main optimization constraints which dictate the behavior of the mutation and crossover operations in the genetic algorithm. Additionally, each individual in the population represents the value assignment of the decision variables, which linearizes the (max, +) model. A hierarchic genetic structure is proposed for individuals such that variable dependence is modeled. For each individual, the (max, +)-linear model is solved through a matrix product which determines the daters for alignment enabling for transfer operations. The study is extendable to complex net-structured systems of different nature.