On efficiency of methods and algorithms for solving optimization problems considering objective function specifics

Abstract

Introduction. The estimation of efficiency of methods and algorithms for solving optimization problems with a vector criterion and a set of nonlinear constraints is considered. The approach that allows proceeding to an optimization problem with a single objective function (i.e., an unconditional optimization problem) after equivalent transformations is described. However, the objective function obtained in this way has properties (nonlinearity, multimodality, ravine, high dimension) that do not allow classical methods to be used to solve it. The presented work objective is to develop hybrid methods, based on combinations of the algorithms inspired by wildlife with other approaches (gravitational and gradient) for the solution to this problem.Materials and Methods. New methods to solve the specified problem are developed. A computer experiment was conducted on a number of test functions; its analysis was performed, showing the efficiency of various combinations on various functions.Research Results. The efficiency of hybrid algorithms that combine the following approaches is evaluated: genetic and immune; methods of swarm intelligence and genetic and immune; immune and swarm with gravity and gradient.Discussion and Conclusions. The hybrid algorithms in optimization problems are studied. In particular, decisions can be made on their basis under the management of compound objects in the military and industrial sectors, in the creation of innovative projects related to the digital economy. It is established that the type of the objective function affects the result much more than the combination of algorithms.

Keywords

• combination
• hybrid
• bio-inspired algorithm
• swarm intelligence
• gradient-based algorithm
• gravity search algorithm
• efficiency
• convergence.