EVOLUTIONARY ALGORITHM OF LEXICOGRAPHIC OPTIMIZATION FOR TUBE GAS HEATERS

Abstract

This article is devoted to multi-criteria decision-making for parametric optimization problems involving tubular gas heaters. It addresses the problem of finding an optimal solution given several sequential criteria and constraints in the form of inequalities. The problem is reduced to finding a binary selection relation that incorporates the requirements of sequential selection and the satisfaction of constraints in the form of inequalities. The following parametric optimization problems for tubular gas heaters were reduced to this form: optimization of heaters with natural convection of the heat transfer fluid, optimization of heater parameters with a screen on the heater surface, and optimization of heater parameters when the heater is located in a water space with a free surface. An alternative to the problem with lexicographic optimization is the sequential solution of several nonlinear programming problems, whereby the search may narrow down only in the final step of the solution sequence. Reducing the optimization problem to lexicographic selection allows solutions to be found in a single process. An iterative algorithm with multiple solution evolution branches is applied, in which the solution generation and selection functions are implemented sequentially. The convergence of the evolutionary search to a solution that is optimal with respect to a binary selection relation has been proven in the authors’ previous works, provided that sufficiently general conditions for the binary selection relation are satisfied. A solution to a test problem with sequential criteria and an inequality constraint is presented. This problem is presented in two forms: as a nonlinear programming problem and as a stochastic programming problem with a random effect on one of the criteria during its calculation. The results of the test problems show sufficiently good convergence, and the optimal solution is found fairly quickly. The developed algorithmic approach can be used in the future for the parametric optimization of tubular gas heaters in autonomous heat supply systems.