Abstract <p>The problem of finding rational solutions to a multiextremal parametric problem using the ant colony method is considered. Rational solutions are solutions that are close to the optimal one in terms of the value of the objective function, but are not necessarily optimal. To solve a multiextreme problem, a modification of the ant colony method is proposed, which does not converge to a single solution, but continues to search for a solution. The ant colony method underlying the modification allows us to consider all rational solutions at the earliest iterations. The lack of convergence to a single solution solves the problem of stagnation of the proposed algorithm of the ant colony method. The solutions considered are stored in a hash table, which allows avoiding recalculation of the value of the objective function for the given solution on the computer and searching for a new solution for each agent. There is a new formula for determining the probability of the ant’s (agent’s) transition to a new parameter. The purpose of this formula is to solve the problem of algorithm stagnation in early iterations by increasing the probability of the agent visiting components of solutions that have not yet been considered. The algorithm of this modification of the ant colony method allows solving discrete parametric problems and determining rational values of parameters from a discrete set. This paper studies the dependence of the efficiency of the method on the parameters of the proposed modification of the ant colony method. The study on test problems and large-scale problems shows the dependence on the parameters of the additive convolution and the evaporation coefficient, which is responsible for reducing the weights obtained in previous iterations.</p>