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Abstract

The timetable problem of classes is an urgent problem in higher education institutions. There are a number of classical methods for solving it: dynamic programming methods, integer programming, nonlinear programming, the branch and bound method, simulation methods, the graph coloring method, assignment problem, and others. The peculiarity of these methods is the mathematical rigor of both the formulation of the timetable problem of classes and algorithms for its solution. They have predetermined convergence time and accuracy of the solution and allow to estimate the inux of dierent factors for time of nding the solution. The disadvantage of all classic methods is that they basically use an iterative search procedure or renement of some initial approximation, whereby the result is searched around that approximation. This means that the result directly depends on some initial approximation and naturally there is a problem of its choice, which leads to the need for a multiple experiment with dierent values of the initial approximation, which signicantly increases the time to nd the nal solution. Also, the classical methods are characterized by the complexity of the mathematical model obtained and the sharp (exponential) increase in time spent nding an acceptable solution as the volume of source information increases. To avoid the above disadvantages of the classical methods, the timetable problem of classes can be solved by applying a genetic algorithm. The paper proposes one variant of setting a objective function for timetable optimization and dening a tness function based on it. The article describes the implementation of classical genetic operators: crossover, mutations, and selection for a population of timetables, and also proposes a correction operator that improves the variants of timetables obtained by calls of classical genetic operators. For the implementation of crossover and correction operators, the concept of a local target function is introduced. The general scheme of the genetic algorithm for solving the timetable problem is presented in the paper, and the results of the numerical experiment are given.