A multi-objective mathematical model in an educational system with online and face-to-face learning courses during the Coronavirus pandemic

The correct and optimal planning of the educational system is essential to guarantee the current and future achievements of any country. In recent years, due to the coronavirus pandemic, many organizations and scientific institutions have decided to hold educational, research, and courses for learners in the form of electronic (online) courses. Then, by passing the time and the vaccination of an acceptable population of the communities, the aforementioned organizations and institutions have decided that the courses should be conducted as a combination of electronic and in-person courses. In this article, according to the mentioned problem, a mathematical model is built based on how to plan the educational system with the aim of minimizing the multi-objective costing related to this system. Educational institutions and the Internethave been noted. In the parts of the modeling that are related to in-person courses, elements (e.g., the costs of providing facilities, equipment, and the space for holding courses) have been taken into consideration with regard to the points related to the Covid-19 disease. Due to the complexity of the problem, it is considered one of the NP-hard ones. Therefore, to solve small-sized problems, GAMS software was used. To obtain the set of Pareto solutions in medium- and large-sized problems, two meta-heuristic algorithms, namely genetic algorithm and Krill herd optimization, are used. Finally, the results with selected strategies have shown the achievement of optimal solutions in less and faster time by using meta-heuristic algorithms than the exact method and the optimal efficiency of the aforementioned algorithms.