A Binary Integer Programming Model for Global Optimization of Learning Path Discovery.
Nabil Belacel, Guillaume Durand, François LaPlante · NPARC · 2014
This paper introduces a method based on graph theory and operations research techniques to optimize learning path discovery. In this method, learning objects are considered as nodes and competencies as vertices of a learning graph. A first step consists in reducing the solution space by obtaining an induced subgraph H. In a second step, the search of an optimal learning path in H is considered as a binary integer programming problem which we propose to solve using an exact method based on the well-known branch-and-bound algorithm. The method detailed in the paper takes into account the prerequisite and gained competencies as constraints of the optimization problem by minimizing the total competencies needed to reach the learning objective. Keywords Learning path, learning object recommendation, graph theory, clique, mathematical programming, binary integer programming, branch-and-bound algorithm. 1.