Curriculum Sequencing as a Generalised Travelling Salesperson Problem: A Novel Perspective on Learning Path Generation

Curriculum sequencing has been crucial for enabling personalised and adaptive online education for the past two decades. Swarm Intelligence, particularly Ant Colony Optimisation (ACO) algorithms, is commonly used to address this problem. Despite the ubiquitous interest in optimising individual learning paths, few studies on adaptive instructional systems (AIS) provide a mathematical formulation and analysis of the underlying optimisation problem. Hence, this work aims to reformulate the Curriculum Sequencing Problem (CSP) for a class of scenarios with multiple content options into a graph-based Generalised Travelling Salesperson Problem (GTSP) and presents proofs for the existence of solution sequences under a given set of Learning Object relations. To demonstrate feasibility, a knowledge graph is constructed based on 51 Learning Objects (LO). Learning Object Metadata (LOM) defines weights and edges, connecting two LOs and measuring their probability for optimal content flow. The ACO algorithm incorporates the VARK (visual, auditory, reading/writing, kinaesthetic) learning styles to exemplify adapting the CSP to 16.704 individual user models (leading to 16.704 individual CSPs). The results indicate that the resulting Curriculum Sequences suggested by the developed ACO algorithm do not occur in more than 4/16.704 CSP experiments. To conclude, the research describes and proves the applicability of a novel and transparent formulation of CSPs as a graph optimisation problem and illustrates how wide-spread data standards can be incorporated to develop AISs. This research aims to function as a manual and inspiration for developing further AIS based on graph theory.