An innovative technique based on multi-objective grammar guided genetic programming (MOG3P-MI) is proposed to detect the most relevant activities that a student needs to pass a course based on features extracted from logged data in an education web-based system. A more flexible representation of the available information based on multiple instance learning is used to prevent the appearance of a great number of missing values. Experimental results with the most relevant proposals in multiple instance learning in recent years demonstrate that MOG3P-MI successfully improves accuracy by finding a balance between specificity and sensitivity values. Moreover, simple and clear classification rules which are markedly useful to identify the number, type and time of activities that a student should do within the web system to pass a course are provided by our proposal.