The demand for high education in an environment of an insufficient number of experts requires efficient knowledge management. The introduction of knowledge extensionists in higher learning institutions remains relevant to bridge the gap created by this imbalance. In this work, we developed a new multi-objective mathematical model for optimizing the knowledge transfer capability of extensionists and knowledge management in higher learning institutions in Nigeria. The Model provides the information needed for a detailed analysis of the design trade-off between conflicting objectives that are most interesting to a decision-maker. The binary Integer MultiObjective Model is a suitable model for a population of potential solutions. The Model focused on practical factors for effective knowledge transfer. Several indices were considered, such as number of task types, number of clusters (groups), number of employees, etc., as the knowledge transfer (KT) assessment factors. Some parameters are adequate to recognize the KT potential in an employee, such as whether task type can be handled by an employee, whether the employee is interested in cooperating with another employee, used the minimum size of the cluster in terms of the number of employees. The concept of “interest to work with each other” is a novel aspect considered in the recommended algorithm. Therefore, for illustration, an intelligent algorithm based on matrix and clustering concepts to evaluate data collected via a questionnaire from Waziri Umaru Federal Polytechnic Birnin Kebbi, Nigeria was developed. The model is suitable for any given set of data to be applied elsewhere