One of the most frequently studied areas in finance is the classical mean-variance portfolio selection model pioneered by Harry Markowitz; which is also, undoubtedly recognized as the foundation of modern portfolio theory. The model in its basic form deals with the selection of portfolio of assets such that a reasonable trade-off is achieved between the conflicting objectives of maximum possible return at a minimum risk, given that the right choice of constituent assets is made and proper weights are allocated. However, despite its enormous contribution to this branch of knowledge, the model is not immune from criticisms ranging from those associated with its in ability to capture the realism of an investment setting - such as transaction costs, cardinality constraints, floor and ceiling constraints, etc. In this research we extended the classical model by incorporating into it the cardinality as well as the floor & ceiling constraints after which we implemented six different metaheuristic algorithms to solve this advanced model. We then designed and implemented some neighbourhood transition strategies to enable our designed algorithms solve the problem in an efficient and intelligent way. Furthermore, we proposed a new portfolio selection model with target-semivariance (as defined in a previous research) as the objective, and constrained by additional real life (cardinality and floor & ceiling) constraints.