In this paper, comprehensive thermodynamic analysis and optimisation of a cascade active magnetic regenerative refrigeration system are performed. A parametric study is conducted to investigate the effects of various design parameters on the cycle performance through energy and exergy efficiencies. A multi-objective optimisation method based on a fast and elitist non-dominated sorting genetic algorithm is applied to determine the best design parameters for the system. Two objective functions utilised in the optimisation study are the total cost rate of the system and the system exergy efficiency. The total cost rate of the system is minimised while the cycle exergy efficiency is maximised using an evolutionary algorithm. To provide insight, the Pareto frontier is shown for a multi-objective optimisation. The results show that exergy efficiency could be increased by 14.53% using exergy-based optimisation and the cost could be reduced by 12% using the cost-based optimisation.