Submitted in fulfilment of the requirements of the Degree of Doctor of Engineering, Durban University of Technology, 2017. / Water is an essential natural resource for human existence and survival on the earth. South Africa, a water stressed country, allocates a high percentage of its available consumptive water use to irrigation. Therefore, it is necessary that we optimize water use in order to enhance food security. This study presents the development of mathematical models for irrigation scheduling of crops, optimal irrigation water release and crop yields in Vaal Harts irrigation scheme (VIS) of South Africa. For efficient irrigation water management, an accurate estimation of reference evapotranspiration (ETₒ) should be carried out. However, due to non-availability of enough historical data for the study area, mathematical models were developed to estimate ETₒ. A 20-year monthly meteorological data was collected and analysed using two data–driven modeling techniques namely principal component analysis (PCA) and adaptive neuro-fuzzy inference systems (ANFIS). Furthermore, an artificial neural network (ANN) model was developed for real time prediction of future ETₒ for the study area. The real time irrigation scheduling of potatoes was developed using a crop growth simulation model called CROPWAT. It was used to determine the crop water productivity (CWP), which is a determinant of the relationship between water applied and crop yield. Finally, a new and novel evolutionary multi-objective optimization algorithm called combined Pareto multi-objective differential evolution (CPMDE) was applied to optimize irrigation water use and crop yield on the VIS farmland. The net irrigation benefit, land area and irrigation water use of maize, potatoes and groundnut were optimized. Results obtained show that ETₒ increases with temperature and windspeed. Other variables such as rainfall and relative humidity have less significance on the value of ETₒ. Also, ANN models with one hidden layer showed better predictive performance compared with other considered configurations. A 5-day time step irrigation schedule data and graphs showing the crop water requirements and irrigation water requirements was generated. This would enable farmers know when, where, and how much water to apply to a given farmland. Finally, the employed CPMDE optimization algorithm produced a set of non-dominated Pareto optimal solutions. The best solution suggests that maize, groundnut and potatoes should be planted on 403543.44 m2, 181542.00 m2 and 352876.05 m2areas of land respectively. This solution generates a total net benefit of ZAR 767,961.49, total planting area of 937961.49 m2 and irrigation water volume of 391,061.52 m3. Among the three crops optimized, maize has the greatest land area, followed by potatoes and groundnut. This shows that maize is more profitable than potatoes and groundnut with respect to crop yield and water use in the study area. / D