A hybrid mathematical model for urban land-use planning in association with environmental–ecological consideration under uncertainty

Various uncertainties exist in most urban land-use allocation systems; however, they have not been considered in most traditional urban land-use allocation methods. In this study, an interval-probabilistic urban land-use allocation model is developed based on a hybrid interval-probabilistic programming method. The developed interval-probabilistic urban land-use allocation model can deal with uncertainties expressed as intervals and probability distributions; moreover, it can also help examine the reliability of satisfying (or risk of violating) system constraints under uncertainty; the interval-probabilistic urban land-use allocation model not only considers economic factors, but also involves environmental and ecological constraints, which can effectively reflect various interrelations among different aspects in the urban land-use system. The developed model is applied to a case of long-term land-use allocation planning in the city of Wuhan, China. Interval solutions associated with different risk levels of constraint violation are obtained. The desired system benefit from the land-use system will be between $ [1781.921, 2290.970] × 10 9 under the minimum violating probabilities, and in this condition, the optimized areas of industrial land, commercial land and landfill will be [35,739, 42,402] ha, [58,572, 62,450] ha, and [903, 1087] ha. Results provide the decision makers of Wuhan with desired land-use allocation patterns and environmental policies, which are related to a variety of trade-offs between system benefit and constraint-violation risk. Willingness to accept low benefit from land-use system will guarantee meeting the environmental protection objective. A strong desire to acquire high system benefit will run into the risk of violating environmental constraint.