Many resource allocation issues, such as land use- or irrigation planning, require input from extensive spatial databases and involve complex decision-making problems. Recent developments in this field focus on the design of allocation plans that utilize mathematical optiniization techniques. These techniques, often referred to as multi criteria decision-making (MCDM) techniques, run into numerical problems when faced with the high dimensionality encountered in spatial applications. In this paper, it is demonstrated how both Simulated annealing, a heuristic algorithm, and Goal Programming techniques can be used to solve high-dimensional optimization problems for multi-site land use allocation (MLUA) problems. The optimization models both minimize development costs and maximize spatial compactness of the allocated land use. The method is applied to a case study in The Netherlands.