Estimating the Boundary Lines of Land Lots with a Multiobjective Optimization Approach

Data on the shape of land lots are needed in urban planning analyses. However, large amounts of shape data are often unavailable. In this paper we develop a method of estimating the boundary lines of land lots. With the assumption that the vertices of lots are tentatively given and that their deviations from true positions follow certain kinds of probability distributions, the problem is formulated as an optimization problem of adjusting the positions of tentatively given vertices, subject to the constraints of available information such as lot size and frontage. In this problem, two objectives are considered: one is to maximize the log-likelihood function and the other is to minimize distortion of lot shape. An index called the ‘suitability degree’, based on the concept of fuzzy logic, is proposed for evaluating the quality of estimates and is used as a decisionmaking rule for determining the weight parameter in the objective function. The proposed method is empirically tested with real lots and the results are satisfactory. It reveals the feasibility of applying this method in urban planning.