Seeking the Pareto front for multiobjective spatial optimization problems

Spatial optimization problems, such as route selection, usually involve multiple, conflicting objectives relevant to locations. An ideal approach to solving such multiobjective optimization problems (MOPs) is to find an evenly distributed set of Pareto-optimal alternatives, which is capable of representing the possible trade-off among different objectives. However, these MOPs are commonly solved by combining the multiple objectives into a parametric scalar objective, in the form of a weighted sum function. It has been found that this method fails to produce a set of well spread solutions by disregarding the concave part of the Pareto front. In order to overcome this ill-behaved nature, a novel adaptive approach has been proposed in this paper. This approach seeks to provide an unbiased approximation of the Pareto front by tuning the search direction in the objective space according to the largest unexplored region until a set of well-distributed solutions is reached. To validate the proposed methodology, a case study on multiobjective routing has been performed using the Singapore road network with the support of GIS. The experimental results confirm the effectiveness of the approach.