Hierarchical Clustering of Evolutionary Multiobjective Programming Results to Inform Land Use Planning


Multiobjective optimization is a branch of mathematical programming for modelling problems with multiple conflicting objectives. Multiobjective optimization problems can be solved using Pareto optimization techniques including evolutionary multiobjective optimization algorithms. Many real world applications involve multiple objective functions and can be addressed within a multiobjective optimization framework. Multiobjective optimization methods allow exploration of the attainable values of the objective functions and trade- offs between objective functions without soliciting preference information from the decision maker(s) before potential solutions are presented. In order to be sufficiently representative of the possibilities and trade-offs, the results of multiobjective optimization may be too numerous or complex in shape for decision makers to reasonably consider. Previous approaches to this problem have aimed to reduce the solution set to a smaller representative set. The methodology developed and evaluated in this thesis employs hierarchical cluster analysis to organize the solutions from multiobjective optimiation into a tree structure based on their objective function values. Unlike previous approaches none of the solutions are removed from consideration before being presented to the decision makers. A hierarchical cluster structure is desirable since it presents a nested organization of the plans which can be used in decision making as shown in an example decision. The resulting dendrogram is a tree of clusters that can be used to see the attainable trade-offs on the Pareto front. As well, it can be used to interactively reduce the set of solutions under consideration or consider several subsets of solutions that lie in different regions of the Pareto front. A land use change problem in an urban fringe area in Southern Ontario, Canada is used as motivation and as an example application to evaluate the proposed methodology. Relevant literature in planning support systems is reviewed in order to focus the methodology on the application. The multiobjective optimization problem for this application was formulated and analyzed by Roberts (2003); the optimization algorithm used to generate the approximation of the optimal solutions is the Non-dominated Sorting Genetic Algorithm II, NSGA-II, developed by Deb et al. (2002). Future work will link the resulting objective function-based tree to map visualizations of the landscape under consideration. Decision makers will be able to use the tree structure to explore different potential land use plans based on their performance on the objective functions representing the quality of those plans for natural and human uses. This approach is applicable to multiobjective problems with more than three objective functions and discrete decision variables or hierarchically clustered Pareto optimal sets. The suitability for reuse with other datasets or other applications is discussed as well as the potential for inclusion in a decision support system (DSS).