(350e) Identifying Similar Environmental Objectives in Multi-Objective Optimization Via Clustering Methods

Multi-objective optimization has recently emerged as a useful technique in environmental engineering, as it allows treating environmental aspects as additional objectives to be optimized rather than constraints on the system. One major limitation of these models (as applied to environmental engineering) is that they typically include a large number of objectives, which causes difficulties regarding the computation and visualization of the Pareto solutions.

Previous works by the authors focused on reducing the number of objectives in these problems using rigorous mixed-integer linear programs (MILP). In this piece of research, we have addressed a broader problem: given a multi-objective optimization model, we aim at grouping the environmental objectives into clusters, with the property that the minimization of any objective within a cluster will result in the minimization of the rest of objectives within the same cluster. Our final goal is to aid decision-makers by providing information on the structure of the problem, thereby offering them the opportunity of selecting the objectives to be minimized according to their preferences and the similarities between the environmental indicators of concern.     

We present herein several theoretical and algorithmic developments in this area. We first provide a rigorous definition of clustering error in multi-objective optimization to quantify deviations from the Pareto structure of the problem that take place when optimizing in a reduced domain of objectives defined according to some clustering. We then introduce a new algorithm to perform such a clustering, and compare it with other traditional clustering methods available in the literature. Our clustering strategy is based on finding structural dominance relations between objectives, which are quantified according to different metrics

Finally, examples are taken from the literature to perform the comparison with other clustering methods. The main advantages of our method are its low running time and quality (i.e., error) of the clustering generated. The clusters identified provide in turn valuable insight for designers in multi-objective optimization.