Multi-objective optimization (MOO) is increasingly being used for environmental applications. One of the main advantages of this technique is that it treats environmental performance indicators as individual objectives rather than as constraints imposed on the system. This allows identification of process alternatives that can lead to the minimization of environmental impacts.
The selection of a suitable environmental performance indicator is a key issue in the application of MOO to environmental problems. Amongst environmental indicators that are in use today, those based on life cycle assessment (LCA) principles (Guinée et al., 2002) are becoming the preferred choice. However, the computational burden of existing solution methods for MOO grows rapidly with the number of objectives. This limitation is critical in environmental applications, particularly in those based on the combined use of MOO and LCA where the simultaneous analysis of a wide range of environmental metrics is sought. Furthermore, increasing the number of objectives in multi-objective optimization models leads to solutions that are not only difficult to generate, but also to visualize and interpret.
Previous attempts to ameliorate this difficulty focused on aggregation methods that relied on the use of single indicators calculated by attaching weights to the individual environmental metrics considered in the analysis. These weights, which are typically defined by a panel of experts, may not necessarily reflect the decision-maker’s preference. Furthermore, aggregation methods modify the Pareto structure of the problem in a manner that some parts of the search space might be left out of the analysis.
We investigate the use of two systematic methods, one based on a rigorous mixed-integer linear programming (MILP) formulation, and the other on principal component analysis, to reduce the dimensionality of MOO problems for environmental applications. We introduce a novel heuristic procedure that can be coupled with these techniques to improve their computational performance. Our final goal is to keep the size of the MOO model at a manageable level while still preserving its Pareto structure to the extent possible. An additional objective of our study is to enhance our knowledge of the Pareto structure of a given problem. This would facilitate analysis of the Pareto frontier by the decision-maker, by extracting the relationships between the different environmental impacts associated with a process. The capabilities of these computational strategies are highlighted by applying them to a generic industrial network. For this case study, the most relevant environmental metrics are chosen and redundant metrics are eliminated using the proposed approaches.
Guinée, J. B.; Gorrée, M.; Heijungs, R.; Huppes, G.; Kleijn, R.; de Koning, A.; van Oers, L.; Sleeswijk, A. W.; S. Suh, S.; de Haes, H. A. U.; de Bruijn, H.; van Duin, R.; Huijbregts, M. A. J. Handbook on Life Cycle Assessment. Operational Guide to the ISO Standards; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2002.
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