MILP-Based Clustering Method for Multi-Objective Optimization: Application to Environmental Problems

DIEGO G. OLIVA; GUILLÉN-GOSÁLBEZ, G.; JIMÉNEZ-ESTELLER, L.

San Francisco

Congreso; 2013 Annual Meeting; 2013

American Institute of Chemical Engineers

Multi-objective optimization (MOO) has recently emerged as a useful technique in environmental engineering. One major limitation of this approach is that its computational burden grows rapidly with the number of environmental objectives, which causes difficulties regarding the computation and visualization of the Pareto solutions. In this work, we present several theoretical and algorithmic developments for grouping environmental objectives into clusters on the basis of which the multi-objective optimization can be performed, thereby facilitating the computation and analysis of the Pareto solutions. Particularly, we study how to group objectives of a MOO problem into meaningful 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 method is based on a novel mixed-integer linear program (MILP) that identifies in a systematic manner groups of objectives that behave similarly. The capabilities of the approach presented are tested through its application to several case studies, in which we compare the results of the MILP with those produced by a statistical method. The statistical method consists of a standard clustering algorithm. The first case study deals with the design of petrochemical supply chains considering several environmental indicators simultaneously (Pozo et al., 2012). The second example deals with the design of bio-ethanol supply chains in Argentina considering 6 objectives (Kostin et al., 2012). The third example addresses the multi-objective optimization of hydrogen supply chains for vehicle use in Spain considering several Life Cycle Assessment impacts (Sabio et al., 2012). In the last example, we study an artificial dataset with 10 objectives and 41 points generated randomly. The goal is to test the performance of the statistical method when the objectives are poorly correlated. Numerical results show that when the objectives are highly correlated, both methods (i.e., the MILP and the statistical method) lead to similar results, being the statistical approach the one with lower CPU times. In contrast, the statistical method leads to clusters with larger errors that differ from those produced by the rigorous MILP approach when the correlation between objectives is low. Our rigorous MILP-based approach is the only one that guarantees the minimum approximation error.