Evaluation of multi-objective optimization approaches for solving green supply chain design problems. (April 2017) - Kadziński, Miłosz; Tervonen, Tommi; Tomczyk, Michał K.; Dekker, Rommert
Abstract: This paper evaluates the applicability of different multi-objective optimization methods for environmentally conscious supply chain design. We analyze a case study with three objectives: costs, CO2 and fine dust (also known as PM – Particulate Matters) emissions. We approximate the Pareto front using the weighted sum and epsilon constraint scalarization methods with pre-defined or adaptively selected parameters, two popular evolutionary algorithms, SPEA2 and NSGA-II, with different selection strategies, and their interactive counterparts that incorporate Decision Maker׳s (DM׳s) indirect preferences into the search process. Within this case study, the CO2 emissions could be lowered significantly by accepting a marginal increase of costs over their global minimum. NSGA-II and SPEA2 enabled faster estimation of the Pareto front, but produced significantly worse solutions than the exact optimization methods. The interactive methods outperformed their a posteriori counterparts, and could discover solutions corresponding better to the DM preferences. In addition, by adjusting appropriately the elicitation interval and starting generation of the elicitation, the number of pairwise comparisons needed by the interactive evolutionary methods to construct a satisfactory solution could be decreased. Abstract : Highlights: The shape of the Pareto front in our three-objective case is irregular. Almost minimal CO2 solutions can be obtained at little extra costs. The scalarization methods yield good solutions in reasonable time. The solution quality increases when using an interactive preference elicitation. Less preference statements are needed when an initial optimization is performed.