(662a) Bilevel Optimization Applied to the Exhaustive Exploration of Pareto Fronts in Sustainability Studies: Application to the Redesign of the UK Electricity Mix | AIChE

(662a) Bilevel Optimization Applied to the Exhaustive Exploration of Pareto Fronts in Sustainability Studies: Application to the Redesign of the UK Electricity Mix

Authors 

Guillén-Gosálbez, G. - Presenter, Imperial College of Science, Technology and Medicine
Sustainability principles have recently emerged as a powerful driver in our society that aims to become more environmentally-friendly and socially responsible. The practical implementation of sustainability principles is deemed challenging, since this task requires the simultaneous satisfaction of economic, environmental and social objectives, where inherent trade-offs naturally arise. In addition, these criteria are difficult to compare and ultimately aggregate into a single indicator (Bhaskar et al., 2000). Therefore, there is still a clear need to devise systematic tools to assist in the design and planning of sustainable systems that could provide an effective and meaningful analysis of sustainability performance.

Multi-objective optimization (MOO) has recently become the preferred approach to assist in the design and planning of sustainable systems (Grossmann and Guillen-Gosalbez, 2010). MOO provides a set of Pareto alternatives rather than a single optimal solution. This set of Pareto optima forms the Pareto frontier, which features non-inferiority (i.e. no objective can be improved without worsening at least another one). Furthermore, MOO requires no articulation of preferences via weights, a controversial step in sustainability problems.

Here, we focus on the systematic exploration of Pareto fronts so as to support decision-making in the post-optimal analysis of the Pareto solutions of MOO models. We mathematically pose the task of exploring the Pareto frontier of an MOO model as a bilevel programming problem. Bilevel programming problems consist of two nested optimization problems where the outer problem is constrained by the optimal solution of the inner one. The outer problem is generally referred to as upper-level problem or leader, while the inner one corresponds to the lower-level problem or follower. The combine use of MOO and bilevel programming was addressed in other works (Calvete and Galé, 2010; Yin, 2002; Ankhili and Mansouri, 2009; Calvete and Galé, 2011), but not in the same manner as we do here. More precisely, in our case the inner problem systematically explores the Pareto front of the MOO model while the outer problem seeks the point in the frontier that best reflects the decision-makers’ preferences.

We illustrate the capabilities of this approach through its application to the optimisation of the UK electricity mix according to specific sustainability criteria. The task of redesigning the UK mix is formulated as a linear bi-level programming problem where several economic, environmental and social indicators are considered. This bi-level model is solved to find the closest Pareto point to the current mix considering different distance metrics.

Overall, our approach is an effective technique to support decision-making in the post-optimal analysis of Pareto frontiers. This approach is capable of systematically identifying, from the set of Pareto solutions, the best one according to the decision-makers’ preferences, without relying on controversial weighting schemes. Furthermore, it establishes improvement targets for suboptimal alternatives and provides valuable guidelines on how to improve them. The model also offers the flexibility to predefine the strategy that best matches the users’ preferences.

References

Ankhili, Z., Mansouri, A., 2009. An exact penalty on bilevel programs with linear vector optimization lower level. Eur. J. Oper. Res. 197, 36–41. doi:10.1016/j.ejor.2008.06.026

Bhaskar, V., Gupta, S.K., Ray, A.K., 2000. Applications of multiobjective optimization in Chemical Engineering. Rev. Chem. Eng. 16, 1–54. doi:10.1515/REVCE.2000.16.1.1

Calvete, H.I., Galé, C., 2010. Linear bilevel programs with multiple objectives at the upper level. J. Comput. Appl. Math. 234, 950–959. doi:10.1016/j.cam.2008.12.010

Calvete, H.I., Galé, C., 2011. On linear bilevel problems with multiple objectives at the lower level. Omega 39, 33–40. doi:10.1016/j.omega.2010.02.002

Grossmann, I.E., Guillen-Gosalbez, G., 2010. Scope for the application of mathematical programming techniques in the synthesis and planning of sustainable processes. Comput. Chem. Eng. 34, 1365–1376. doi:10.1016/j.compchemeng.2009.11.012

Yin, Y., 2002. Multiobjective bilevel optimization for transportation planning and management problems. J. Adv. Transp. 36, 93–105. doi:10.1002/atr.5670360106