MILP-based decomposition algorithm for dimensionality reduction in multi-objective optimization: Application to environmental and systems biology problems

Abstract Multi-objective optimization has recently gained wider interest in different domains of engineering and science. One major limitation of this approach is that its complexity grows rapidly as we increase the number of objectives. This work proposes a computational framework to reduce the dimensionality of multi-objective optimization (MOO) problems that identifies and eliminates in a systematic manner redundant criteria from the mathematical model. The method proposed builds on a mixed-integer linear programming (MILP) formulation introduced in a previous work by the authors. We illustrate the capabilities of our approach by its application to two case studies: the design of supply chains for hydrogen production and the multi-objective optimization of metabolic networks. Numerical examples show that our method outperforms other existing algorithms for dimensionality reduction.