Enhancing the ϵ-constraint method through the use of objective reduction and random sequences: Application to environmental problems

• We propose an enhanced epsilon-constraint method for multi-objective problems arising in PSE.
• The algorithm proposed combines objective reduction with random sampling.
• Our method outperforms others in terms of hypervolume indicator.

The ϵ-constraint method is an algorithm widely used to solve multi-objective optimization (MOO) problems. In this work, we improve this algorithm through its integration with rigorous dimensionality reduction methods and pseudo/quasi-random sequences. Numerical examples show that the enhanced algorithm outperforms the standard ϵ-constraint method in terms of quantity and quality of the Pareto points produced by the algorithm. Our approach, which is particularly suited for environmental problems that tend to contain several redundant objectives, allows dealing with complex MOO models with many objectives.