A multi-objective approach with soft constraints for water supply and wastewater coverage improvements

In Brazil, due to public health, social and economic cohesion problems, access to water and wastewater services is certainly one of the main concerns of the different stakeholders in the Brazilian water sector. But as the focus is mainly on the expansion and building of new infrastructures, other features such as the robustness and resiliency of the systems are being forgotten. This reason, among others, highlights the importance of sustainable development and financing for the Brazilian water sector. In order to assess that goal, a multi-objective optimization model was built with the aim of formulating strategies to reach a predefined coverage minimizing time and costs incurred, under specific hard and soft constraints, assembled to deal with key sustainability concepts (e.g., affordability and coverage targets features) as they should not be left apart. For that purpose, an achievement scalarizing function was adopted with three distinct scaling coefficient vectors for a given reference point. To solve this combinatorial optimization problem, we used a mixed integer-linear programming optimizer that resorts to branch-and-bound methods. The work developed, paves the way toward the creation of a decision-aiding tool, without disregarding the number of steps that need to be taken to achieve the proposed objectives.