Mathematics for optimal design of sustainable infrastructures

The central aim of this paper is to show that mathematical sciences—in particular a smart combination of modeling, numerical simulation and optimization—can be seen as a useful tool in the design of sustainable infrastructures. Thus, in the first part of this work, we clarify what we mean by systems optimization and suggest how to apply these techniques to improve sustainability. Then, in the second part, we present three interesting environmental problems—all of them involving sustainable infrastructures—that we have studied in the last decade and fit well within this framework: (a) the design of a river fishway to help migratory fish to climb a dam, (b) the design of an irrigation channel to minimize sedimentation and erosion, and (c) the management of an urban road network from an environmental perspective. Based on our experiences, we believe that this innovative use of non-trivial mathematical tools is destined to play a leading role in achieving the United Nations Sustainable Development Goals by helping stakeholders develop the best scientifically informed strategies.