Sensitivity-based mathematical optimization models for sustainable infrastructure planning under resource constraints

Abstract

Sustainable infrastructure planning over the long haul — including eco-friendly electricity grids, water-resource systems, and green transport routes — takes place within the framework of stringent budgetary, material, and ecological constraints that are often unknown during the planning process. Unlike what is typically regarded as a problem of design optimization, infrastructure planning should be viewed more as a problem of parametrization, whereby optimal solutions shift as parameters of resource perturbation change, and vulnerability is indicated by the magnitude of shift. Conventional sensitivity analysis of nonlinear programming makes use of parametric optimization algorithms, with design and allocation variables responding to the elements of perturbation vector pertaining to environmental condition. In order to guard against multi-source uncertainty and parametric instability, a robust minimax methodology has been developed. Moreover, the generalized Karush-Kuhn-Tucker conditions have been derived using the generalized Mangasarian-Fromovitz qualification, thereby demonstrating the non-empty, convex, bounded structure of the set of multipliers failing to work under conventional Linear Independence Constraint Qualification conditions for non-unique projects. It has been shown that the mapping of the set of constraints is metric subregular, thus ensuring controlled local error bounds close to active boundaries of constraints. Moreover, by imposing strict second-order efficiency requirements on critical cones, the design solutions become locally unique and stable. The results of numerical tests performed on a model network dealing with multiple resources in conditions of interrelated stress, capacity, and ecological impact constraints indicate that both sustainability of the multiplier behavior and performance limit preservation are proven for the given approach.