Interval Uncertainty-Based Robust Optimization for Convex and Non-Convex Quadratic Programs with Applications in Network Infrastructure Planning

Planning infrastructure networks such as roads, pipelines, waterways, power lines and telecommunication systems, require estimations on the future demand as well as other uncertain factors such as operating costs, degradation rates, or the like. When trying to construct infrastructure that is either optimal from a social welfare or profit perspective (depending on a public or private sector focus), typically researchers treat the uncertainties in the problem by using robust optimization methods. The goal of robust optimization is to find optimal solutions that are relatively insensitive to uncertain factors. This paper presents an efficient and tractable approach for finding robust optimum solutions to linear and, more importantly, quadratic programming problems with interval uncertainty using a worst case analysis. For linear, mixed-integer linear, and mixed-integer problems with quadratic objective and constraint functions, our robust formulations have the same complexity and tractability as their deterministic counterparts. Numerous examples with differing difficulties and complexities, especially with selected ones on network planning/operations problems, have been tested to demonstrate the viability of the proposed approach. The results show that the computational effort of the proposed approach, in terms of the number of function calls, for the robust problems is comparable to or even better than that of deterministic problems in some cases.