Constraint decomposition-based mathematical strategies for multi-stage infrastructure planning and optimization

Abstract

Multi-stage infrastructure planning is characterized by complex decisions that are interdependent with different constraints, demand uncertainties, limited resources and investments that change in nature. Traditional monolithic methods of optimization tend to become highly computation-intensive as the number of decision variables, constraints and planning stages increase. This research develops a new approach called Constraint Decomposition-Based Minimax Strategy which will be used to make multi-stage infrastructure planning more manageable and robust. In the developed mathematical formulation, the constraint set is decomposed to include local constraints, capacity constraints, resource constraints, budget constraints, temporal constraints, and inter-stage coupling constraints. Optimization problems are defined on the basis of each stage and are linked through state transitions and inter-stage coupling conditions. Due to uncertainty in construction cost and infrastructure demands, minimax problem reformulation based on auxiliary variable is adopted. This strategy will be validated through a four-stage urban infrastructure expansion scenario. It is seen from the numerical results that the cost of the computation time with the decomposition scheme is decreased from 31.6 s to 18.4 s relative to the monolithic formulation; hence, the cost decrease is about 41.8%. The cost of the worst case in the proposed approach is 51.42, which is better than the one in conventional robust optimization of 53.76 and the nominal optimization of 61.84 while keeping the maximum constraint violation at the level of (3.2times10{−7}). The resource and capacity usage are 91.6% and 94.1%, respectively.