Successive smoothing algorithm for solving large-scale optimization models with fixed cost

This study addresses the solution of large-scale, non-convex optimization problems with fixed and linear variable costs in the objective function and a set of linear constraints. A successive smoothing algorithm (SSA) is developed to solve a non-convex optimization problem by solving a sequence of approximated convex problems. The performance of the SSA is tested on a series of randomly generated problems. The computation time and the solution quality obtained by the SSA are compared to a mixed integer linear programming (MILP) solver (CPLEX) over a wide variety of randomly generated problems. The results indicate that the SSA performs consistently well and produces high-quality near optimal solutions using substantially shorter time than the MILP solver. The SSA is also applied to solving a real-world problem related to regional biofuel development. The model is developed for a “system of systems” that consists of refineries, transportation, agriculture, water resources and crops and energy market systems, resulting in a large-scale optimization problem. Based on both the hypothetical problems and the real-world application, it is found that the SSA has considerable advantage over the MILP solver in terms of computation time and accuracy, especially when solving large-scale optimization problems.