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.