A method for solving nested combinatorial optimization problems - a case of optimizing a large-scale distribution network

The optimization of a large-scale distribution network is considered to be a nested combinatorial problem consisting of the following steps: (1) the decision about part delivery volume per part manufacturer; (2) the decision about depots and trucks for the transportation of parts; and (3) the generation of delivery routes for each truck. In such a nested combinatorial problem, a high-level and mathematically strict optimization is desirable as the first step. In addition, at each step, human multi-sided inspection is desired, which requires interactive simulation. Thus, for the first step, a method using linear programming (LP) is proposed. For the second and third steps, a method using a genetic algorithm (GA) is proposed. The latter guarantees interactive responsiveness and realizes expert-level accuracy, through enabling the solution of 1000 mid-scale traveling salesman problems (TSPs) for a distribution network within 30 seconds and within a 3% error. Experimental results proved that the proposed method enables the optimization of a nationwide large-scale distribution network.