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) Decision of parts delivery volume per parts maker. 2) Decision of depots and trucks for parts' transportation 3) Generation of delivery routes for each truck. In such a nested combinatorial problem, a high-level and mathematically strict optimization is desirable at the first step. As well, 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 2nd and 3rd step, a method using GA is proposed. The latter guarantees interactive responsiveness and realizes experts' level accuracy, through enabling to solve 1000 middle scale Traveling Salesman Problems (TSPs) for a distribution network within 30 seconds within 3% errors. Experimental results proved that the proposed method enables to optimize a nation wide large-scale distribution network.