Generalized Benders Decomposition Algorithm Incorporating Matheuristics to Solve Large-Scale Power Facility Location Problems

With the change of energy structure and the development of energy internet technology, the penetration rate of distributed generation is gradually increasing, and the location of distributed generation has an important impact on the distribution network line losses. In this paper, a mixed integer quadratic programming model with separability is considered to optimize the location of distributed generation and to reduce line losses in distribution networks, which measures line losses in distribution networks in terms of the quadratic term of current. In order to solve the problem of large-scale distributed power facility location problems with separability, a Benders decomposition algorithm incorporating matheuristics is proposed, which first decomposes the original problem into a mixed-integer linear programming master problem and a convex quadratic subproblem with separability, and then separates the generalized Benders cuts form solving the subproblem at the root node relaxed solution of the master problem. A simple in-out Stabilization technique is applied in order to efficiently raise the lower bound of the master problem at the root node. In order to avoid the use of branch-and-cut algorithms to solve the master problem to obtain optimal feasible solutions, two matheuristic repair strategies are proposed for the root node relaxation solution to obtain high-quality feasible solutions. Experimental results on 90 large-scale power facility location problems show that matheuristic repair strategies for the root node relaxation solution can find the global optimal solution.