Optimal Load Control and Scheduling through Distributed Mixed-integer Linear Programming

This paper presents a mixed-integer linear programming-based optimization model for simultaneous optimal load control and scheduling of distributed systems coupled through their energy consumptions. The subsystems are able to adjust their energy consumption during the execution of a task and aim at minimizing their completion time and energy cost. The overall problem is solved in a distributed fashion, where each subsystem optimizes its individual operation without sharing sensitive information. To this end, dual decomposition is employed and a new algorithm to update the dual variables is presented. It relies on a transformation of the gradient of the quadratically approximated dual function and the subsequent solution of a regression problem. The proposed algorithm makes efficient use of information collected in previous iterations. The solution obtained from the distributed optimization of the subsystems is compared to both a decentral and a system-wide solution, showing that the distributed solution lies close to the global optimum of the process.