Aircraft Loading Optimization: MemComputing the 5th Airbus Problem

On the January 22nd 2019, Airbus launched a quantum computing challenge to solve a set of problems relevant for the aircraft life cycle (https://www.airbus.com/newsroom/press-releases/en/2019/01/airbus-launches-quantum-computing-challenge-to-transform-the-aircraft-lifecycle.html). The challenge consists of a set of 5 problems that ranges from design to deployment of aircraft. This work addresses the 5th problem. The formulation exploits an Integer programming framework with a linear objective function and the solution relies on the MemComputing paradigm. It is discussed how to use MemCPU$^{\text{TM}}$ software to solve efficiently the proposed problem and assess scaling properties, which turns out to be polynomial for meaningful solutions of the problem at hand. Also discussed are possible formulations of the problem utilizing non-linear objective functions, allowing for different optimization schemes implementable in modified MemCPU software, potentially useful for field operation purposes.