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In many applications the design of a system needs to be optimised but the effectiveness of the design choices can only be evaluated by considering the behaviour of the system over a longer time period or multiple scenarios. Here we develop a general hybrid matheuristic method that can be used in such situations and apply it to a particular problem that arises in the design of a Remote Area Power Supply (RAPS) system in the presence of storage. The major elements of our RAPS system include the load (demand for power), solar energy from photovoltaic (PV) panels, a diesel generator and a battery based storage facility. The aim is to find a fixed strategy is for using the diesel generator and battery storage facility to efficiently meet demand. Similar types of problems arise in a range of other design applications such as expansion planning of electricity transmission networks; selection and sizing of power generation facilities in a RAPS or electricity grid; or supply chain design (sizing warehouse storage and transport infrastructure). All of these applications can be formulated as large MIP models with have a similar structure: high level design variables relating to infrastructure or policy, and additional variables for evaluating the effectiveness of these decisions in a number of scenarios. In this paper we consider how to deal with such problems by combining ideas from progressive hedging, a Lagrangian decomposition based method, with the cross-entropy optimisation meta-heuristic. We describe the general structure of mixed integer programming (MIP) problems to which this applies, show how our application can be formulated in this structure and then describe the new hybrid matheuristic. Indicative computational results are provided comparing the new method against the CPLEX integer programming solver, progressive hedging and cross-entropy optimisation.

A Hybrid Cross-Entropy and Progressive Hedging Matheuristic with application to a RAPS System