Intl. Trans. in Op. Res. 00 (2013) 1–11 DOI: 10.1111/itor.12034 INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH MIP-and-refine matheuristic for smart grid energy management Matteo Fischetti, Giorgio Sartor and Arrigo Zanette DEI, University of Padova, via Gradenigo 6/A, 35131 Padova, Italy E-mail: matteo.fischetti@unipd.it [Fischetti]; gio.srt@gmail.com [Sartor]; zanettea@gmail.com [Zanette] Received 13 December 2012; accepted 22 May 2013 Abstract In the past years, we have witnessed an increasing interest in smart buildings, in particular for optimal energy management, renewable energy sources, and smart appliances. In this paper, we investigate the problem of scheduling smart appliance operation in a given time horizon with a set of energy sources and accumulators. Appliance operation is modeled in terms of uninterruptible sequential phases with a given power demand, with the goal of minimizing the energy bill fulfilling duration, energy, and user preference constraints. A mixed-integer linear programming (MIP) model and greedy heuristic algorithm are given, which are used in a synergic way. We show how a general purpose (off-the-shelf) MIP-refining procedure can be effectively used for improving, in short computing time, the quality of the solutions provided by the initial greedy heuristic. Computational results confirm the viability of the overall approach, in terms of both solution quality and speed. Keywords: matheuristics; mixed-integer programming; refinement heuristics; energy management; smart houses 1. Prologue Many successful matheuristic schemes use a black-box mixed integer linear programming (MIP) solver to generate high-quality heuristic solutions for difficult optimization problems. The hall- mark of this approach is the availability of an (possibly incomplete) MIP model, and an external metascheme that iteratively solves sub-MIPs obtained by introducing invalid constraints (e.g., vari- able fixings) defining “interesting” neighborhoods of certain solutions. The goal of the approach is to iteratively refine the incumbent solution, producing a sequence of improved feasible solutions in short (or, at least, acceptable) computing times. The above solution-refinement approach is com- pletely general, that is, it can in principle be applied to the original MIP without the need of ad hoc adaptations. C  2013 The Authors. International Transactions in Operational Research C  2013 International Federation of Operational Research Societies Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main St, Malden, MA02148, USA.