Contents lists available at ScienceDirect Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes The application of portfolio selection to fuel channel inspection in advanced gas-cooled reactors Claire E. Watson, Peter C. Robinson, Jenny F. Burrow, Philip R. Maul ⁎ Quintessa Ltd, The Hub, 14 Station Road, Henley-on-Thames RG9 1AY, UK ARTICLE INFO Keywords: Advanced gas cooled reactors Fuel channel inspection Genetic algorithms Portfolio analysis ABSTRACT The continued operation of the UK’s advanced gas-cooled nuclear reactors is dependent upon inspections of the graphite core to provide information on the evolution of core properties (such as the shapes of individual graphite bricks). It is necessary to optimise the information that is obtained, and the question of which fuel channels to inspect is a portfolio selection problem, complicated by the fact that the solution space is large and cannot be searched exhaustively. In addition, a number of portfolio–specific selection criteria must be applied, including the need to inspect channels in an even distribution across the core. A genetic algorithm is used to find a near-optimal solution, adapted so that portfolios potentially able to breed better offspring in future generations are accounted for. Analysis of the portfolios is an important part of the channel selection problem and algorithms have been developed to determine the significance of individual elements within the portfolio and the sensitivity of utility to portfolio size. The methods developed have been implemented in the CHANSELA software, the use of which contributes to the demonstration of the continued safe operation of the reactors. 1. Introduction The UK currently has 14 advanced gas-cooled reactors (AGRs) op- erated by EDF Energy, making a major contribution to the country’s total electricity supply. The cores of reactors have thousands of inter- locking graphite bricks which, when viewed from above, resemble a honeycomb of circular channels, as shown in Fig. 1. It is within these channels that the fuel rods are lowered to initiate the nuclear reaction. The continued safe operation of the reactors is underpinned by an extensive programme of testing and analysis, including the use of data gathered from the reactor during periodic shutdowns. The inspection of the channels within the graphite core, by remote TV cameras, sample removal and other techniques during these routine shutdowns provides information on the status of the core. The amount of information that can obtained at an inspection must be balanced against economic and other considerations. It is not prac- tical to inspect every channel in the reactor, but sufficient information on the state of the core can be obtained by inspecting far fewer chan- nels. An AGR contains approximately 300 fuel channels and typically around 30 are inspected at each shutdown. Bricks in the reactors have different characteristics: some may be more or less prone to weight loss or cracking because of factors such as their position in the reactor, or the batch of virgin graphite from which they were produced; some channels may have a long history of repeat inspections whilst other channels may never have been inspected. Inspecting different selections of these channels will therefore provide different types and amounts of information on the status of the graphite core. The problem faced, therefore, is which channels, out of the 300 or so that are available to inspect, are likely to provide the optimum in- formation at a given inspection. 2. Theory 2.1. Overall approach The problem described in the Introduction is an example of a multi- criteria portfolio decision analysis (MCPDA) problem. Portfolio selec- tion is a challenge faced by decision makers in numerous fields, for example: selecting the best portfolio for financial investment (e.g. Markowitz, 1952; Steuer et al., 2008); creating a menu (e.g. Chien & Sainfort, 1998); military and defence planning (e.g. Burk & Parnell, 2011; Kangaspunta et al., 2012); selecting projects for research and development (e.g. Henriksen & Traynor, 1999; Bitman and Sharif, 2008); and planning land use (e.g. Stewart et al., 2004). There are many approaches that have been employed to tackle such problems. The simplest is the scoring model, where elements (a generic term for the items to be chosen) are scored on each of the criteria for selection and the scores are then weighted and combined to give an https://doi.org/10.1016/j.nucengdes.2018.01.013 Received 28 August 2017; Received in revised form 1 January 2018; Accepted 3 January 2018 ⁎ Corresponding author. E-mail address: philipmaul@quintessa.org (P.R. Maul). Nuclear Engineering and Design 328 (2018) 145–153 0029-5493/ © 2018 Elsevier B.V. All rights reserved. T