The gravitational attraction algorithm: a new metaheuristic applied to a nuclear reactor core design optimization problem

A new metaheuristic called 'Gravitational Attraction Algorithm' (GAA) is introduced in this article. It is an analogy with the gravitational force field, where a body attracts another proportionally to both masses and inversely to their distances. The GAA is a populational algorithm where, first of all, the solutions are clustered using the Fuzzy Clustering Means (FCM) algorithm. Following that, the gravitational forces of the individuals in relation to each cluster are evaluated and this individual or solution is displaced to the cluster with the greatest attractive force. Once it is inside this cluster, the solution receives small stochastic variations, performing a local exploration. Then the solutions are crossed over and the process starts all over again. The parameters required by the GAA are the 'diversity factor', which is used to create a random diversity in a fashion similar to genetic algorithm's mutation, and the number of clusters for the FCM. GAA is applied to the reactor core design optimization problem which consists in adjusting several reactor cell parameters in order to minimize the average peak-factor in a 3-enrichment-zone reactor, considering operational restrictions. This problem was previously attacked using the canonical genetic algorithm (GA) and a Niching Genetic Algorithm (NGA). The new metaheuristic is then compared to those two algorithms. The three algorithms are submitted to the same computational effort and GAA reaches the best results, showing its potential for other applications in the nuclear engineering field as, for instance, the nuclear core reload optimization problem. (author)