ETEA: a Euclidean minimum spanning tree-based evolutionary algorithm for multi-objective optimization

The Euclidean minimum spanning tree (EMST), widely used in a variety of domains, is a minimum spanning tree of a set of points in space where the edge weight between each pair of points is their Euclidean distance. Since the generation of an EMST is entirely determined by the Euclidean distance between solutions (points), the properties of EMSTs have a close relation with the distribution and position information of solutions. This paper explores the properties of EMSTs and proposes an EMST-based evolutionary algorithm (ETEA) to solve multi-objective optimization problems (MOPs). Unlike most EMO algorithms that focus on the Pareto dominance relation, the proposed algorithm mainly considers distance-based measures to evaluate and compare individuals during the evolutionary search. Specifically, in ETEA, four strategies are introduced: (1) An EMST-based crowding distance (ETCD) is presented to estimate the density of individuals in the population; (2) A distance comparison approach incorporating ETCD is used to assign the fitness value for individuals; (3) A fitness adjustment technique is designed to avoid the partial overcrowding in environmental selection; (4) Three diversity indicators-the minimum edge, degree, and ETCD-with regard to EMSTs are applied to determine the survival of individuals in archive truncation. From a series of extensive experiments on 32 test instances with different characteristics, ETEA is found to be competitive against five state-of-the-art algorithms and its predecessor in providing a good balance among convergence, uniformity, and spread.