A biased random-key genetic algorithm for the chordal completion problem

A graph is chordal if all its cycles of length greater than or equal to four contain a chord, i.e., an edge connecting two nonconsecutive vertices of the cycle. Given a graph G = (V, E), the chordal completion problem consists in finding the minimum set of edges to be added to G to obtain a chordal graph. It has applications in sparse linear systems, database management and computer vision programming. In this article, we developed a biased random-key genetic algorithm (BRKGA) for solving the chordal completion problem, based on the strategy of manipulating permutations that represent perfect elimination orderings of triangulations. Computational results show that the proposed heuristic improve the results of the constructive heuristics fill-in and min-degree. We also developed a strategy for injecting externally constructed feasible solutions coded as random keys into the initial population of the BRKGA that significantly improves the solutions obtained and may benefit other implementations of biased random-key genetic algorithms.