Automatic generation of a hybrid algorithm for the maximum independent set problem using genetic programming

Abstract

One of graph optimization’s fundamental and most challenging problems is determining the maximum set of unconnected vertices in a graph, called the maximum independent set problem. This problem consists of finding the largest independent set in a graph, where an independent set is a set of vertices such that no two vertices are adjacent. This paper presents a new artificially generated algorithm for the maximum independent set problem. The new algorithm is generated by the automatic generation of algorithms, a technique that allows the construction of new hybrid algorithms, taking advantage of existing algorithms. Thus, the automatic generation of algorithms combines basic heuristics for the problem, a tabu search method selected from the literature, and an exact method that solves the problem’s mathematical formulation working for a limited computational time. With these components, the space of possible algorithms is traversed by employing genetic programming. Algorithms of small sizes are generated to study their structure and discover new algorithmic combinations. Then, we select the algorithm that finds solutions with the best computational performance among all the generated algorithms. This best algorithm is compared with three state-of-the-art algorithms for the problem, presenting the best computational performance for the 131 instances in the literature.