An edge-swap heuristic for generating spanning trees with minimum number of branch vertices

This paper presents a new edge-swap heuristic for generating spanning trees with a minimum number of branch vertices, i.e. vertices of degree greater than two. This problem was introduced in Gargano et al. (Lect Notes Comput Sci 2380:355-365, 2002) and has been called the minimum branch vertices problem by Cerulli et al. (Comput Optim Appl 42:353-370, 2009). The heuristic starts with a random spanning tree and iteratively reduces the number of branch vertices by swapping tree edges with edges not currently in the tree. It can be easily implemented as a multi-start heuristic. We report on extensive computational experiments comparing single-start and multi-start variants on our heuristic with other heuristics previously proposed in the literature

Automatic Tuning of GRASP with Path-Relinking Heuristics with a Biased Random-Key Genetic Algorithm

GRASP with path-relinking (GRASP+PR) is a metaheuristic for finding optimal or near-optimal solutions of combinatorial optimization problems. This paper proposes a new automatic parameter tuning procedure for GRASP+PR heuristics based on a biased randomkey genetic algorithm (BRKGA). Given a GRASP+PR heuristic with n input parameters, the tuning procedure makes use of a BRKGA in a first phase to explore the parameter space and set the parameters with which the GRASP+PR heuristic will run in a second phase. The procedure is illustrated with a GRASP+PR for the generalized quadratic assignment problem with n = 30 parameters. Computational results show that the resulting hybrid heuristic is robust