A hybrid Lagrangian Particle Swarm Optimization Algorithm for the degree-constrained minimum spanning tree problem

This paper presents a new hybrid heuristic combining particle swarm optimization with a Lagrangian heuristic along the lines first proposed by Wedelin. We will refer to this as a Combinatorial Lagrangian Particle Swarm Optimization Algorithm (CoLaPSO). It uses a problem representations that works simultaneously in the dual space (Lagrangian multipliers) and the primal space in the form of cost perturbations. The CoLaPSO method is applied to solving the degree constrained minimum spanning tree problem. This NP-hard problem consists of finding a minimum cost spanning tree on a graph such that none of the vertices is connected to more than a fixed number of edges. The hybrid heuristic inherits from the Lagrangian parent an ability to calculate lower bounds on the objective and from the particle swarm optimization the ability to effectively parallelise the algorithm. Empirical evaluation using standard test problems from the literature show that the new method outperforms previously published heuristics for this problem and also computes useful lower bounds.