Abstract. The problem of computing spanning trees along with specific constraints is mostly NP-hard. Many approximation and stochastic algorithms which yield a single solution, have been proposed. In this paper, we formulate the generic multi-objective spanning tree (MOST) problem and consider edge-cost and diameter as the two objectives. Since the problem is hard, and the Pareto-front is unknown, the main issue in such problem-instances is how to assess the convergence. We use a multiobjective evolutionary algorithm (MOEA) that produces diverse solutions without needing a priori knowledge of the solution space, and generate solutions from multiple tribes in order to assess movement of the solution front. Since no experimental results are available for MOST, we consider three well known diameter-constrained minimum spanning tree (dc-MST) algorithms including randomized greedy heuristics (RGH) which represents the current state of the art on the dc-MST, and modify them to yield a (near-) optimal solutionfronts. We quantify the obtained solution fronts for comparison. We observe that MOEA provides superior solutions in the entire-range of the Pareto-front, which none of the existing algorithms could individually do. 1

Network topology design problems find application in several real life scenarios. However, most designs in the past either optimize for a single criterion like delay or assume simplistic traffic models like Poisson. Such assumptions make the solutions inapplicable in the practical world. In this paper, we formulate and solve a multiobjective network topology design problem for a realistic Internet traffic model which is assumed to be self similar. We optimize for the average packet delivery delay and network layout cost to construct realistic network topologies. We present a multiobjective evolutionary algorithm (MOEA) to obtain the diverse near-optimal network topologies. For fair comparison, we design a multiobjective deterministic heuristic based on branch exchange – we call the heuristic Pareto Branch Exchange (PBE). We empirically show that the MOEA used performs well for real networks of various sizes, and generated topologies are quite different with significantly larger delays for the self similar traffic model.

Finding a minimum-weight spanning tree

In this paper, a novel automatic approach for the concurrent topology and routing optimization that achieves a high quality network layout is proposed. This optimization is based on a specialized binary Integer Linear Program (ILP) in combination with a Multi-Objective Evolutionary Algorithm (MOEA). The ILP is formulated such that each solution represents a topology and routing that fulfills all requirements and demands of the network. Thus, in an iterative process, this ILP is solved to obtain feasible networks whereas the MOEA is used for the optimization of multiple even non-linear objectives and ensures a fast convergence towards the optimal solutions. Additionally, a domain specific preprocessing algorithm for the ILP is presented that decreases the problem complexity and, thus, allows to optimize large and complex networks efficiently. The experimental results validate the performance of this methodology on two state-of-the-art prototype automotive networks.

Evolutionary algorithms have been shown to be very successful for a wide range of NP-hard combinatorial optimization problems. We investigate the NP-hard problem of computing a spanning tree that has a maximal number of leaves by evolutionary algorithms in the context of fixed parameter tractability (FPT) where the maximum number of leaves is the parameter under consideration. Our results show that simple evolutionary algorithms working with an edge-set encoding are confronted with local optima whose size of the inferior neighborhood grows with the value of an optimal solution. Investigating two common mutation operators, we show that an operator related to spanning tree problems leads to an FPT running time in contrast to a general mutation operator that does not have this property.

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