this paper we apply (appropriately modified) the best of recent methods for the (degree-constrained) single objective MST problem to the multiobjective MST problem, and compare with a method based on Zhou and Gen's approach. Our evolutionary computation approaches, using the different encodings, involve a new population-based variant of Knowles and Corne's PAES algorithm. We find the direct encoding to considerably outperform the Prufer encoding. And we find that a simple iterated approach, based on Prim's algorithm modified for the multiobjective MST, also significantly outperforms the Prufer encoding.

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

Finding a minimum-weight spanning tree

Abstract. The degree-constrained minimum spanning tree (DCMST) is relevant in the design of networks. It consists of finding a spanning tree whose nodes do not exceed a given maximum degree and whose total edge length is minimum. We design a primal branch-and-cut algorithm that solves instances of the problem to optimality. Primal methods have not been used extensively in the past, and their performance often could not compete with their standard ‘dual ’ counterparts. We show that primal separation procedures yield good bounds for the DCMST problem. On several instances, the primal branch-and-cut program turns out to be competitive with other methods known in the literature. This shows the potential of the primal method. 1

Wire routing in a VLSI chip often requires minimization of wire-length as well as the number of intersections among multiple nets. Such an optimization problem is computationally hard for which no efficient algorithm or good heuristic is known to exist. Additionally, in a biobjective setting, the major challenge to solve a problem is to obtain representative diverse solutions across the (near-) Pareto-front. In this work, we consider the problem of constructing spanning trees of two geometric graphs corresponding to two nets, each with multiple terminals, with a goal to minimize the total edge cost and the number of intersections among the edges of the two trees. We first design simple heuristics to obtain the extreme points in the solution space, which however, could not produce diverse solutions. Search algorithms based on evolutionary multiobjective optimization (EMO) are then proposed to obtain diverse solutions in the feasible solution space. Each element of this solution set is a tuple of two spanning trees corresponding to the given geometric graphs. Empirical evidence shows that the proposed evolutionary algorithms cover a larger range and are much superior to the heuristics.

Abstract not found

Backbone wireless mesh networks (BWMNs) consisting of wireless mesh routers are emerging alternatives to implementations of metropolitan area networks (MANs). In a BWMN, gateways connect to the Internet via wireline links and provide Internet access services for users. Due to the limited wireless channel bit rate, multiple gateways are usually required in a BWMN, which costs budget and takes time to set up. In this paper, we study the network topology design and the gateway arrangement so that the construction cost of a BWMN is minimal. Two algorithms, namely, the Predefined Gateway Set Algorithm (PGSA) and the Self-Constituted Gateway Algorithm (SCGA), are proposed for the BWMN design. A genetic algorithm and a proposed enhanced Djikstra’s algorithm are employed to search for the low-cost network configuration with constraints such as survivability, link capacity, degree limitation and maximum tolerable delay. Computational results show that the PGSA can give an acceptable network configuration rapidly. In case the gateway cost is high, using the SCGA can lower the network construction cost at the expense of more computational time.