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A Comparison of Encodings and Algorithms for Multiobjective Minimum Spanning Tree Problems
 In Proceedings of the 2001 Congress on Evolutionary Computation (CEC'01
, 1997
"... this paper we apply (appropriately modified) the best of recent methods for the (degreeconstrained) 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, inv ..."
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this paper we apply (appropriately modified) the best of recent methods for the (degreeconstrained) 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 populationbased 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.
Multiobjective EA approach for improved quality of solutions for spanning tree problem
 in: Proc. Internat. Conf. Evolutionary MultiCriterion Optimization (EMO), Lecture Notes in Computer Science
, 2005
"... Abstract. The problem of computing spanning trees along with specific constraints is mostly NPhard. Many approximation and stochastic algorithms which yield a single solution, have been proposed. In this paper, we formulate the generic multiobjective spanning tree (MOST) problem and consider edge ..."
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Abstract. The problem of computing spanning trees along with specific constraints is mostly NPhard. Many approximation and stochastic algorithms which yield a single solution, have been proposed. In this paper, we formulate the generic multiobjective spanning tree (MOST) problem and consider edgecost and diameter as the two objectives. Since the problem is hard, and the Paretofront is unknown, the main issue in such probleminstances 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 diameterconstrained minimum spanning tree (dcMST) algorithms including randomized greedy heuristics (RGH) which represents the current state of the art on the dcMST, 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 entirerange of the Paretofront, which none of the existing algorithms could individually do. 1
A Comparative Assessment of Memetic, Evolutionary, and Constructive Algorithms for the Multiobjective dMST Problem
 Proc. of 2001 Genetic and Evolutionary Computation Conference Workshop Program
, 1997
"... Finding a minimumweight spanning tree ..."
A Primal BranchandCut Algorithm for the DegreeConstrained Minimum Spanning Tree Problem
"... Abstract. The degreeconstrained 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 branchandcut algorithm that solves instances of t ..."
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Abstract. The degreeconstrained 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 branchandcut 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 branchandcut program turns out to be competitive with other methods known in the literature. This shows the potential of the primal method. 1
Biobjective Evolutionary and Heuristic Algorithms for Intersection of Geometric Graphs
"... Wire routing in a VLSI chip often requires minimization of wirelength 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 ma ..."
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Wire routing in a VLSI chip often requires minimization of wirelength 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) Paretofront. 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.
Survivable and delayguaranteed backbone wireless mesh network design
, 2008
"... 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 ch ..."
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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 SelfConstituted 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 lowcost 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.
Ant Colony Optimization Approaches to the Degreeconstrained Minimum Spanning Tree Problem
"... This paper presents the design of two Ant Colony Optimization (ACO) approaches and their improved variants on the degreeconstrained minimum spanning tree (dMST) problem. The first approach, which we call pACO, uses the vertices of the construction graph as solution components, and is motivated by ..."
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This paper presents the design of two Ant Colony Optimization (ACO) approaches and their improved variants on the degreeconstrained minimum spanning tree (dMST) problem. The first approach, which we call pACO, uses the vertices of the construction graph as solution components, and is motivated by the wellknown Prim’s algorithm for constructing MST. The second approach, known as kACO, uses the graph edges as solution components, and is motivated by Kruskal’s algorithm for the MST problem. The proposed approaches are evaluated on two different data sets containing difficult dMST instances. Empirical results show that kACO performs better than pACO. We then enhance the kACO approach by incorporating the tournament selection, global update and candidate lists strategies. Empirical evaluations of the enhanced kACO indicate that on average, it performs better than Prüfercoded evolutionary algorithm (FEA), problem search space (PSS), simulated annealing (SA), branch and bound (B&B), Knowles and Corne’s evolutionary algorithm (KEA) and antbased algorithm (AB) on most problem instances from a wellknown class of data set called structured hard graphs. Results also show that it is very competitive with two other evolutionary algorithm based methods, namely weightcoded evolutionary algorithm (WEA), and edgeset representation evolutionary algorithm (SEA) on the same class of data set.