The bounded diameter minimum spanning tree problem is an NP-hard combinatorial optimiza-tion problem with applications in various fields like communication network design. We propose a general variable neighborhood search approach for it, utilizing four different types of neighbor-hoods. They were designed in a way enabling an efficient incremental evaluation and search for the best neighboring solution. An experimental comparison on instances with complete graphs with up to 1000 nodes indicates that this approach consistently outperforms the so far leading evolutionary algorithms with respect to solution quality and computation time.

The bounded diameter minimum spanning tree (BDMST) problem is NP-hard and appears e.g. in communication network design when considering certain quality of service requirements. Prior exact approaches for the BDMST problem mostly rely on network flow-based mixed integer linear programming and Miller-Tucker-Zemlin-based formulations. This article presents a new, compact 0–1 integer linear programming model, which is further strengthened by dynamically adding violated connection and cycle elimination constraints within a branch-and-cut environment. The proposed approach is empirically compared to two recently published formulations. It turns out to work well in particular on dense instances with tight diameter bounds.

In numerous practical applications, it is necessary to find the smallest possible tree with a bounded diameter. A diameter-constrained minimum spanning tree (DCMST) of a given undirected, edge-weighted graph, G, is the smallest-weight spanning tree of all spanning trees of G which contain no path with more than k edges, where k is a given positive integer. The problem of finding a DCMST is NP-complete for all values of k; 4 k (n -- 2), except when all edge-weights are identical. A DCMST is essential for the efficiency of various distributed mutual exclusion algorithms, where it can minimize the number of messages communicated among processors per critical section. It is also useful in linear lightwave networks, where it can minimize interference in the network by limiting the traffic in the network lines. Another practical application requiring a DCMST arises in data compression, where some algorithms compress a file utilizing a tree data-structure, and decompress a path in the tree to access a record. A DCMST helps such algorithms to be fast without sacrificing a lot of storage space. We present a survey of the literature on the DCMST problem, study the expected diameter of a random labeled tree, and present five new polynomial-time algorithms for an approximate DCMST. One of our new algorithms constructs an approximate DCMST in a modified greedy fashion, employing a heuristic for selecting an edge to be added to iii the tree in each stage of the construction. Three other new algorithms start with an unconstrained minimum spanning tree, and iteratively refine it into an approximate DCMST. We also present an algorithm designed for the special case when the diameter is required to be no more than 4. Such a diameter-4 tree is also used for evaluating the quality of o...

We consider the Bounded Diameter Minimum Spanning Tree problem and describe four neighbourhood searches for it. They are used as local improvement strategies within a variable neighbourhood search (VNS), an evolutionary algorithm (EA) utilising a new encoding of solutions, and an ant colony optimisation (ACO). We compare the performance in terms of effectiveness between these three hybrid methods on a suite of popular benchmark instances, which contains instances too large to solve by current exact methods. Our results show that the EA and the ACO outperform the VNS on almost all used benchmark instances. Furthermore, the ACO yields most of the time better solutions than the EA in long-term runs, whereas the EA dominates when the computation time is strongly restricted.

Given an undirected connected graph G = (V,E) with a set V of vertices, a set E of edges, and costs cij associated to every edge [i,j] ∈ E, with i < j, the Diameter Minimum Spanning Tree Problem (DCMST) consists in finding a minimum spanning tree T = (V,E ′), with E ′ ⊆ E, where the diameter

. In the operation of communication and computer networks, it may become desirable or necessary to add a new function to the network through the placement of the corresponding electronic device within certain existing user locations. This will involve deciding which user locations will have devices placed at them as well as deciding an assignment of users to device locations. The objective when adding the new function is to choose these locations and assignments such that the combined cost of placing the devices and routing users to their assigned device locations is minimized. This problem, which we call the device placement problem, is closely related to the simple plant location problem and the p-median problem. Like these problems, the device placement problem is NP-hard, and thus it is highly unlikely that efficient methods for solving this problem to optimality exist. We discuss and test several heuristic methods for the device placement problem, as well as a very efficient meth...

this paper we consider a restricted version of the problem of locating "access facilities", or concentration points, to permit economical connection of users to resources. This problem has been already studied [16]. Actually, we consider only one resource that does not have a important place in the optimization problem. This assumption leads to a strong relation with the problem of finding a minimum r-rooted 2-height spanning tree, giving as result conceptually easy heuristics, that are easilly implemented as well. In the next section we describe in details the restricted concentrator location problem, and some related problems often found in the literature. In section

Abstract — In this paper, a new hybrid genetic algorithm – known as HGA – is proposed for solving the Bounded Diameter Minimum Spanning Tree (BDMST) problem. We experiment with HGA on two sets of benchmark problem instances, both Euclidean and Non-Euclidean. On the Euclidean problem instances, HGA is shown to outperform the previous best two Genetic Algorithms (GAs) reported in the BDMST literature, while on the Non-Euclidean problem instance, HGA performs comparably with these two GAs. T I.

combinatorial optimization problems which have their main application in network design. In this thesis an existing relax-and-cut approach for finding lower bounds and approximate solutions to those problems is enhanced and extended, and a hybrid algorithm based on the relax-and-cut approach as well as on an existing metaheuristic, namely an ant colony optimization (ACO), is presented. The enhanced relax-and-cut (R&C) approach is based on an integer linear programming (ILP) formulation which relies on so called jump constraints. The number of jump constraints in this formulation is exponential by means of the instance size. Therefore, violated constraints are identified and relaxed on the fly. The enhanced R&C algorithm is a so called non deleayed relax-and-cut algorithm which is based on subgradient optimization. Since the number of separated jump inequalities can be large, a sophisicated management of a pool of such constraints is used. The two main extensions to this R&C approach are the initial identification of jump constraints with