Dynamic programming based heuristics for the topological design of local access networks

This paper deals with the terminal layout problem, which is a problem arising in data communication network design. The problem consists of finding the best way to link terminals to a computer site and, in graph-theoretical terms, it resorts to determining a minimal spanning tree with an additional constraint (CMST). We present a class of heuristics that combine dynamic programming with clustering and decomposition techniques. More specifically, the original problem is transformed, either by clustering or decomposition, in order to obtain smaller size problems that can be handled by a dynamic programming approach. Such heuristics were specifically aimed at improving solutions produced by the Esau-Williams algorithm, which is one of the most effective heuristics presented in the literature for the CMST. Actually, computational experience confirms that such improvements can be achieved by the new heuristic.This research was partially supported by JNICT (Junta Nacional de Investigação Científica e Tecnológica) under Research Contract No. 87383/MIC.     

Greedy heuristics for the diameter-constrained minimum spanning tree problem

The diameter-constrained minimum spanning tree problem is an NP-hard combinatorial optimization problem that seeks a minimum cost spanning tree with a limit D imposed upon the length of any path in the tree. We begin by presenting four constructive greedy heuristics and, secondly, we present some second-order heuristics, performing some improvements on feasible solutions, hopefully leading to better objective function values. We present a heuristic with an edge exchange mechanism, another that transforms a feasible spanning tree solution into a feasible diameter-constrained spanning tree solution, and finally another with a repetitive mechanism. Computational results show that repetitive heuristics can improve considerably over the results of the greedy constructive heuristics, but using a huge amount of computation time. To obtain computational results, we use instances of the problem corresponding to complete graphs with a number of nodes between 20 and 60 and with the value of D varying between 4 and 9.     

Fast heuristics for protection networks for dynamic routing

Traffic volatility and network reliability are important issues in the provision of high speed network services. We consider the construction of a second network, the protection network which can carry overload traffic due to the failure or congestion of any two links in the original network. The level of protection against such contingencies can be specified by a traffic requirement matrix. We construct a fully connected protection network, for an n node network, using an O(n²) heuristic based on the largest two traffic requirements for each node. This procedure is then modified to generate a more effective O(n⁴) heuristic, both methods facilitate fast processing for two-hop dynamic routing. We compare the performance of the heuristics with the O(n¹⁵) optimal solution.     

A five facets frame for the design of heuristics

The author suggested to distinguish between the ‘engineering approach’ and the ‘mathematical approach’ in connection with the design of heuristics. Stainton and Papoulias extended the scope by suggesting the ‘relational approach’. Based upon this extension, a five facets frame is presented here which is suggested to precede and accompany the ‘technical’ design of the heuristic. The facets are: coverage by participation, experience by doing, abstraction by structuring, extension by comparison, exploration by creativity.     

Randomized heuristics for handover minimization in mobility networks

A mobile device connects to the cell tower (base station) from which it receives the strongest signal. As the device moves it may connect to a series of towers. The process in which the device changes the base station it is connected to is called handover. A cell tower is connected to a radio network controller (RNC) which controls many of its operations, including handover. Each cell tower handles an amount of traffic and each radio network controller has capacity to handle a maximum amount of traffic from all base stations connected to it. Handovers between base stations connected to different RNCs tend to fail more often than handovers between base stations connected to the same RNC. Handover failures result in dropped connections and therefore should be minimized. The Handover Minimization Problem is to assign towers to RNCs such that RNC capacity is not violated and the number of handovers between base stations connected to different RNCs is minimized. We describe an integer programming formulation for the handover minimization problem and show that state-of-the-art integer programming solvers can solve only very small instances of the problem. We propose several randomized heuristics for finding approximate solutions of this problem, including a GRASP with path-relinking for the generalized quadratic assignment problem, a GRASP with evolutionary path-relinking, and a biased random-key genetic algorithm. Computational results are presented.     

Efficient implementation of heuristics for the continuous network design problem

In this paper, we present an efficient implementation of heuristic procedures for solving the continuous network design problem where network users behave according to Wardrop's first principle of traffic equilibrium. Numerical results involving a standard benchmark problem are given. Also, it is shown that the cost mapping arising in the Iterative-Optimization-Assignment algorithm is integrable if and only if the volume-delay function is of either the BPR or some logarithmic form.Research supported by the National Sciences and Engineering Research Council of Canada (Grant A5789) and the Academic Research Program of the Department of National Defense (Grant FUHBP).     

Fast heuristics for the Steiner tree problem with revenues,budget and hop constraints

This article describes and compares three heuristics for a variant of the Steiner tree problem with revenues, which includes budget and hop constraints. First, a greedy method which obtains good approximations in short computational times is proposed. This initial solution is then improved by means of a destroy-and-repair method or a tabu search algorithm. Computational results compare the three methods in terms of accuracy and speed.     

A five facet frame for the design of heuristics —A rejoinder

An argument was put forward by Stainton and Papoulias for an additional category of heuristics to those proposed by Müller-Merbach, which the authors called ‘relational’. In response to the subsequent suggestion by Müller-Merbach of a five facet frame for the design of heuristics, this paper sets out to expand upon and clarify the characteristics of the relational approach, as defined by the authors.     

Analysis of heuristics for finding a maximum weight planar subgraph

The problem of identifying a planar subgraph of maximum total weight in an edge-weighted graph has application to the layout of facilities in a production system and elsewhere in industrial engineering.This problem is NP-hard, and so we confine our attention to polynomial-time heuristics. In this paper we analyse the performance of some heuristics for this problem.     

Performance evaluation of scheduling control of queueing networks: Fluid model heuristics

Motivated by dynamic scheduling control for queueing networks, Chen and Yao [8] developed a systematic method to generate dynamic scheduling control policies for a fluid network, a simple and highly aggregated model that approximates the queueing network. This study addresses the question of how good these fluid policies are as heuristic scheduling policies for queueing networks. Using simulation on some examples these heuristic policies are compared with traditional simple scheduling rules. The results show that the heuristic policies perform at least comparably to classical priority rules, regardless of the assumptions made about the traffic intensities and the arrival and service time distributions. However, they are certainly not always the best and, even when they are, the improvement is seldom dramatic. The comparative advantage of these policies may lie in their application to nonstationary situations such as might occur with unreliable machines or nonstationary demand patterns.     

树状网络上的Web代理服务器最优放置问题

一般网络上Web代理服务器(Web proxy)最优放置问题是一个NP困难问题.此文讨论树状网络上的最优放置问题,改进了已有结果,得到了一个时间复杂度为O(nhk)的多项式时间算法,这里n为网络结点数,h为树的高度,而k为要放置的代理服务器个数.     

Minimal length tree networks on the unit sphere

This paper considers the problem of finding minimal length tree networks on the unit sphere of a given point set (V) where distance is measured along great circular arcs. The related problems of finding a Steiner Minimal TreeSMT(V) and of finding a Minimum Spanning TreeMST(V) are treated through a simplicial decomposition technique based on computing the Delaunay TriangulationDT(V) and the Voronoi DiagramVD(V) of the given point set.O(N logN) algorithms for computingDT(V),VD(V), andMST(V) as well as anO(N logN) heuristic for finding a sub-optimalSMT(V) solution are presented, together with experimental results for randomly distributed points on .     

An optimization-based approach for the design of Bayesian networks

Bayesian networks model conditional dependencies among the domain variables, and provide a way to deduce their interrelationships as well as a method for the classification of new instances. One of the most challenging problems in using Bayesian networks, in the absence of a domain expert who can dictate the model, is inducing the structure of the network from a large, multivariate data set. We propose a new methodology for the design of the structure of a Bayesian network based on concepts of graph theory and nonlinear integer optimization techniques.     

A self-tuning heuristic for the design of communication networks

This paper addresses the design of communication networks that has a large application area. The problem is to design a minimum cost network subject to a given reliability level. Complexity of the problem is twofold: (1) finding a minimum-cost network topology that every pair of nodes can communicate with each other and (2) computing overall reliability to provide the reliability constraint. Over the last two decades, metaheuristic algorithms have been widely applied to solve this problem due to its NP-hardness. In this study, a self-tuning heuristic (STH), which is a new approach free from parameter tuning, is applied to the design of communication networks. Extensive computational results confirm that STH generates superior solutions to the problem in comparison to some well-known local search metaheuristics, and also more sophisticated metaheuristics proposed in the literature. The practical advantage of STH lies in both its effectiveness and simplicity in application to the design problem.     

Long-term optimization model of tree water networks

This paper describes an optimization method to design, over a period of time, a radial water network consisting of pipes, pumps and pressure reducing valves. The network structure can be modified during the planning period by the addition or removal of certain nodes and elements. The evolution of the consumption at the nodes is known. The hydraulic constraints of pressure and flow velocity are respected throughout the studied period.The investment decisions are determined in such a manner as to minimize the sum of the present worth values of the investment costs and operation costs over the planning period.The choice of pipe lengths to be invested in each branch as variables allows one to formulate the dynamic investment problem as a multi-stage linear program. Each stage corresponds to the state of the network at a time of the planning period. Such a formulation of a combinatorial problem of investments allows one to design networks of large dimensions in the long term whilst maintaining acceptable times of computation.An application of the model to a real problem is presented.     

Design of tariff zones in public transportation networks: theoretical results and heuristics

The problem of fair zone design for local public transportation networks is considered. A network model which was introduced by Hamacher and Schöbel in [2] is investigated. We present theoretical results for special transportation networks and heuristic algorithms for the general problem.     

Constructive heuristics for the canister filling problem

The canister filling problem arises when optimizing the spent nuclear fuel repository in hard rock. It is shown the problem is NP-hard. Constructive heuristics followed by remove and reinsert local optimization are considered. Additionally, some theoretical insight on the algorithm operation is provided. Several variants of the algorithm are compared on random and realistic datasets. The obtained results have shown that constructive heuristics give satisfactory results for both random and realistic input data, although there is still some room for improvements.