Breakout local search for the Steiner tree problem with revenue, budget and hop constraints

Fu, Zhang-Hua; Hao, Jin‐Kao

doi:10.1016/j.ejor.2013.06.048

Cited by 22 publications

(26 citation statements)

References 15 publications

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“…The two latter works provide computational results on the instances from sets B and C1 to C5, but offer no consistent speed up, when compared to [6]. Recently, a breakout local search algorithm (see [13]) and a memetic algorithm (see [14]) have been proposed. These two recent papers provide improved feasible solutions for some of the unsolved instances (C6 to C20).…”

Section: Figure 1 Depicts An Instance Of the Stprbh And Its Optimal Smentioning

confidence: 99%

“…For all G3 instances, heuristics from [7,13,14] were able to establish corresponding feasible (and, thus, optimal) solutions connecting all profitable nodes within the given budget. The size of this group is 124.…”

Section: Instancesmentioning

confidence: 99%

“…In this work, we consider a variant of the SPG known as the Steiner tree problem with revenues, budget and hop-constraints (STPRBH), whose definition is given below. The problems has been intensively studied in the last years using exact [7,22,27] and heuristic [6,13,14] approaches.…”

Section: Introductionmentioning

confidence: 99%

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A node-based layered graph approach for the Steiner tree problem with revenues, budget and hop-constraints

Sinnl

Ljubić

2016

Math. Prog. Comp.

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The Steiner tree problem with revenues, budget and hop-constraints (STPRBH) is a variant of the classical Steiner tree problem. The goal is to find a tree maximizing the collected revenue, which is associated with nodes, subject to a given budget for the edge cost of the tree and a hop-limit for the distance between the given root node and any other node in that tree. In this work, we introduce a novel generic way to model hop-constrained tree problems as integer linear programs and apply it to the STPRBH. Our approach is based on the concept of layered graphs that gained widespread attention in the recent years, due to their computational advantage when compared to previous formulations for modeling hop-constraints. Contrary to previous MIP formulations based on layered graphs (that are arc-based models), our model is node-based. Thus it contains much less variables and allows to tackle largescale instances and/or instances with large hop-limits, for which the size of arc-based layered graph models may become prohibitive. The aim of our model is to provide a good compromise between quality of root relaxation bounds and the size of the underlying MIP formulation. We implemented a branch-and-cut algorithm for the STPRBH based on our new model. Most of the instances available for the DIMACS challenge, including 78 (out of 86) previously unsolved ones, can be solved to proven optimality within a time limit of 1000 s, most of them being solved within a few seconds only. These instances contain up to 500 nodes and 12,500 edges, with hop-limit up to 25.

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Section: Figure 1 Depicts An Instance Of the Stprbh And Its Optimal Smentioning

confidence: 99%

Section: Instancesmentioning

confidence: 99%

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A node-based layered graph approach for the Steiner tree problem with revenues, budget and hop-constraints

Sinnl

Ljubić

2016

Math. Prog. Comp.

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“…Nevertheless, TPS is distinguished by its local optima exploring phase and its perturbation mechanisms which share similarities with breakout local search (Benlic & Hao, 2013a;2013c;Fu & Hao, 2014). …”

Section: General Frameworkmentioning

confidence: 99%

“…Like the compact tree representation used in (Cordone & Passeri, 2012;Fu & Hao, 2014), we uniquely represent each feasible solution T as a rooted tree (with vertex 1 fixed as the root vertex, being different from (Cordone & Passeri, 2012) where the root changes dynamically during the search process), corresponding to a one-dimensional vector T = {t i , i ∈ V }, where t i denotes the parent vertex of vertex i only except the root vertex 1 (let t 1 = null). Inversely, given a vector T = {t i , i ∈ V }, the corresponding solution tree can be easily reconstructed.…”

Section: Solution Presentationmentioning

confidence: 99%

A three-phase search approach for the quadratic minimum spanning tree problem

Hao

2015

Engineering Applications of Artificial Intelligence

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Given an undirected graph with costs associated with each edge as well as each pair of edges, the quadratic minimum spanning tree problem (QMSTP) consists of determining a spanning tree of minimum total cost. This problem can be used to model many real-life network design applications, in which both routing and interference costs should be considered. For this problem, we propose a three-phase search approach named TPS, which integrates 1) a descent-based neighborhood search phase using two different move operators to reach a local optimum from a given starting solution, 2) a local optima exploring phase to discover nearby local optima within a given regional search area, and 3) a perturbation-based diversification phase to jump out of the current regional search area. Additionally, we introduce dedicated techniques to reduce the neighborhood to explore and streamline the neighborhood evaluations. Computational experiments based on hundreds of representative benchmarks show that TPS produces highly competitive results with respect to the best performing approaches in the literature by improving the best known results for 31 instances and matching the best known results for the remaining instances only except two cases. Critical elements of the proposed algorithms are analyzed.

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An improved EDA for solving Steiner tree problem

Liu

Wang

Kong

2015

Concurrency and Computation

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SUMMARYSteiner tree problem and its derivations are widely employed to optimize the design of transportation, communication networks, biological engineering and the QoS multicast routing problem. It is one of well-defined open issues which have attracted many research efforts. Different from the existing works, this paper develops a new method of solving Steiner tree problem by using the improved estimation of distribution algorithms (EDA). Further, the performance of developed method is validated by applying on multicast routing optimization. The developed method randomly initializes n trees which contain the source node and the destination nodes. And some individuals select the crossover operation randomly to add the population diversity and avoid the algorithm premature convergence. The algorithm constructs a probabilistic model according to the selected elites, which is capable of estimating the probability distribution of the solution. The probabilistic model is updated according to the new population. New trees are generated based on the probabilistic model. This process iterated until designated termination criteria are met. The improved EDA algorithm gradually evolves trees to obtain a better solution. Simulation validations suggest that the developed method leads to better performance. In particular, the complexity in terms of the converging speed improves significantly compared to other algorithms.

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Breakout local search for the Steiner tree problem with revenue, budget and hop constraints

Cited by 22 publications

References 15 publications

A node-based layered graph approach for the Steiner tree problem with revenues, budget and hop-constraints

A node-based layered graph approach for the Steiner tree problem with revenues, budget and hop-constraints

A three-phase search approach for the quadratic minimum spanning tree problem

An improved EDA for solving Steiner tree problem

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