# A Global Optimization Algorithm For Solving The Minimum Multiple Ratio Spanning Tree Problem

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### An Analysis of Feature Selection Algorithm and their

on problem-solving issues in engineering progresses and influence in the advancement of artificial intelligence . Metaheuristics algorithms implement Evolutionary feature selection algorithms. The purpose of Evolutionary feature selection algorithms is to search space with the assessment of global and local functions.

### Optimization Modeling with LINGO by Linus Schrage

Optimization Modeling with LINGO by Linus Schrage Preface

### IEEE TRANSACTIONS ON ROBOTICS, VOL. 32, NO. 5, OCTOBER 2016

common global objectives for MPP. The resulting algorithms, in particular the one for computing the minimum makespan, are highly effective in solving challenging problem instances with a robot-vertex ratio up to 100%. Second, we introduce several principled heuristics, in particular a k-way split heuristic that

### An FPTAS for optimizing a class of low-rank functions over a

spanning tree problem and the shortest path problem. 3. Hardness of approximation result: We show that unless P = NP, it is not pos-sible to approximate the minimum of a positive valued concave function over a polytope to within any factor, even if the polytope is the unit hypercube (Sect. 6).

### Parallel Minimum Spanning Tree Heuristic for the Steiner

while when N = V the problem reduces to the minimum spanning tree problem. Both these problems can be solved in polynomial time. On the other hand, the Steiner tree problem is NP-hard when the graph G is a chordal graph, a bipartite graph or a complete graph with edge weights either 1 or 2. Thus in the general case the problem is an NP-hard

### An FPTAS for Optimizing a Class of Low-Rank Functions

of low-rank functions over a polytope. An FPTAS for a minimization (resp. maximization) problem is a family of algorithms such that for all >0 there is a (1 + )-approximation (resp. (1 )-approximation) algorithm for the problem, and the running time of the algorithm is polynomial in the input size of the problem, as well as in 1=

### quantity of that product. Such models, wherein functions

R. Chandrasekaran considers in  the minimal spanning tree problem. For a given undirected connected graph G - ( JP, E) with node set N and edge set E and given numbers xt and yt, i e E, the problem is to find a spanning tree T such that the ratio is minimized. гет ieT W. T. Ziemba, F. J. Brooks-Hill and C. Parkan ,  arrive

### Research Article Geometry-Experiment Algorithm for Steiner

It is well known that the Steiner minimal tree problem is one of the classical nonlinear combinatorial optimization problems. A visualization experiment approach succeeds in generating Steiner points automatically and showing the system shortest path, named Steiner minimum tree, physically and intuitively.

### Oleg A. Prokopyev

Sep 05, 2019 oleg a. prokopyev curriculum vitae (updated 9/5/2019) department of industrial engineering university of pittsburgh 1031 benedum hall, pittsburgh, pa 15261 phone: (412) 624-9833 fax: (412) 624-9831

### Computational Intelligence Based Efficient Routing in MANET

ratio and end-to-end delay but still it has a routing problem when it turn out to be dynamic optimization problem in MANET s. Sathish, Thangavel and Vaidehi . In this paper proposed a cache based ant colony routing for mobile adhoc networks for building highly adaptive and on-demand routing algorithm initiated by source.

### Shorten the Trajectory of Mobile Sensors in Sweep Coverage

sensors to visit all PoIs with minimum energy consumption is a challenging problem. In this paper, we introduce an optimization problem to minimize the makespan of mobile sweep routes (M3SR) and prove its NP-hardness on 2D plane. We then a greedy algorithm named GD-Sweep and an approximation named BS-Sweep to solve M3SR. We prove theoretically

### Improved Minimum Spanning Tree Heuristics for Steiner Tree

heuristic algorithm about Steiner tree problem has important practical and theoretical significance. In this paper we first review one of the existing algorithms for solving the Steiner problem in graphs, Minimum Spanning Tree Heuristic algorithm, then presenting a new heuristic algorithm IMSTH to improve it.

### Hybrid Two-Stage Algorithm for Solving Transportation Problem

exploit the spanning tree special data structure for the TP to develop a GA for solving the bicriteria TP. Kutcha and Chanas (1998) proposed an algorithm to solve the TP when the integrality condition imposed on the solution.

### Convergent Propagation Algorithms via Oriented Trees

ing algorithm for a speciﬁc variational setup, namely the Tree-Reweighted (TRW) optimization problem of Wainwright et al. . The algorithm we propose is guaranteed to converge to the global optimum of the free energy, and does not require additional parame-ters such as the damping ratio. A key step in obtain-

### Learning Local Algorithms with Global Views for Graph

The best known algorithm for solving a general linear system takes time 𝒪𝒪(𝑛𝑛 2.373) Kelner et al. (2013) proposed an algorithm for solving Laplacian system: 𝐿𝐿𝐿𝐿= 𝑏𝑏, where 𝐿𝐿is Laplacian matrix in nearly-linear time. Step 1: Find a low-stretch spanning tree and obtain an initial solution on the tree.

### Solving the MDBCS Problem Using the Metaheuric Genetic Algorithm

spanning tree for the subgraph The following theorem proves the correctness of the above ILP model.  The MDBCS problem can be solved if and - (7) holds or their equivalent set of conditions. II. METAHEURISTIC GENETIC ALGORITHM FOR SOLVING THE MDBCS PROBLEM Genetic algorithms (GA) are a family of algorithms, which

### Oleg A. Prokopyev

Apr 26, 2019 OLEG A. PROKOPYEV 4 45.O. Ursulenkoz, S. Butenko, O.A. Prokopyev, A Global Optimization Algorithm for Solving the Min- imum Multiple Ratio Spanning Tree Problem, Journal of Global Optimization, Vol. 56/3 (2013), pp.

### Optimization Modeling with LINGO - Gunadarma

Preliminary Edition Optimization Modeling with LINGO Sixth Edition LINDO Systems, Inc. 1415 North Dayton Street, Chicago, Illinois 60622 Phone: (312)988-7422 Fax: (312)988-9065

### Memetic Algorithm-Based Multi-Objective Coverage Optimization

Section 3 discusses the multi-objective optimization coverage problem of WSNs. Section 4 presents the key schemes for the proposed coverage algorithm for WSNs. Section 5 describes the multi-objective optimization coverage algorithm based on memetic algorithms. The simulation experiments and evaluation are given in Section 6.

### Multifactorial Evolutionary Algorithm For Clustered Minimum

Multifactorial Evolutionary Algorithm For Clustered Minimum Routing Cost Problem SoICT 2019, December 4 6, 2019, Hanoi - Ha Long Bay, Viet Nam In recent literature, MFEA  is a newly founded

### Oleg A. Prokopyev

Nov 14, 2014 Ursulenkoz, S. Butenko, O.A. Prokopyev, A Global Optimization Algorithm for Solving the Min- imum Multiple Ratio Spanning Tree Problem, Journal of Global Optimization, Vol. 56/3 (2013), pp. 1029 1043.

### A Study on Applying Parallelism for Construction of Steiner

the rectilinear minimum spanning tree (RMST) to that of an optimum RST is no greater than 3/2. Therefore the rectilinear MST is a suitable starting point for deriving low cost RST. Ho,Vijayan and CK Wong  presented a new approach to construct an RST of a given set of points in the plane starting from a Minimum Spanning tree.

### Shorten the Trajectory of Mobile Sensors in Sweep Coverage

sensors to visit all PoIs with minimum energy consumption is a challenging problem. In this paper, we introduce an optimization problem to minimize the makespan of mobile sweep routes (M3SR) and prove its NP-hardness on 2D plane. We then design a greedy algorithm named GD-Sweep and an approximation named BS-Sweep to solve M3SR. We prove

### SHORTEST PATH IDENTIFICATION USING PSO AND ABC ALGORITHM

In [Fábio Hernandes et.al] shortest problem on network is implemented with fuzzy parameter. Oriented Spanning tree based genetic algorithm is used for shortest path. Here Multi-criteria shortest path is considered. ACO is also one of the optimization technique, in [Andrei Lissovoi and Carsten Wit] International Journal of Mathematics and

### Tree Growth Based ACO Algorithm for Solving the Bandwidth

jitter, and packet loss ratio. The main problem of QoS routing is to set up a least-cost multicast tree, i.e. a tree covering a group of destinations with the minimum total cost over all the links, which satisfies certain QoS parameters. However, the problem of constructing a multicast tree under multiple constraints is NP Complete .

### Particle Swarm Optimization with Minimum Spanning Tree

To this end, we propose a minimum spanning tree (MST) topology for PSO to solve multimodal problems. Particles are viewed as vertices in the search space. In each iteration, a fully connected graph is constructed based on the configuration of particles. Each pair of particles are connected by a weighted edge. A minimum spanning tree is

### Chemical reaction optimization for solving longest common

Tree search method for solving LCS problem was initiated by and Hsu where they used minimum spanning tree (Tsai and optimization algorithm is proposed by Islam et al. (2015)

### Wisdom of the Crowd in Locality Aware Graph Traversals

optimization problems. Such problems require coordinating multiple pieces of information, as opposed to estimating a single numerical value (e.g. the height of a person). Yi et al.  studied the wisdom of the crowd phenomenon for the minimum spanning tree problem (MSTP) and extended it to the traveling salesman problem (TSP) in 

### Modularity Based Image Segmentation

deﬁned as the largest weight in the minimum spanning tree of component C; ˝(C) = k=jCj, and kis a constant parameter to control the minimize size of the segment. This algorithm gives nearly linear time complexity, however, it is very difﬁcult to tune the parameter kfor optimal segmentation. Normalized Cut , as another popular graph

### Physarum Optimization: A Biology-inspired Algorithm for the

The Steiner tree problem is superﬁcially similar to the minimum spanning tree problem. solving the Steiner tree problem. stochastic optimization algorithm with a global search for

### Oleg A. Prokopyev - Pitt

Sep 29, 2020 oleg a. prokopyev curriculum vitae (updated 9/29/2020) department of industrial engineering university of pittsburgh 1031 benedum hall, pittsburgh, pa 15261 phone: (412) 624-9833 fax: (412) 624-9831

### Preferred Direction Steiner Trees

The general Steiner tree problem is to construct a tree of minimal cost or minimal length, spanning a set of demand points and possibly some additional Steiner points. Without Steiner points, the problem is simply one of constructing a minimum spanning tree (MST), and the algorithms of Kruskal  and Prim  are well known and computa-

### Peng Hou,Student Member, IEEE Member, IEEE Senior Member

minimum investment, more and more researchers are concen-141 trating on solving the wind farm layout optimization (WFLO) 142 problem with evolutional algorithms.

### Oleg A. Prokopyev - Pitt

May 11, 2020 oleg a. prokopyev curriculum vitae (updated 5/11/2020) department of industrial engineering university of pittsburgh 1031 benedum hall, pittsburgh, pa 15261 phone: (412) 624-9833 fax: (412) 624-9831

### A Genetic Algorithm for Steiner Tree Optimization with

A Genetic Algorithm for Steiner Tree Optimization with Multiple Constraints 275 The Steiner trees contain a variable number of nodes in the range from m+1 to n, and their associated Prüfer

### Energy Efficient Routing Protocol for Maximizing the Lifetime

selects optimum one for route. Comparison with minimum spanning tree algorithm, least energy tree algorithm, and Dijkstra algorithm is presented. Numerical experiments show that the proposed routing algorithm gained lifetime best than the other three routing algorithms along with keeping power consumption in low level.

### ThomasLengauer,MajidSarrafzadeh, DorotheaWagner(editors

service radius and total wiring length. To solve the problem, we restrict the points to tree topology, e.g., a minimum spanning tree. We then solve a bounded fan out p center problem on the tree to cluster the points. An (ˇ)(n log2 n) algorithm is given for solving this problem. Experimental results show that this approach is promising.

### Optimization Modeling with LINGO

Optimization Modeling with LINGO Preface

### EXACT METHODS IN FRACTIONAL COMBINATORIAL OPTIMIZATION

three, probably, most classical FCOPs: Minimum Multiple Ratio Spanning Tree (MMRST), Minimum Multiple Ratio Path (MMRP) and Minimum Multiple Ratio Cycle (MMRC). The rst two problems are studied in detail, while for the other one only the theoretical complexity issues are addressed.