Showing papers on "Minimum weight published in 2018"
01 Jul 2018
TL;DR: A fast local search algorithm for the minimum weight dominating set problem, which aims to obtain a good solution on massive graphs within a short time, and proposes the three-valued two-level configuration checking strategy to improve local search, which is interestingly a variant of configuration checking with two levels and multiple values.
Abstract: The minimum weight dominating set (MWDS) problem is NP-hard and also important in many applications. Recent heuristic MWDS algorithms can hardly solve massive real world graphs effectively. In this paper, we design a fast local search algorithm called FastMWDS for the MWDS problem, which aims to obtain a good solution on massive graphs within a short time. In this novel local search framework, we propose two ideas to make it effective. Firstly, we design a new fast construction procedure with four reduction rules to cut down the size of massive graphs. Secondly, we propose the three-valued two-level configuration checking strategy to improve local search, which is interestingly a variant of configuration checking (CC) with two levels and multiple values. Experiment results on a broad range of massive real world graphs show that FastMWDS finds much better solutions than state of the art MWDS algorithms.
38 citations
TL;DR: The results of this research show that the proposed PSO-SA hybrid algorithm can reliably and effectively be used for composite weight optimization problems subjected to a variety of constraints.
36 citations
01 Jul 2018
TL;DR: This work proposes two dynamic strategies that adjust the behavior of the algorithm during search, which are used to improve a state of the art local search for MWVC named FastWVC, resulting in two local search algorithms called DynW VC1 and DynWVC2.
Abstract: The minimum weight vertex cover (MWVC) problem is an important combinatorial optimization problem with various real-world applications. Due to its NP hardness, most works on solving MWVC focus on heuristic algorithms that can return a good quality solution in reasonable time. In this work, we propose two dynamic strategies that adjust the behavior of the algorithm during search, which are used to improve a state of the art local search for MWVC named FastWVC, resulting in two local search algorithms called DynWVC1 and DynWVC2. Previous MWVC algorithms are evaluated on graphs with random or hand crafted weights. In this work, we evaluate the algorithms on the vertex weighted graphs that obtained from an important real world problem, the map labeling problem. Experiments show that our algorithm obtains better results than previous algorithms for MWVC and maximum weight independent set (MWIS) on these real world instances. We also test our algorithms on massive graphs studied in previous works, and show significant improvements there.
28 citations
Posted Content•
16 Nov 2018
TL;DR: It is empirically show that the minimum norm solution is not necessarily the proper gauge of good generalization in simplified scenaria, and different models found by adaptive methods could outperform plain gradient methods.
Abstract: This work is substituted by the paper in arXiv:2011.14066. Stochastic gradient descent is the de facto algorithm for training deep neural networks (DNNs). Despite its popularity, it still requires fine tuning in order to achieve its best performance. This has led to the development of adaptive methods, that claim automatic hyper-parameter optimization. Recently, researchers have studied both algorithmic classes via toy examples: e.g., for over-parameterized linear regression, Wilson et. al. (2017) shows that, while SGD always converges to the minimum-norm solution, adaptive methods show no such inclination, leading to worse generalization capabilities. Our aim is to study this conjecture further. We empirically show that the minimum weight norm is not necessarily the proper gauge of good generalization in simplified scenaria, and different models found by adaptive methods could outperform plain gradient methods. In practical DNN settings, we observe that adaptive methods can outperform SGD, with larger weight norm output models, but without necessarily reducing the amount of tuning required.
26 citations
TL;DR: An improved heuristic algorithm for finding minimum weight vertex covers and a quantum-behaved particle swarm optimization with immune mechanism is presented, which can avoid the phenomenon of premature, improve the global searching ability, and enhance the convergence speed.
20 citations
18 citations
TL;DR: The basis of the methodology is the cylindrical algebraic decomposition algorithm, in tandem with powerful symbolic computation for the discovery of stationary points, for the minimum weight design of trusses.
Abstract: In this study, a method for the analytical evaluation of globally optimal solutions for the minimum weight design of trusses is presented. The basis of the methodology is the cylindrical algebraic decomposition algorithm, in tandem with powerful symbolic computation for the discovery of stationary points. Certain final answers to well-known benchmark problems are produced, while future improvements in both the algorithm implementation and the computer capabilities may allow the solution of even more difficult problems. To the best of our knowledge, no similar attempt can be found in the literature.
17 citations
23 Jul 2018
TL;DR: In this paper, the authors presented a randomized O(D + √ )-round O(logn )-approximation algorithm for 2-ECSS, for a graph with n vertices and diameter D. The time complexity of this algorithm is almost tight and almost matches the time complexity for the MST problem.
Abstract: In the minimum k-edge-connected spanning subgraph (k-ECSS) problem the goal is to find the minimum weight subgraph resistant to up to k-1 edge failures. This is a central problem in network design, and a natural generalization of the minimum spanning tree (MST) problem. While the MST problem has been studied extensively by the distributed computing community, for k ≥2 less is known in the distributed setting. In this paper, we present fast randomized distributed approximation algorithms for k-ECSS in the CONGEST model. Our first contribution is an O (D + √ )-round O(logn )-approximation for 2-ECSS, for a graph with n vertices and diameter D. The time complexity of our algorithm is almost tight and almost matches the time complexity of the MST problem. For larger constant values of k we give an O (n) -round O(logn ) -approximation. Additionally, in the special case of unweighted 3-ECSS we show how to improve the time complexity to O(D log^3n ) rounds. All our results significantly improve the time complexity of previous algorithms.
15 citations
Posted Content•
TL;DR: It is empirically show that the minimum weight norm is not necessarily the proper gauge of good generalization in simplified scenaria, and different models found by adaptive methods could outperform plain gradient methods.
Abstract: This work is substituted by the paper in arXiv:2011.14066.
Stochastic gradient descent is the de facto algorithm for training deep neural networks (DNNs). Despite its popularity, it still requires fine tuning in order to achieve its best performance. This has led to the development of adaptive methods, that claim automatic hyper-parameter optimization. Recently, researchers have studied both algorithmic classes via toy examples: e.g., for over-parameterized linear regression, Wilson et. al. (2017) shows that, while SGD always converges to the minimum-norm solution, adaptive methods show no such inclination, leading to worse generalization capabilities. Our aim is to study this conjecture further. We empirically show that the minimum weight norm is not necessarily the proper gauge of good generalization in simplified scenaria, and different models found by adaptive methods could outperform plain gradient methods. In practical DNN settings, we observe that adaptive methods can outperform SGD, with larger weight norm output models, but without necessarily reducing the amount of tuning required.
13 citations
TL;DR: In this article, an approach to fault tolerant quantum computing based on a simple error detecting code operating as the substrate for a conventional surface code is presented. But the approach is not suitable for the case of asymmetric noise.
Abstract: We consider an approach to fault tolerant quantum computing based on a simple error detecting code operating as the substrate for a conventional surface code. We develop a customised decoder to process the information about the likely location of errors, obtained from the error detect stage, with an advanced variant of the minimum weight perfect matching algorithm. A threshold gate-level error rate of 1.42% is found for the concatenated code given highly asymmetric noise. This is superior to the standard surface code and remains so as we introduce a significant component of depolarising noise; specifically, until the latter is 70% the strength of the former. Moreover, given the asymmetric noise case, the threshold rises to 6.24% if we additionally assume that local operations have 20 times higher fidelity than long range gates. Thus for systems that are both modular and prone to asymmetric noise our code structure can be very advantageous.
13 citations
TL;DR: In this paper, a classification of four-circulant singly even self-dual [60, 30,d] codes for $$d=10$$ and 12 was given.
Abstract: We give a classification of four-circulant singly even self-dual [60, 30, d] codes for $$d=10$$
and 12. These codes are used to construct extremal singly even self-dual [60, 30, 12] codes with weight enumerator for which no extremal singly even self-dual code was previously known to exist. From extremal singly even self-dual [60, 30, 12] codes, we also construct optimal singly even self-dual [58, 29, 10] codes with weight enumerator for which no optimal singly even self-dual code was previously known to exist. Finally, we give some restriction on the possible weight enumerators of certain singly even self-dual codes with shadow of minimum weight 1.
TL;DR: It is formally proved that Prim's minimum spanning tree algorithm is correct for various optimisation problems with different aggregation functions and new algebraic structures are worked in that capture key operations used in Prim's algorithm and its specification.
TL;DR: In this article, the authors studied binary linear complementary dual codes with the largest minimum weight for small dimensions and provided a complete classification of binary LCLPDD codes with minimum weights.
Abstract: Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study binary linear complementary dual $[n,k]$ codes with the largest minimum weight among all binary linear complementary dual $[n,k]$ codes. We characterize binary linear complementary dual codes with the largest minimum weight for small dimensions. A complete classification of binary linear complementary dual $[n,k]$ codes with the largest minimum weight is also given for $1 \le k \le n \le 16$.
TL;DR: The Multiway-Cut problem is a fundamental graph partitioning problem in which the objective is to find a minimum weight set of edges disconnecting a given set of special vertices called termina...
Abstract: The \sf Multiway-Cut problem is a fundamental graph partitioning problem in which the objective is to find a minimum weight set of edges disconnecting a given set of special vertices called termina...
TL;DR: This work introduces a hybrid matheuristic combining a tabu search with an integer programming solver to solve the problem of a minimum dominating set in a graph, and introduces an adaptive penalty to promote the exploration of intermediate infeasible solutions during the search.
TL;DR: A binary particle swarm optimization (FBPSO) for solving the MWDSP approximately is proposed, which designs a new position updating rule to guide the search to a promising area and grows much more slowly than that of other existing algorithms.
Abstract: The minimum weight dominating set problem (MWDSP) is an NP-hard problem with a lot of real-world applications. Several heuristic algorithms have been presented to produce good quality solutions. However, the solution time of them grows very quickly as the size of the instance increases. In this paper, we propose a binary particle swarm optimization (FBPSO) for solving the MWDSP approximately. Based on the characteristic of MWDSP, this approach designs a new position updating rule to guide the search to a promising area. An iterated greedy tabu search is used to enhance the solution quality quickly. In addition, several stochastic strategies are employed to diversify the search and prevent premature convergence. These methods maintain a good balance between the exploration and the exploitation. Experimental studies on 106 groups of 1 060 instances show that FBPSO is able to identify near optimal solutions in a short running time. The average deviation between the solutions obtained by FBPSO and the best known solutions is 0.441%. Moreover, the average solution time of FBPSO is much less than that of other existing algorithms. In particular, with the increasing of instance size, the solution time of FBPSO grows much more slowly than that of other existing algorithms.
29 Apr 2018
TL;DR: Adaptive Single Objective method was chosen as an optimizer method and the results show that the structural weight of the bus frame can be reduced about 8% without changing its dynamic characteristic.
Abstract: The objective of this work is to analyze and optimize a bus frame structure using Finite Element Method in dynamic conditions. The bus body geometry was obtained directly from the three-dimensional Computer-Aided Design files. The optimization was conducted to determine the minimum weight of the bus frame structure without violating the specified natural frequency constraints. The design variable is the thickness of the bus body frame. In present study, Adaptive Single Objective method was chosen as an optimizer method. The results show that the structural weight of the bus frame can be reduced about 8% without changing its dynamic characteristic.
TL;DR: It is shown that for q even all minimum weight codewords are equivalent and that symplectic line-Grassmann codes are proper subcodes of codimension 2 n of the orthogonal ones.
01 Jan 2018
TL;DR: In this paper, a planar graph G = V,E with polynomially bounded edge weight function w:E -> [0, poly(n)] is considered, and the main results of this paper are NC algorithms for finding minimum weight perfect matching in G.
Abstract: Consider a planar graph G=(V,E) with polynomially bounded edge weight function w:E -> [0, poly(n)]. The main results of this paper are NC algorithms for finding minimum weight perfect matching in G. In order to solve this problems we develop a new relatively simple but versatile framework that is combinatorial in spirit. It handles the combinatorial structure of matchings directly and needs to only know weights of appropriately defined matchings from algebraic subroutines.
Moreover, using novel planarity preserving reductions, we show how to find: maximum weight matching in G when G is bipartite; maximum multiple-source multiple-sink flow in G where c:E -> [1, poly(n)] is a polynomially bounded edge capacity function; minimum weight f-factor in G where f:V -> [1, poly(n)]; min-cost flow in G where c:E -> [1, poly(n)] is a polynomially bounded edge capacity function and b:V -> [1, poly(n)] is a polynomially bounded vertex demand function. There have been no known NC algorithms for these problems previously.
TL;DR: It is shown that codewords corresponding to Schubert decomposable elements are of minimum weight and also that the converse is true in many cases, and a lower bound, and in some cases, an exact formula, for the number ofminimum weight codeword of SchUbert codes is given.
TL;DR: This paper studies the minimum weight (1, m)-CDS problem, and presents an (H(δ + m) + 2H( δ − 1))-approximation algorithm, where δ is the maximum degree of the graph and H(·) is the Harmonic number.
Abstract: Finding a connected dominating set (CDS) in a given graph is a fundamental problem and has been studied intensively for a long time because of its application in computer science and operations research, e.g., connected facility location and wireless networks. In some cases, fault-tolerance is desirable. Taking wireless networks as an example, since wireless nodes may fail due to accidental damage or energy depletion, it is desirable that the virtual backbone has some fault-tolerance. Such a problem can be modeled as finding a minimum k-connected m-fold dominating set ((k, m)-CDS) of a graph G = (V, E), which is a node set D such that every node outside of D has at least m neighbors in D and the subgraph of G induced by D is k-connected. In this paper, we study the minimum weight (1, m)-CDS problem ((1, m)-MWCDS), and present an (H(δ + m) + 2H(δ − 1))-approximation algorithm, where δ is the maximum degree of the graph and H(·) is the Harmonic number. Notice that the state-of-the-art algorithm achieves O(l...
TL;DR: Given a binary nonlinear code, this work provides a deterministic algorithm to compute its weight and distance distribution, and in particular its minimum weight and its minimum distance, which takes advantage of fast Fourier techniques.
Abstract: Given a binary nonlinear code, we provide a deterministic algorithm to compute its weight and distance distribution, and in particular, its minimum weight and its minimum distance, which takes advantage of fast Fourier techniques. This algorithm's performance is similar to that of best-known algorithms for the average case, while it is especially efficient for codes with low information rate. We provide complexity estimates for several cases of interest.
01 Dec 2018
TL;DR: The purpose of this study is minimizing the weight and the center distance of one pair of spur gears by the means of the GA under some constraint such as bending strength, a contact stress and each dimension conditions of gears, which must be satisfied.
Abstract: Gears are used in most types of machinery and vehicles for the power transmission system. The design of gears is highly complicated involving the satisfaction of many constraints such as strength, pitting resistance, bending stress, scoring wear, and interference in involute gears. In addition, using conventional or traditional optimization techniques to solve this problem could not give optimum results. A stochastic approach as a Genetic Algorithm (GA) is applied in this paper to find the optimal combination of design parameters for minimum weight of spur gears. The purpose of this study is minimizing the weight and the center distance of one pair of spur gears. This objective was accomplished by the means of the GA under some constraint such as bending strength, a contact stress and each dimension conditions of gears, which must be satisfied. The results are calculated by using Matlab tools of Genetic algorithm with four type of materials, which are standard steel, stainless steel, gray cast iron, and Alloy copper.
TL;DR: It is proved that the problem with simple connectivity cannot be approximated better than the traveling salesman problem, in particular, the problem is APX-hard.
Abstract: Finding low-cost spanning subgraphs with given degree and connectivity requirements is a fundamental problem in the area of network design. We consider the problem of finding d-regular spanning subgraphs (or d-factors) of minimum weight with connectivity requirements. For the case of k-edge-connectedness, we present approximation algorithms that achieve constant approximation ratios for all d≥2⋅⌈k/2⌉. For the case of k-vertex-connectedness, we achieve constant approximation ratios for d≥2k−1. Our algorithms also work for arbitrary degree sequences if the minimum degree is at least 2⋅⌈k/2⌉ (for k-edge-connectivity) or 2k−1 (for k-vertex-connectivity). To complement our approximation algorithms, we prove that the problem with simple connectivity cannot be approximated better than the traveling salesman problem. In particular, the problem is APX-hard.
TL;DR: In this letter, subcodes constructed from Reed–Muller codes by removal of generator matrix rows are considered, and the greedy algorithm outperforms the three other construction methods, generating the best codes among all presented subcodes.
Abstract: In this letter, subcodes constructed from Reed–Muller codes by removal of generator matrix rows are considered. A new greedy algorithm based on the overlap of generator matrix rows is developed. To select the best subcode generated by the greedy algorithm, the number of minimum weight code words is determined. Computer simulations confirm that the greedy algorithm outperforms the three other construction methods, generating the best codes among all presented subcodes.
TL;DR: In this paper, a genetic algorithm-based method is proposed to globally optimize the stacking sequence of multi-sandwich-panel composite structures for minimum weight with strength and buckling considerations.
Abstract: Abstract A genetic algorithm-based method is proposed to globally optimize the stacking sequence of multi-sandwich-panel composite structures for minimum weight with strength and buckling considerations. The prerequisites for the continuity between sandwich panels are first studied. To implement the summarized continuity rules in the evolutionary optimization, three newly constructed chromosomes are developed to encode the global stacking sequence with no additional repair. Genetic operators, including specialized mutation, swapping and crossover operators, are also developed to effectively explore the design space and keep the continuity rules followed. The Hashin criterion and maximum stress criterion are used to evaluate the strength of sandwich panels. A typical multi-sandwich-panel composite structure with identical and different core thicknesses is optimized to verify the validity and efficiency of the proposed method. It is found that much lighter solutions are obtained with an acceptable efficiency in all cases. It is also found that the weight of the multi-sandwich-panel composite structures can be further reduced when the core thicknesses are not identical.
TL;DR: In this paper, the authors used Colliding Body Optimization (CBO), Enhanced Colliding Bodies Optimization and Vibrating Particles System (VPS) algorithms and the force method for the simultaneous analysis and design of truss structures.
Abstract: In this paper, the Colliding Bodies Optimization (CBO), Enhanced Colliding Bodies Optimization (ECBO) and Vibrating Particles System (VPS) algorithms and the force method are used for the simultaneous analysis and design of truss structures. The presented technique is applied to the design and analysis of some planer and spatial trusses. An efficient method is introduced using the CBO, ECBO and VPS to design trusses having members of prescribed stress ratios. Finally, the minimum weight design of truss structures is formulated using the CBO, ECBO and VPS algorithms and applied to some benchmark problems from literature. These problems have been designed by using displacement method as analyzer, and here these are solved for the first time using the force method. The accuracy and efficiency of the presented method is examined by comparing the resulting design parameters and structural weight with those of other existing methods.
TL;DR: These subcodes of the Grassmann codes associated to the $2$-Grassmannian of a Hermitian polar space defined over a finite field of square order are introduced and studied.
TL;DR: A multi-objective constrained optimum design of deep groove ball bearing is proposed in this study, which has been solved by implementing a hybrid particle swarm optimization and teaching learning based optimization algorithm due to its convergence capability.
Abstract: Minimum weight, Long fatigue life and adequate film thickness are some of the key design objectives in the optimum design of rolling element bearing (REB). The design approach by considering bearing envelop, fatigue life and wear life results in a low cost bearing. So a multi-objective constrained optimum design of deep groove ball bearing is proposed in this study. The weight, dynamic load capacity and minimum elasto-hydrodynamic film thickness of bearing are considered as the design objectives with some kinematic constraint. The optimum design has been solved by implementing a hybrid particle swarm optimization and teaching learning based optimization algorithm due to its convergence capability. A statistical test was performed to test the superiority of the proposed algorithm. The convergence study identifies the critical design variables. A constraint conformation study has been performed to investigate the relative importance of the constraints. In order to comprehend the changes in objective functions a response analysis is performed on the critical design variables. In addition, the optimum design variables obtained through the design optimization of the bearing are used for preparation of a CAD model. Then the stress analysis using the finite element method is performed on the bearing to identify the critical stress region in the optimized bearing.The validation of this optimum design of the rolling element bearing is performed by developing a prototype with a 3D printer (using rapid prototyping). An approach for simulation model updates and the interactive design is also suggested in this study.
TL;DR: This paper investigates the existence and equivalence of [5, 3] error correcting codes over GF(5), and appears that these codes are all mutually equivalent.
Abstract: In papers [1,2], we were able to classify all 1-error correcting [5, 3] and [5, 2] codes over GF(4). In this paper, we investigate the existence and equivalence of [5, 3] error correcting codes over GF(5). It appears that these codes are all mutually equivalent. We also calculate their weight distribution as well as the weight distribution of their orthogonal codes.