Showing papers on "Minimum weight published in 2015"

Minimum weight perfect matching of fault-tolerant topological quantum error correction in average O(1) parallel time

Abstract: Consider a 2-D square array of qubits of extent L × L. We provide a proof that the minimum weight perfect matching problem associated with running a particular class of topological quantum error correction codes on this array can be exactly solved with a 2-D square array of classical computing devices, each of which is nominally associated with a fixed number N of qubits, in constant average time per round of error detection independent of L provided physical error rates are below fixed nonzero values, and other physically reasonable assumptions. This proof is applicable to the fully fault-tolerant case only, not the case of perfect stabilizer measurements.

Weight Optimization of a Cooling System Composed of Fan and Extruded-Fin Heat Sink

Abstract: This paper details the weight optimization of forced convection cooling systems, composed of a fan and an extruded-fin heat sink, required for a dc–dc converter of an airborne wind turbine system. The presented investigations detail the optimization of the heat sink's fins with respect to minimum weight and the selection of a suitable fan for minimum overall system weight. A new analytical cooling system model is introduced, and the calculated results are compared to the results determined with a preexisting analytical model and finite-element model simulations. The comparison to experimental results demonstrates the accuracy improvements achieved with the proposed methods. Compared to commercially available products, a weight reduction of 52% is achieved with the proposed optimization procedure for the required heat sink system with $R_{{\rm th},{\rm S}\hbox{-}{\rm a}}=1\ \hbox{K/W}$ .

A PTAS for the Weighted Unit Disk Cover Problem

Abstract: We are given a set of weighted unit disks and a set of points in Euclidean plane. The minimum weight unit disk cover (WUDC) problem asks for a subset of disks of minimum total weight that covers all given points. WUDC is one of the geometric set cover problems, which have been studied extensively for the past two decades (for many different geometric range spaces, such as (unit) disks, halfspaces, rectangles, triangles). It is known that the unweighted WUDC problem is NP-hard and admits a polynomial-time approximation scheme (PTAS). For the weighted WUDC problem, several constant approximations have been developed. However, whether the problem admits a PTAS has been an open question. In this paper, we answer this question affirmatively by presenting the first PTAS for WUDC. Our result implies the first PTAS for the minimum weight dominating set problem in unit disk graphs. Combining with existing ideas, our result can also be used to obtain the first PTAS for the maxmimum lifetime coverage problem and an improved constant approximation ratio for the connected dominating set problem in unit disk graphs.

On Minimum- and Maximum-Weight Minimum Spanning Trees with Neighborhoods

Abstract: We study optimization problems for the Euclidean Minimum Spanning Tree (MST) problem on imprecise data. To model imprecision, we accept a set of disjoint disks in the plane as input. From each member of the set, one point must be selected, and the MST is computed over the set of selected points. We consider both minimizing and maximizing the weight of the MST over the input. The minimum weight version of the problem is known as the Minimum Spanning Tree with Neighborhoods (MSTN) problem, and the maximum weight version (max-MSTN) has not been studied previously to our knowledge. We provide deterministic and parameterized approximation algorithms for the max-MSTN problem, and a parameterized algorithm for the MSTN problem. Additionally, we present hardness of approximation proofs for both settings.

Revisiting approximate reanalysis in topology optimization: on the advantages of recycled preconditioning in a minimum weight procedure

Abstract: An efficient procedure for three-dimensional continuum structural topology optimization is proposed. The approach is based on recycled preconditioning, where multigrid preconditioners are generated only at selected design cycles and re-used in subsequent cycles. Building upon knowledge regarding approximate reanalysis, it is shown that integrating recycled preconditioning into a minimum weight problem formulation can lead to a more efficient procedure than the common minimum compliance approach. Implemented in MATLAB, the run time is roughly twice faster than that of standard minimum compliance procedures. Computational savings are achieved without any compromise on the quality of the results in terms of the compliance-to-weight trade-off achieved. This provides a step towards integrating interactive 3-D topology optimization procedures into CAD software and mobile applications. MATLAB codes complementing the article can be downloaded from the author's personal webpage.

Colliding bodies optimization for size and topology optimization of truss structures

Abstract: This paper presents the application of a recently developed meta-heuristic algorithm, called Colliding Bodies Optimization (CBO), for size and topology optimization of steel trusses. This method is based on the one-dimensional collisions between two bodies, where each agent solution is considered as a body. The performance of the proposed algorithm is investigated through four benchmark trusses for minimum weight with static and dynamic constraints. A comparison of the numerical results of the CBO with those of other available algorithms indicates that the proposed technique is capable of locating promising solutions using lesser or identical computational effort, with no need for internal parameter tuning.

Approximation Algorithm for Minimum Weight (k,m)-CDS Problem in Unit Disk Graph

Abstract: In a wireless sensor network, the virtual backbone plays an important role. Due to accidental damage or energy depletion, it is desirable that the virtual backbone is fault-tolerant. A fault-tolerant virtual backbone can be modeled as a $k$-connected $m$-fold dominating set ($(k,m)$-CDS for short). In this paper, we present a constant approximation algorithm for the minimum weight $(k,m)$-CDS problem in unit disk graphs under the assumption that $k$ and $m$ are two fixed constants with $m\geq k$. Prior to this work, constant approximation algorithms are known for $k=1$ with weight and $2\leq k\leq 3$ without weight. Our result is the first constant approximation algorithm for the $(k,m)$-CDS problem with general $k,m$ and with weight. The performance ratio is $(\alpha+2.5k\rho)$ for $k\geq 3$ and $(\alpha+2.5\rho)$ for $k=2$, where $\alpha$ is the performance ratio for the minimum weight $m$-fold dominating set problem and $\rho$ is the performance ratio for the subset $k$-connected subgraph problem (both problems are known to have constant performance ratios.)

Thermo-structural optimization of integrated thermal protection panels with one-layer and two-layer corrugated cores based on simulated annealing algorithm

Abstract: Toexplore weight saving potential capability, a multidisciplinary optimization procedure based on simulated annealing algorithm was proposed to unveil the minimum weight design for integrated thermal protection system subjected to in-service thermal and mechanical loads. The panel configurations with one-layer and two-layer corrugated cores are considered for comparison. Heat transfer and structural field analysis for each panel configuration were performed to obtain the temperature, buckling, stress and deflection responses for structural components of interest, which were then considered as critical constraints of the optimization problem. Sensitivity analysis was performed to disclose the effect of individual design variables on the thermo-structural extreme responses, and the designed thermal protection system performance and weight for the two configurations were discussed. The results demonstrated that the two-layer structure provides superior structural efficiency and performance to resist thermal buckling deformation in comparison with the one-layer panel. Its area-specific weight is reduced by more than 14---29 % with respect to the one-layer panel design, and 30---50 % weight efficient can be implemented at higher thermal buckling constraint levels, while keeping considerable temperature, stress and deflection margins.

Two decomposition algorithms for solving a minimum weight maximum clique model for the air conflict resolution problem

Abstract: In this paper, we tackle the conflict resolution problem using a new variant of the minimum-weight maximum-clique model. The problem involves identifying maneuvers that maintain the required separation distance between all pairs of a set of aircraft while minimizing fuel costs. We design a graph in which the vertices correspond to a finite set of maneuvers and the edges connect conflict-free maneuvers. A maximum clique of minimal weight yields a conflict-free situation that involves all the aircraft and minimizes the costs induced. The model uses a different cost structure compared to classical clique search problems: the costs of the vertices cannot be determined a priori, since they depend on the vertices in the clique. We formulate the problem as a mixed integer linear program. Since the modeling of the aircraft dynamics and the computation of trajectories is separated from the solution process, our mathematical framework is valid for any hypotheses on the aircraft dynamics and any choice of the available maneuvers. In particular, the aircraft can perform dynamic velocity, heading, and flight-level changes. To solve instances involving a large number of aircraft spread over several flight levels, we introduce two decomposition algorithms. The first is a sequential mixed integer linear programming procedure that iteratively refines the discretization of the maneuvers to yield a trade-off between computational time and cost. The second is a large neighborhood search heuristic that uses the first procedure as a subroutine. The best solutions for the available set of maneuvers are obtained in less than ten seconds for instances with up to 250 aircraft randomly allocated to bisten flight levels.

Models and Algorithms for Genome Rearrangement with Positional Constraints

Abstract: Traditionally, the merit of a rearrangement scenario between two genomes has been measured based on a parsimony criteria alone; two scenarios with the same number of rearrangements are considered equally good. In this paper, we acknowledge that each rearrangement has a certain likelihood of occurring based on biological constraints, e.g. physical proximity of the DNA segments implicated, or repetitive sequences. Accordingly, we propose optimization problems with the objective of maximizing overall likelihood, by weighting the rearrangements. We study a binary weight function suitable to the representation of sets of genome positions that are most likely to have swapped adjacencies. We give a polynomial-time algorithm for the problem of finding a minimum weight double cut and join (DCJ) scenario among all minimum length scenarios. In the process, we solve an optimization problem on colored noncrossing partitions which is a generalization of the Maximum Independent Set problem on circle graphs.

Efficient representation of binary nonlinear codes: constructions and minimum distance computation

Abstract: A binary nonlinear code can be represented as a union of cosets of a binary linear subcode. In this paper, the complexity of some algorithms to obtain this representation is analyzed. Moreover, some properties and constructions of new codes from given ones in terms of this representation are described. Algorithms to compute the minimum distance of binary nonlinear codes, based on known algorithms for linear codes, are also established, along with an algorithm to decode such codes. All results are written in such a way that they can be easily transformed into algorithms, and the performance of these algorithms is evaluated.

A matheuristic for the minimum weight rooted arborescence problem

Abstract: The combinatorial optimization problem tackled in this work is from the family of minimum weight rooted arborescence problems. The problem is NP-hard and has applications, for example, in computer vision and in multistage production planning. We describe an algorithm which makes use of a mathematical programming solver in order to find near-optimal solutions to the problem both in acyclic directed graphs and in directed graphs possibly containing directed circuits. It is shown that the proposed technique compares favorably to competiting approaches published in the related literature. Moreover, the experimental evaluation demonstrates that, although mathematical programming solvers are very powerful for this problem, with growing graph size and density they become unpractical due to excessive memory requirements.

A Fast Procedure for the Design of Composite Stiffened Panels

Abstract: This paper describes the analysis and the minimum weight optimisation of a fuselage composite stiffened panel made from carbon/epoxy material and stiffened by five omega stringers. The panel investigated inside the European project MAAXIMUS is studied using a fast tool, which relies on a semi-analytical procedure for the analysis and on genetic algorithms for the optimisation. The semi-analytical approach is used to compute the buckling load and to study the post-buckling response. Different design variables are considered during the optimisation, such as the stacking sequences of the skin and the stiffener, the geometry and the cross-section of the stiffener. The comparison between finite element and fast tool results reveals the ability of the formulation to predict the buckling load and the post-buckling response of the panel. The reduced CPU time necessary for the analysis and the optimisation makes the procedure an attractive strategy to improve the effectiveness of the preliminary design phases.

Optimum design of steel space frames with composite beams using genetic algorithm

Abstract: This paper presents an optimization process using Genetic Algorithm (GA) for minimum weight by selecting suitable standard sections from a specified list taken from American Institute of Steel Construction (AISC). The stress constraints obeying AISC-LRFD (American Institute of Steel Construction - Load and Resistance Factor Design), lateral displacement constraints being the top and inter-storey drift, mid-span deflection constraints for the beams and geometric constraints are considered for optimum design by using GA that mimics biological processes. Optimum designs for three different space frames taken from the literature are carried out first without considering concrete slab effects in finite element analyses for the constraints above and the results are compared with the ones available in literature. The same optimization procedures are then repeated for the case of space frames with composite (steel and concrete) beams. A program is coded in MATLAB for the optimization processes. Results obtained in the study showed that consideration of the contribution of the concrete on the behavior of the floor beams results with less steel weight and ends up with more economical designs.

Minimum-weight design of stiffened shell under hydrostatic pressure by genetic algorithm

Abstract: In this paper, optimization of cylindrical shells under external pressure to minimize its weight has been studied. Buckling equations are based on standard of ABS underwater vehicles. Dimension and type of circumferential stiffeners, and its distance from each other are assumed as variables of optimization problem. Considering the extent of these variables, genetic algorithms have been used for optimization. To study the effect of hydrostatic pressure on the shell and its fabrication according to the existing standards, geometrical and construction as well as stress and buckling constraints have been used in optimization algorithm and also penalty functions are applied to eliminate weak model. Finally, the best model which has the minimum weight considering the applied pressure has been presented.

Structural Topology Optimization with Stress Constraint Considering Loading Uncertainties

Abstract: This paper deals with the consideration of loading uncertainties in topology optimization via a fundamental optimization problem setting. Variability of loading in engineering design is realized e.g. in the action of various load combinations. In this study this phenomenon is modelled by the application of two mutually excluding (i.e. alternating) forces such that the magnitudes and directions are varied parametrically in a range. The optimization problem is stated as to find the minimum volume (i.e. the minimum weight) load-bearing elastic truss structure that transfers such loads acting at a fix point of application to a given line of support provided that stress limits are set. The aim of this paper is to numerically determine the layout, size, and volume of the optimal truss and to support the numerical results by appropriate analytical derivations. We also show that the optimum solution is non-unique, which aects the static determinacy of the structure as well. In this paper we also create a truss-like structure with rigid connections based on the results of the truss optimization and analyse it both as a bar structure (frame model) and a planar continuum (disk) structure to compare with the truss model. The comparative investigation assesses the validity of computational models and proves that the choice aects design negatively since rigidity of connections resulted by usual construction technologies involve extra stresses leading to significant undersizing.

Determination of optimum particle size of Al2O3/SiCp reinforced hybrid composites materials in wear testing

Abstract: Purpose – The purpose of this study is to optimize input parameters of particle size and applied load to determine minimum weight loss and friction coefficient for Al2O3/SiC particles-reinforced hybrid composites by using Taguchi’s design methodology. Design/methodology/approach – The experimental results demonstrate that the applied size is the major parameter influencing the weight loss for all samples, followed by particle size. The applied load, however, was found to have a negligible effect on the friction coefficient. Moreover, the optimal combination of the testing parameters was predicted. The predicted weight loss and friction coefficient for all the test samples were found to lie close to those of the experimentally observed ones. Findings – The optimum levels of the control factors to obtain better weight loss and friction coefficient were A8 (particle size, 60 μm) and B1 (applied load, 20 N), respectively. Taguchi’s orthogonal design was developed to predict the quality characteristics (weight...

Minimum Weight Perfect Matching via Blossom Belief Propagation

Abstract: Max-product Belief Propagation (BP) is a popular message-passing algorithm for computing a Maximum-A-Posteriori (MAP) assignment over a distribution represented by a Graphical Model (GM). It has been shown that BP can solve a number of combinatorial optimization problems including minimum weight matching, shortest path, network flow and vertex cover under the following common assumption: the respective Linear Programming (LP) relaxation is tight, i.e., no integrality gap is present. However, when LP shows an integrality gap, no model has been known which can be solved systematically via sequential applications of BP. In this paper, we develop the first such algorithm, coined Blossom-BP, for solving the minimum weight matching problem over arbitrary graphs. Each step of the sequential algorithm requires applying BP over a modified graph constructed by contractions and expansions of blossoms, i.e., odd sets of vertices. Our scheme guarantees termination in O(n^2) of BP runs, where n is the number of vertices in the original graph. In essence, the Blossom-BP offers a distributed version of the celebrated Edmonds' Blossom algorithm by jumping at once over many sub-steps with a single BP. Moreover, our result provides an interpretation of the Edmonds' algorithm as a sequence of LPs.

A New Variant of the Minimum-Weight Maximum-Cardinality Clique Problem to Solve Conflicts between Aircraft

Abstract: In this article, we formulate a new variant of the problem of finding a maximum clique of minimum weight in a graph applied to the detection and resolution of conflicts between aircraft. The innovation of the model relies on the cost structure: the cost of the vertices cannot be determined a priori, since they depend on the vertices in the clique. We apply this formulation to the resolution of conflicts between aircraft by building a graph whose vertices correpond to a set of maneuvers and whose edges link conflict-free maneuvers. A maximum clique of minimal weight yields a conflict-free situation involving all aircraft and minimizing the costs induced. We solve the problem as a mixed integer linear program. Simulations on a benchmark of complex instances highlight computational times smaller than 20 seconds for situations involving up to 20 aircraft.

Minimum weight design of sinusoidal corrugated web beam using differential evolution algorithm

Abstract: Due to their many advantages, corrugated steel plates are widely used in various applications including bridges. Starting with airplane design, these corrugated steel plates have been used in civil engineering applications such as buildings and bridges, and many studies on corrugated steel plates are being conducted. However, most of these studies focused on the strength of girders through analysis and experiment of corrugated steel plates and studies on the optimization of corrugated steel plates are still insufficient. The present study developed the weight optimum design using the differential evolution and investigated the effects of parameters. The optimization program was verified with differential evolution through the numerical analysis examples of simple beams and fixed beams. For this verification, the optimization program using the genetic algorithm that has been studied was compared with the weight optimum graph of the optimization program of differential evolution proposed in this study. As a result, the graphs of these two optimization programs increased similarly. The change rate was 3.57% or lower in the example of uniformly load for fixed beam, 1.60% or lower in the example of concentrated load for fixed beam, and 1.44% or lower in the example of uniformly load for simple beam. Furthermore, in the graph of changing design variables, the changing web thickness showed a similar trend as the increasing trend of the optimum sectional area.

Minimum spanning acycle and lifetime of persistent homology in the Linial-Meshulam process

Abstract: This paper studies a higher dimensional generalization of Frieze's $\zeta(3)$-limit theorem in the Erd\"os-R\'enyi graph process. Frieze's theorem states that the expected weight of the minimum spanning tree converges to $\zeta(3)$ as the number of vertices goes to infinity. In this paper, we study the $d$-Linial-Meshulam process as a model for random simplicial complexes, where $d=1$ corresponds to the Erd\"os-R\'enyi graph process. First, we define spanning acycles as a higher dimensional analogue of spanning trees, and connect its minimum weight to persistent homology. Then, our main result shows that the expected weight of the minimum spanning acycle behaves in $O(n^{d-1})$.

A randomized population-based iterated greedy algorithm for the minimum weight dominating set problem

Abstract: Iterated greedy algorithms belong to the class of stochastic local search strategies that have been shown to be very successful for solving a considerable number of difficult optimization problems. They are based on the simple and effective principle of generating a sequence of solutions by iterating over a constructive greedy heuristic using destruction and construction phases. This paper presents an efficient randomized iterated greedy approach for the minimum weight dominating set problem, whose goal is to identify a subset of vertices in a vertex-weighted graph with minimum total weight such that each vertex of the graph is either in the subset or has a neighbor in the subset. Our proposed approach works on a population of solutions rather than on a single one. Moreover, it is based on a fast randomized construction procedure making use of two different greedy heuristics. The performance evaluation done on a commonly used set of benchmark instances shows that our proposed algorithm outperforms current state-of-the-art approaches both in term of solution quality and computational time.

Configuration Analysis of a High-Altitude Airship’s Regenerative Power System

Abstract: In the design of the power system of a high-altitude airship (HAA), the principal target is to satisfy the needs of the power demand and achieve the best balance of minimum weight and maximum reliability. To handle this problem, configuration analysis of the power system is performed. Mathematical models of output power, reliability, and weight are presented. Relationships between weight, reliability, and configurations are discussed in detail. Several design rules related to the design of the HAA’s power system are deduced. For obtaining the optimal configuration, the self-adaptive genetic algorithm (GA) is applied. Results show that the optimal configuration, compared to the configuration without redundancy, has a 258% increase in reliability and a 55.9% increase in weight. The weight increase is necessary to achieve more reliability improvement.

Online route computation and traffic engineering with segment routing

Abstract: Various exemplary embodiments relate to a method of online segment routing in a network having an ingress node, an egress node, and a plurality of links, l. The method may include determining for a plurality of links l dual weights θ(l); receiving a new flow; determining an intermediate node k providing a minimum weight two segment path from the ingress node to egress node for the new flow based upon the flow that results on link l from the new flow through intermediate node k and the dual weight values θ(l) for the links l; and routing the new flow to the intermediate node k along the minimum weight path when the minimum weight path has a weight less than or equal to one.

A $1.75$ LP approximation for the Tree Augmentation Problem

Abstract: In the Tree Augmentation Problem (TAP) the goal is to augment a tree $T$ by a minimum size edge set $F$ from a given edge set $E$ such that $T \cup F$ is $2$-edge-connected. The best approximation ratio known for TAP is $1.5$. In the more general Weighted TAP problem, $F$ should be of minimum weight. Weighted TAP admits several $2$-approximation algorithms w.r.t. to the standard cut LP-relaxation, but for all of them the performance ratio of $2$ is tight even for TAP. The problem is equivalent to the problem of covering a laminar set family. Laminar set families play an important role in the design of approximation algorithms for connectivity network design problems. In fact, Weighted TAP is the simplest connectivity network design problem for which a ratio better than $2$ is not known. Improving this "natural" ratio is a major open problem, which may have implications on many other network design problems. It seems that achieving this goal requires finding an LP-relaxation with integrality gap better than $2$, which is a long time open problem even for TAP. In this paper we introduce such an LP-relaxation and give an algorithm that computes a feasible solution for TAP of size at most $1.75$ times the optimal LP value. This gives some hope to break the ratio $2$ for the weighted case. Our algorithm computes some initial edge set by solving a partial system of constraints that form the integral edge-cover polytope, and then applies local search on $3$-leaf subtrees to exchange some of the edges and to add additional edges. Thus we do not need to solve the LP, and the algorithm runs roughly in time required to find a minimum weight edge-cover in a general graph.

Investigation the efficiency of gravitational search algorithm in optimization of sandwich structures under longitudinal loading with yielding and buckling constraints

Abstract: Original Research Paper Received 10 April 2015 Accepted 07 June 2015 Available Online 20 June 2015 Sandwich structures have low weight and high stiffness. Sandwich panels with open and prismatic cores are kind of these structures that have special properties. These panels are named based on the number of corrugations of the core. In this paper weight optimization of these panels is carried out by Gravitational Search Algorithm based on yielding and buckling constraints. This algorithm is heuristic algorithm that is based upon the Newtonian gravity force and the laws of motion. For optimization of the weight, core and surface thickness and panel height are assumed as design variables. The results show that for specific panel, the design variables and the weight of panel are increased by increasing the load. Also the core and surface thickness are decreased and the weight and panel height are increased by increasing core corrugate number at specific loading. Also, the panels with one and two corrugates in the core, have the minimum weight and highest structural efficiency. By comparing the results with some previous studies, it is shown that the Gravitational Search Algorithm is useful tool in achieving lower weight in these panels and has good convergence rate.