Showing papers on "Minimum weight published in 2017"

Sizing and topology optimization of truss structures using genetic programming

Abstract: This paper presents a genetic programming approach for simultaneous optimization of sizing and topology of truss structures It aims to find the optimal cross-sectional areas and connectivities of the joints to achieve minimum weight in the search space The structural optimization problem is subjected to kinematic stability, maximum allowable stress and deflection This approach uses the variable-length representation of potential solutions in the shape of computer programs and evolves to the optimum solution This method has the capability to identify redundant truss elements and joints in the design space The obtained results are compared with existing popular and competent techniques in literature and its competence as a tool in the optimization problem are demonstrated in solving some benchmark examples, the proposed approach provided lighter truss structures than the available solutions reported in the literature

Topology optimization for minimum weight with compliance and simplified nominal stress constraints for fatigue resistance

Abstract: This work investigates a simplified approach to cope with the optimization of preliminary design of structures under local fatigue constraints along with a global enforcement on the overall compliance. The problem aims at the minimization of the weight of linear elastic structures under given loads and boundary conditions. The expected stiffness of the optimal structure is provided by the global constraint, whereas a set of local stress---based constraints ask for a structure to be fatigue resistant. A modified Goodman fatigue strength comparison is implemented through the same formalism to address pressure---dependent failure in materials as in Drucker---Prager strength criterion. As a simplification, the Sines approach is used to define the equivalent mean and alternating stresses to address the fatigue resistance for an infinite life time. Sines computation is based on the equivalent mean and alternate stress depending on the invariants of the stress tensor and its deviatoric part, respectively. The so---called singularity phenomenon is overcome by the implementation of a suitable qp-relaxation of the equivalent stress measures. Numerical examples are presented to illustrate the features of the achieved optimal layouts and of the proposed algorithm.

Local Search for Minimum Weight Dominating Set with Two-Level Configuration Checking and Frequency Based Scoring Function

Abstract: The Minimum Weight Dominating Set (MWDS) problem is an important generalization of the Minimum Dominating Set (MDS) problem with extensive applications. This paper proposes a new local search algorithm for the MWDS problem, which is based on two new ideas. The first idea is a heuristic called two-level configuration checking (CC2), which is a new variant of a recent powerful configuration checking strategy (CC) for effectively avoiding the recent search paths. The second idea is a novel scoring function based on the frequency of being uncovered of vertices. Our algorithm is called CC2FS, according to the names of the two ideas. The experimental results show that, CC2FS performs much better than some state-of-the-art algorithms in terms of solution quality on a broad range of MWDS benchmarks.

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

Abstract: This paper studies a higher dimensional generalization of Frieze's ζ(3)-limit theorem in the Erdos-Renyi graph process. Frieze's theorem states that the expected weight of the minimum spanning tree converges to ζ(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 Erdos-Renyi 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 ).

Fast procedure for Non-uniform optimum design of stiffened shells under buckling constraint

Abstract: For tailoring the non-uniform axial compression, each sub-panel of stiffened shells should be designed separately to achieve a high load-carrying efficiency. Motivated by the challenge caused by numerous variables and high computational cost, a fast procedure for the minimum weight design of non-uniform stiffened shells under buckling constraint is proposed, which decomposes a hyper multi-dimensional problem into a hierarchical optimization with two levels. To facilitate the post-buckling optimization, an efficient equivalent analysis model of stiffened shells is developed based on the Numerical Implementation of Asymptotic Homogenization Method. In particular, the effects of non-uniform load, internal pressure and geometric imperfections are taken into account during the optimization. Finally, a typical fuel tank of launch vehicle is utilized to demonstrate the effectiveness of the proposed procedure, and detailed comparison with other optimization methodologies is made.

Uncertain programming model for uncertain minimum weight vertex covering problem

Abstract: In this paper, the minimum weight vertex covering problem with uncertain vertex weights is investigated. By virtue of the uncertainty distribution operation of independent uncertain variables, the uncertainty distribution of the minimum weight of vertex cover is derived, and the concept of the $$\alpha $$ź-minimum cover among uncertain weight vertex covers is proposed within the framework of uncertain programming. Then an $$\alpha $$ź-minimum model for uncertain weight vertex covering problem is established and discussed. Taking advantage of some properties of uncertainty theory, the model can be transformed into the corresponding deterministic form. At last, a numerical example is presented to show the performance of the model.

Effect of Levy Flight on the discrete optimum design of steel skeletal structures using metaheuristics

Abstract: Metaheuristic algorithms in general make use of uniform random numbers in their search for optimum designs. Levy Flight (LF) is a random walk consisting of a series of consecutive random steps. The use of LF instead of uniform random numbers improves the performance of metaheuristic algorithms. In this study, three discrete optimum design algorithms are developed for steel skeletal structures each of which is based on one of the recent metaheuristic algorithms. These are biogeography-based optimization (BBO), brain storm optimization (BSO), and artificial bee colony optimization (ABC) algorithms. The optimum design problem of steel skeletal structures is formulated considering LRFD-AISC code provisions and W-sections for frames members and pipe sections for truss members are selected from available section lists. The minimum weight of steel structures is taken as the objective function. The number of steel skeletal structures is designed by using the algorithms developed and effect of LF is investigated. It is noticed that use of LF results in up to 14% lighter optimum structures.

A firefly algorithm for optimum design of new-generation beams

Abstract: This research addresses the minimum weight design of new-generation steel beams with sinusoidal openings using a metaheuristic search technique, namely the firefly method. The proposed algorithm is also used to compare the optimum design results of sinusoidal web-expanded beams with steel castellated and cellular beams. Optimum design problems of all beams are formulated according to the design limitations stipulated by the Steel Construction Institute. The design methods adopted in these publications are consistent with BS 5950 specifications. The formulation of the design problem considering the above-mentioned limitations turns out to be a discrete programming problem. The design algorithms based on the technique select the optimum universal beam sections, dimensional properties of sinusoidal, hexagonal and circular holes, and the total number of openings along the beam as design variables. Furthermore, this selection is also carried out such that the behavioural limitations are satisfied. Numerical ex...

Constraint-based and SAT-based diagnosis of automotive configuration problems

Abstract: We compare the concepts and computation of optimized diagnoses in the context of Boolean constraint based knowledge systems of automotive configuration, namely the preferred minimal diagnosis and the minimum weighted diagnosis. In order to restore the consistency of an over-constrained system w.r.t. a strict total order of the user requirements, the preferred minimal diagnosis tries to keep the most preferred user requirements and can be computed, for example, by the FASTDIAG algorithm. In contrast, partial weighted MinUNSAT solvers aim to find a set of unsatisfied clauses with the minimum sum of weights, such that the diagnosis is of minimum weight. It turns out that both concepts have similarities, i.e., both deliver an optimal minimal correction subset. We show use cases from automotive configuration where optimized diagnoses are desired. We point out theoretical commonalities and prove the reducibility of both concepts to each other, i.e., both problems are FPNP-complete, which was an open question. In addition to exact algorithms we present greedy algorithms. We evaluate the performance of exact and greedy algorithms on problem instances based on real automotive configuration data from three different German car manufacturers, and we compare the time and quality tradeoff.

Solving the Air Conflict Resolution Problem Under Uncertainty Using an Iterative Biobjective Mixed Integer Programming Approach

Abstract: In this paper, we tackle the aircraft conflict resolution problem under uncertainties. We consider errors due to the wind effect, the imprecision of aircraft speed prediction, and the delay in the execution of maneuvers. Using a geometrical approach, we derive an analytical expression for the minimum distance between aircraft, along with the corresponding probability of conflict. These expressions are incorporated into an existing deterministic model for conflict resolution. This model solves the problem as a maximum clique of minimum weight in a graph whose vertices represent possible maneuvers and where edges link conflict-free maneuvers of different aircraft. We then present a solution procedure focusing on two criteria, namely, fuel efficiency and the probability of reissuing maneuvers in the future: we iteratively generate Pareto front solutions to provide the controller with a set of possible solutions where she can choose the one corresponding the most to her preferences. Intensive Monte Carlo simu...

Optimum design of planar steel frames using the Search Group Algorithm

Abstract: This paper presents a design procedure employing the Search Group Algorithm (SGA) for discrete optimization of planar steel frames. SGA is a global optimization heuristic algorithm that has been developed recently. It is based on search groups that explore the design space in a global phase and exploit the best domain regions found in a local phase. The algorithm is used in a structural optimization problem to obtain minimum weight frames subjected to strength and displacement requirements imposed by the American Institute for Steel Construction (AISC) Load and Resistance Factor Design. Designs are obtained by selecting appropriate W-shaped sections from a standard set of steel sections specified by the AISC. Three frame examples from the literature are examined to verify the effectiveness and robustness of the SGA for this type of problem. The results of the SGA are compared to those of state of art algorithms showing that SGA is a competitive meta-heuristic search procedure for engineering design applications.

Multi-objective optimal design of hybrid viscoelastic/composite sandwich beams by using the generalized differential quadrature method and the non-dominated sorting genetic algorithm II

Abstract: In this study, the multi-objective optimal design of hybrid viscoelastic/composite sandwich beams for minimum weight and minimum vibration response is aimed. The equation of motion for linear vibrations of a multi-layer beam is derived by using the principle of virtual work in the most general form. These governing equations together with the boundary conditions are discretized by the generalized differential quadrature method (GDQM) in the frequency domain for the first time. Also, the time and temperature dependent properties of the viscoelastic materials are taken into consideration by a novel ten-parameter fractional derivative model that can realistically capture the response of these materials. The material variability is accounted for by letting an optimization algorithm choose a material freely out of four fiber-reinforced composite materials and five viscoelastic damping polymers for each layer. The design parameters, i.e., the orientation angles of the composites, layer thicknesses and the layer materials that give the set of optimal solutions, namely the Pareto frontier, is obtained for the three and nine-layered clamped-free sandwich beams by using a variant of the non-dominated sorting genetic algorithms (NSGA II).

Optimal design of composite shells based on minimum weight and maximum feasibility robustness

Abstract: A robust design optimization (RDO) approach for minimum weight and safe shell composite structures with minimal variability into design constraints under uncertainties is proposed. A new concept of feasibility robustness associated to the variability of design constraints is considered. So, the feasibility robustness is defined through the determinant of variance–covariance matrix of constraint functions introducing in this way the joint effects of the uncertainty propagations on structural response. A new framework considering aleatory uncertainty into RDO of composite structures is proposed. So, three classes of variables and parameters are identified: deterministic design variables, random design variables and random parameters. The bi-objective optimization search is performed using on a new approach based on two levels of dominance denoted by Co-Dominance-based Genetic Algorithm (CoDGA). The use of evolutionary concepts together sensitivity analysis based on adjoint variable method is a new proposal. The examples with different sources of uncertainty show that the Pareto front definition depends on random design variables and/or random parameters considered in RDO. Furthermore, the importance to control the uncertainties on the feasibility of constraints is demonstrated. CoDGA approach is a powerfully tool to help designers to make decision establishing the priorities between performance and robustness.

Fast Exact Algorithms for Survivable Network Design with Uniform Requirements

Abstract: We design exact algorithms for the following two problems in survivable network design: (i) designing a minimum cost network with a desired value of edge connectivity, which is called Minimum Weight \(\lambda \)-connected Spanning Subgraph and (ii) augmenting a given network to a desired value of edge connectivity at a minimum cost which is called Minimum Weight \(\lambda \)-connectivity Augmentation. Many well known problems such as Minimum Spanning Tree, Hamiltonian Cycle, Minimum 2-Edge Connected Spanning Subgraph and Minimum Equivalent Digraph reduce to these problems in polynomial time. It is easy to see that a minimum solution to these problems contains at most \(2 \lambda (n-1)\) edges. Using this fact one can design a brute-force algorithm which runs in time \(2^{\mathcal {O}(\lambda n(\log n + \log \lambda )}\). However no better algorithms were known. In this paper, we give the first single exponential time algorithm for these problems, i.e. running in time \(2^{\mathcal {O}(\lambda n)}\), for both undirected and directed networks. Our results are obtained via well known characterizations of \(\lambda \)-connected graphs, their connections to linear matroids and the recently developed technique of dynamic programming with representative sets.

Numerical Optimization of the Tube-Cored Induction Magnetometer Weight Under Specific Noise Constraints

Abstract: The aim of this paper is to achieve the minimum weight for the induction magnetometer (IM) with specific noise constraints. First, a tube magnetic core was used to decrease the weight and achieve a similar magnetic concentrating performance as the rod one. The parameters, including the coil resistance, the inductance, the apparent permeability with different coil-to-core length ratios, and the noise equivalent magnetic induction, were evaluated theoretically. A chopping pre-amplifier circuit was used to suppress the $1/f$ noise in low frequencies. Finally, the optimization problem proposed from the practical applications was solved using the penalty function method (interior point method). To verify the theoretical analysis, the optimal IM was manufactured and tested. The experimental results showed 3.1 pT/ $\surd $ Hz at 1 Hz, noise floor 22 fT/ $\surd $ Hz, and total weight 0.52 kg, which were well coincided with the theoretical calculation. Moreover, the relationships among the noise constraints and the coil weight were also discussed.

Local Search for Minimum Weight Dominating Set with Two-Level Configuration Checking and Frequency Based Scoring Function

Abstract: The Minimum Weight Dominating Set (MWDS) problem is an important generalization of the Minimum Dominating Set (MDS) problem with extensive applications. This paper proposes a new local search algorithm for the MWDS problem, which is based on two new ideas. The first idea is a heuristic called two-level configuration checking (CC2), which is a new variant of a recent powerful configuration checking strategy (CC) for effectively avoiding the recent search paths. The second idea is a novel scoring function based on the frequency of being uncovered of vertices. Our algorithm is called CC2FS, according to the names of the two ideas. The experimental results show that, CC2FS performs much better than some state-of-the-art algorithms in terms of solution quality on a broad range of MWDS benchmarks.

Inheritance of Convexity for the P˜min-Restricted Game

Abstract: We consider restricted games on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the subcomponents corresponding to a minimum partition. This minimum partition Pmin is induced by the deletion of the minimum weight edges. We provide a characterization of the graphs satisfying inheritance of convexity from the underlying game to the restricted game associated with P min.

Analysis of a rolling FRP lock gate: + stability during movement

Abstract: Fibre-reinforced polymers (FRPs) are becoming a more commonly used building material in many civil engineering applications including locks. One quality of FRPs is the fact that it has a high strength to weight ratio. By applying FRPs in rolling lock gate design, the self-weight of the gate could be significantly reduced. This in turn could lead to less wear-and-tear to the support carriages, mechanical parts and rails. Self-weight is also an important factor in the stability of a rolling lock gate. A minimum weight is required to counter the moment caused by horizontal loads during opening and closing. If FRPs were to be applied in rolling lock gates an optimization of lightweight versus stability will be required. The objective of this thesis is to investigate the technical feasibility of the FRP rolling lock gate and how the gates design is affected by the stability criteria. Also, the question remains if the FRP design can compete with traditional materials, for example steel. To quantify the problem a case study was chosen: New Lock Terneuzen. A rolling lock gate is set to be constructed to improve the connection between Ghent-Terneuzen. The rolling gates will be very large, with a span of 55 m and a height of approximately 26 m. Initially, the rolling gate is designed with a box shape. The global dimensions of the box gate are determined with a hand calculation based on the boundary conditions and design input from the chosen case study. Basic strength, deflection and stability checks are performed. The box gate is dimensioned in both FRP and steel. The following dimensions are found for the FRP box gate: Width of 8.96 m, with retaining plates: skin:280 mm, core: 200 mm and webs: skin: 200 mm, core: 200 mm. The dimensions found with the hand calculation serve as input for a 3D model of the design. The model is created with Scia Engineer. With this software the gate is checked with finite element analysis. Some additional checks, fatigue and creep, are performed. The box gate model is adjusted to resemble the gate during movement. This is achieved by changing the supports, leaving the top right corner unsupported. In addition to a 3D stability check of the designed box gate, the width between the supports, representing the carriage width, is varied (from 0.5 to 12 m) and the impact on the stability is evaluated. This impact is quantified by the required dead weight to guarantee stability. All the results are used to come up with potential improvements or alternatives to the box gate design. The main objective being a gate with increased stability, which is again quantified by the overweight required. A number of ideas are discussed, where optimizing the shape of the gate is explored further. It is found that the required dead weight to achieve stability increased for all evaluated shapes. The main reason is the distribution of the stabilizing moment, which is split up in a horizontal and vertical component. The shape changes result in an shift from horizontal to vertical, which in turn results in more dead weight required to meet the stability criteria. The application of FRP in rolling gate design is technically feasible. However from a stability point of view it’s questionable if FRP is the better choice over traditional materials. In the chosen case study, the amount dead weight required to fulfil the stability criteria is significant, and the lightweight quality of FRP cannot be fully taken advantage of. Laminates are designed much thicker when compared to the dimensions required to meet strength and deflection criteria. In other words, material is added primarily for the sake of adding weight. Reducing the required dead weight was proven to be much harder than anticipated. Even though a wide base gives a larger arm for the vertical couple, which would lead to a smaller force at an equal moment, the required weight is not necessarily reduced. The applied loads, shape of the gate, location of supports and deflections all affect the distribution of loads over the supports, both horizontal and vertical, of the gate. In a structure of this scale, even small differences can have a significant impact on the stability of the gate and the dead weight required to achieve this stability. The required dead weight to meet the stability criteria must be brought down in order for FRP to be a viable option.

Selection of constructive solutions of car elements with small empty weight

Abstract: Purpose . The work is aimed to identify the reasons for the significantly higher coefficient of the empty weight of 1520 mm gauge cars in comparison with the freight cars in North America and to give recommendations for reducing the empty weight of freight cars. Methodology . As a methodology, a comparative evaluation of the strength, durability and stability of the minimum weight bearing structure made of various materials using the "space 1520" standards is applied. Findings . The authors found that with the use of high-strength steels the product weight can be reduced by a factor of five in comparison with the beam of steel 09G2S. If there is a welded joint in the construction, the weight of the structure will increase approximately by 2 times when calculated according to the "Norms for calculating and designing railroad cars of the Ministry of Railways of Russia, gauge 1520 mm (non-self-propelled)". And during calculations according to State Standard 33211-2013 "Freight cars. Requirements for strength and dynamic qualities" the weight increases almost 5 times and does not depend on the type of steel. Originality . It is revealed that the main criterion determining the empty weight of modern cars is the fatigue strength of the welded joint. It is shown that State Standard 33211-2013 and "Recommendations of the International Welding Institute" designate low endurance limits for high-strength steels and it is impossible to achieve the weight reduction if one adheres these recommendations. Practical value . The direction of actions to find the ways reducing empty weight of cars was developed: conditions for strength of welded joints of cars made of high-strength materials have been experimentally refined; methods for increasing the endurance of welded joints were developed; other types of connections are assumed.

A systematic approach for achieving low bit error rate of LDPC decoder using MWD algorithm

Abstract: One of the most significant barriers for using Low Density Parity Check (LDPC) codes in many wireless communication system and magnetic storage devices is the bit error rate floor phenomena with their complex message passing iterative algorithm. LDPC codes aremostly used in communication system because of its outstanding performance achievement. There are various decoding algorithm for LDPC decoder. In this paper, we presented the mathematical analysis of Minimum Weight Decoding (MWD) algorithm and its error rate performance over Additive White Gaussian Noise (AWGN) channel. A comparison of bit error rate performance over signal to noise ratio (dB) is carried out for different codes such as hamming code, BCH code and LDPC code. This paper shows bit error performance of decoder using minimum weight decoding algorithm. The main significance of this paper is that it shows efficient performance of Minimum Weight Decoding (MWD) algorithm based LDPC Decoder. We presented three classes of codes (1) hamming code, (2) BCH code and (3) LDPC Codes. We demonstrate the effectiveness of LDPC decoder over other two code decoders for the code rate 1/2 and block length (16,8) which is tarnished for its error floors.

Minimum Weight Design of Sinusoidal Corrugated Web Beam Using Real-Coded Genetic Algorithms

Abstract: Fundamental advantage of using corrugated web girder rather than plate girder reinforced with stiffeners is securing stability against shear buckling of web and unnecessary stiffeners despite the thinner web. Nonetheless, because shear buckling behavior of corrugated web is very complex, the design mechanism for beams and local, global, and interactive buckling problems should be considered in designing of its structural optimization for better economics and reasonableness. Therefore, this paper proposes a mathematical model for minimum weight design of sinusoidal web girder for securing better stability with smooth corrugation and aims at developing its optimum design program. The constraints for the optimum design were composed on the basis of the standards of EN 1993-1-5, DASt-R015, and DIN 18800, and the optimum program was coded in accordance with the standards based on Real-Coded Genetic Algorithms. The genetic operators for the developed program resulted in a stable solution with crossover probability between 12.5 and 50%, and the perturbation vector for outbreeding could obtain the best result with the model being applied of feasible design variable space of 20–30%. Additionally, the increase of yield strength resulted in decreased value of the objective function, and it was found through the change of the value of the constraint function that the thickness of web was an important factor in the optimum structural design.

The fourth smallest Hamming weight in the code of the projective plane over $\mathbb{Z}/p \mathbb{Z}$

Abstract: Let $p$ be a prime and let $C_p$ denote the $p$-ary code of the projective plane over ${\mathbb Z}/p\mathbb{Z}$. It is well known that the minimum weight of non-zero words in $C_p$ is $p+1$, and Chouinard proved that, for $p \geq 3$, the second and third minimum weights are $2p$ and $2p+1$. In 2007, Fack et. al. determined, for $p\geq 5$, all words of $C_p$ of these three weights. In this paper we recover all these results and also prove that, for $p \geq 5$, the fourth minimum weight of $C_p$ is $3p-3$. The problem of determining all words of weight $3p-3$ remains open.

Electromagnetic design optimization and sensitivity analysis for IPM synchronous motors

Abstract: This paper presents the electromagnetic design optimization for a 12-slot, 8-pole, concentrated winding, V-shaped magnet Interior Permanent Magnet Synchronous Motor (IPMSM) using a Genetic Algorithm (GA). Three distinct objective functions are considered. These include minimum weight, minimum loss, and a combined multi-objective function to minimize both the weight and the losses. The three optimized machines are compared with a non-optimized preliminary design using 2D-Finite Element Analysis (FEA). The multi-objective optimal design shows major efficiency improvements (1.25%) and weight reduction (0.918 kg) compared to the preliminary design. Sensitivity analysis is conducted on this optimized machine, which evaluates its weight and efficiency variations as a function of deviations in the optimized variables.

Multiobjective Genetic Algorithm for Minimum Weight Minimum Connected Dominating Set

Abstract: Connected Dominating Set (CDS) is a connected subgraph of a graph G with the property that any given node in G either belongs to the CDS or is adjacent to one of the CDS nodes. Minimum Connected Dominating Sets (MCDS), where the CDS nodes are sought to be minimized, are of special interests in various fields like Computer networks, Biological networks, Social networks, etc., since they represent a set of minimal important nodes. Similarly, Minimum Weight Connected Dominating Sets (MWCDS), where the connected weights among the CDS nodes are sought to be minimized, is also of interest in many research application. This work is based on the hypothesis that a CDS with both the properties of minimum size and minimum weight optimized would enhance performance in many applications where CDS is used. Though there are a good number of approximate and heuristic algorithms for MCDS and MWMCDS, there is no work to the best of our knowledge, that optimizes the generated CDS with respect to both the size and weight. A Multiobjective Genetic Algorithm for Minimum Weight Minimum Connected Dominating Set (MOGA-MWMCDS) is proposed. Performance analysis based on a Wireless Sensor Network (WSN) scenario indicates the efficiency of the proposed MOGA-MWMCDS and supports the advantage of MWMCDS use.

Multi-objective Optimization of Non-uniform Beam for Minimum Weight and Sound Radiation

Abstract: A multi-objective optimization of non-uniform beams is presented for minimum radiated sound power and weight The transfer matrix method is used to compute the structural and acoustic responses of a non-uniform beam accurately and efficiently The multi-objective particle swarm optimization technique is applied to search the Pareto optimal solutions that represent various compromises between weight and sound radiation Several constraints are imposed, which substantially reduce the volume fraction of feasible solutions in the design space Two non-uniform beams with different boundary conditions are studied to demonstrate the multi-objective optimal designs of the structure