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Showing papers on "Minimum weight published in 2022"


Journal ArticleDOI
TL;DR: In this article , the continuous-time distributed optimization of a strictly convex summation-separable cost function with possibly nonconvex local functions over strongly connected digraphs is studied.
Abstract: This article addresses the continuous-time distributed optimization of a strictly convex summation-separable cost function with possibly nonconvex local functions over strongly connected digraphs. Distributed optimization methods in the literature require convexity of local functions, or balanced weights, or vanishing step sizes, or algebraic information (eigenvalues or eigenvectors) of the Laplacian matrix. The solution proposed here covers both weight-balanced and unbalanced digraphs in a unified way, without any of the aforementioned requirements.

4 citations


Journal ArticleDOI
TL;DR: In this paper , it was shown that for a given graph, it is NP-hard to decide whether a given RD-function strongly equals a (perfect) Roman dominating function.
Abstract: A Roman dominating function (RD-function) on a graph $G = (V, E)$ is a function $f: V \longrightarrow \{0, 1, 2\}$ satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v) = 2$. An Roman dominating function $f$ in a graph $G$ is perfect Roman dominating function (PRD-function) if every vertex $u$ with $f(u) = 0$ is adjacent to exactly one vertex $v$ for which $f(v) = 2$. The (perfect) Roman domination number $\gamma_R(G)$ ($\gamma_{R}^{p}(G)$) is the minimum weight of an (perfect) Roman dominating function on $G$. We say that $\gamma_{R}^{p}(G)$ strongly equals $\gamma_R(G)$, denoted by $\gamma_{R}^{p}(G)\equiv \gamma_R(G)$, if every RD-function on $G$ of minimum weight is a PRD-function. In this paper we show that for a given graph $G$, it is NP-hard to decide whether $\gamma_{R}^{p}(G)= \gamma_R(G)$ and also we provide a constructive characterization of trees $T$ with $\gamma_{R}^{p}(T)\equiv \gamma_R(T)$.

2 citations


Journal ArticleDOI
TL;DR: In this paper , a new method for structural topology optimization considering minimum weight and local stress constraints is proposed, which is an improvement of the so-called Damage Approach, is used.

2 citations


Journal ArticleDOI
01 Nov 2022
TL;DR: In this paper , a robust deep neural network (DNN)-based parameterization framework is proposed to directly solve the optimum design for geometrically nonlinear trusses subject to displacement constraints.
Abstract: In this paper, a robust deep neural network (DNN)-based parameterization framework is proposed to directly solve the optimum design for geometrically nonlinear trusses subject to displacement constraints. The core idea is to integrate DNN into Bayesian optimization (BO) to find the best optimum structural weight. Herein, the design variables of the structure are parameterized by weights and biases of the network with the spatial coordinates of all joints as the training data. A loss function of the network is built based on the predicted cross-sectional areas and deflection constraints obtained by supporting finite element analysis (FEA) and arc-length method. Accordingly, the optimum weight corresponding to the minimum loss function is indicated as soon as the complete training process. And then it is also serving as an objective of the BO for performing the hyperparameter optimization (HPO) to find the best optimum structural weight. Several illustrative numerical examples for geometrically nonlinear space trusses are examined to determine the efficiency and reliability of the proposed approach. The obtained results demonstrate that our framework can overcome the drawbacks of applications of machine learning in computational mechanics.

2 citations


Journal ArticleDOI
TL;DR: In this article , the Nordhaus-Gaddum type inequalities for the total Italian domination number were presented for a graph with vertex set and the minimum weight of a total Italian dominating function.
Abstract: Let $G$ be a graph with vertex set $V(G)$. A total Italian dominating function (TIDF) on a graph $G$ is a function $f:V(G)\longrightarrow\{0,1,2\}$ such that (i) every vertex $v$ with $f(v)=0$ is adjacent to a vertex $u$ with $f(u)=2$ or to two vertices $w$ and $z$ with $f(w)=f(z)=1$, and (ii) every vertex $v$ with $f(v)\ge 1$ is adjacent to a vertex $u$ with $f(u)\ge 1$. The total Italian domination number $\gamma_{tI}(G)$ on a graph $G$ is the minimum weight of a total Italian dominating function. In this paper, we present Nordhaus-Gaddum type inequalities for the total Italian domination number.

1 citations



Journal ArticleDOI
TL;DR: In this paper , a hollow core construction with a flux concentrator was used to lower the weight of the IM, and the connection between the magnetic flux density and the diameter of the magnetometer was evaluated in the COMSOL software.
Abstract: This paper optimizes the weight of an induction magnetometer (IM) for earthquake precursor monitoring. It has a frequency range of 0.5 to 50 Hz. To begin, a hollow core construction with a flux concentrator was used to lower the weight of the IM, and the connection between the magnetic flux density and the diameter of the flux concentrator was evaluated in the COMSOL software. A weight model and a noise model for IM are also established. Then, as optimization variables, choose the number of coil turns, the length of the magnetic core, the diameter of the magnetic flux concentrator, and the diameter of the copper wire using the PSO (Particle Swarm Optimization) method to optimize the weight of the IM. The diameter of the magnetic flux concentrator and NEMI (Noise Equivalent Magnetic Induction) were used as restrictions. In order to verify the accuracy of the PSO optimization results, the NSGA-II (Non-dominant Sorting Genetic algorithm-II) method was used to optimize the IM weight and NEMI simultaneously with the diameter of the flux aggregator as the constraint. Both strategies yielded nearly identical results. Finally, the preamplifier circuit is designed using a paralleled low noise dual-JFET. We finished the manufacture and testing of the IM based on the optimization results. The weight of the IM is 130g, and the NEMI is 2.94pT/Hz 1/2 @1Hz, according to the testing data. In comparison to previous research, the low-weight sensor developed in this work has higher practical value at the same NEMI level, and hence have a bigger application value in earthquake precursor monitoring.

1 citations


Journal ArticleDOI
TL;DR: In this article , the quasi-total Roman dominating function (QTRD-function) on a bipartite graph G is defined as a function f:V→{0, 1, 2} such that every vertex x for which x = 0 is adjacent to at least one vertex v for which f(v) = 2, and if x is an isolated vertex in the subgraph induced by the set of vertices with nonzero values, then f(x) = 1.

1 citations


Journal ArticleDOI
TL;DR: A binary triply-even code invariant under the sporadic simple group ${rm Co}_1$ is constructed by adjoining the all-ones vector to the faithful and absolutely irreducible 24-dimensional code of length 98280.
Abstract: A binary triply-even $[98280, 25, 47104]_2$ code invariant under the sporadic simple group ${rm Co}_1$ is constructed by adjoining the all-ones vector to the faithful and absolutely irreducible 24-dimensional code of length 98280. Using the action of ${rm Co}_1$ on the code we give a description of the nature of the codewords of any non-zero weight relating these to vectors of types 2, 3 and 4, respectively of the Leech lattice. We show that the stabilizer of any non-zero weight codeword in the code is a maximal subgroup of ${rm Co}_1$. Moreover, we give a partial description of the nature of the codewords of minimum weight of the dual code.

1 citations


Book ChapterDOI
02 Sep 2022
TL;DR: In this article , the minimum weight design of a nanocomposite laminate is investigated subject to a frequency constraint, and Halpin-Tsai micromechanical equations are used to determine the material properties of the three-phase composite.
Abstract: Nanoscale reinforcements are presently being used to produce composites with improved stiffness and weight properties. One of the common nanocomposite material is based on the multiscale polymer/fibre/carbon nanotube (CNT) combination. In this case, the scales are the polymer matrix (macroscale), fibres (microscale) and CNT, leading to a multiscale material. The properties of the nanocomposite laminates can be further improved by optimizing the distribution of the reinforcements. This is due to the fact that the reinforcements contribute more to the stiffness of the laminate when placed in the surface layers. In the present study, minimum weight design of a nanocomposite laminate is investigated subject to a frequency constraint. Halpin-Tsai micromechanical equations are used to determine the material properties of the three-phase composite. Fibre and CNT reinforcements are distributed non-uniformly across the layers resulting higher volume contents of the reinforcements in the surface layers.

1 citations


Journal ArticleDOI
TL;DR: In this paper , a single-criteria parametric optimization algorithm for single-surface shell on the square contour is presented, where the objective function is the weight of the shell and the design variables are the shell thickness from 1 to 100 mm.
Abstract: The optimal design in applied mechanics is used to improve the efficiency of minimal surface shells, this process is carried out until the design can no longer be better given the input data, using a certain optimization method. It has several advantages while building structures are designing. One of the passes is the optimization process, which provides a systematization, a logical procedure for the design of shells. With the correct use of the optimization algorithm, it is possible to reduce the probability of a designer's mistake. Modern optimization methods can be applied to problems that have more than a million design variables and constraints. Optimization algorithms work effectively when there is some regularity in the objective function, such as a convexity or a depression, so when choosing an optimization algorithm, it is necessary to consider their advantages and disadvantages. While minimizing the objective function fmin, the main task is to find the point of the global minimum, the value of fmin (X) will be minimal, taking into account the restrictions. Determining the global minimum is quite a difficult task. Much more often, a point has a local minimum, and the task of the designer is to investigate where the point of the local and global minimum is. The optimization algorithm for single-criteria parametric optimization is performed as follows: the objective function is the weight of the shell of the minimum surface on the square contour, the design variables are the shell thickness from 1 to 100 mm, the constraints are presented - the first forced oscillation frequency is 0.10 Hz. The results of changing the objective function are reduction in the weight of the shell, which is in the percentage equivalent of 9.6% without losing the strength and stability of the minimum surface shell on the square contour. The first forced oscillation frequency after the optimization calculation from the thermoforce load is 0.10187155 Hz, which is actually represented by the limitation. Using the author's methodology and software, it is possible to perform an effective optimization calculation of the minimum surface shell on the square contour.

Journal ArticleDOI
TL;DR: In this paper , the optimal weight design of a reinforced concrete beam subjected to various loading conditions is investigated, and two novel metaheuristics, grey wolf (GW) and backtracking search (BS) optimization algorithms are selected as optimizers.
Abstract: In this study, optimal weight design of a reinforced concrete beam subjected to various loading conditions is investigated. The purpose of the optimization is to attain the minimum weight design of the reinforced concrete beam under distributed and two-point loads. The design problem is handled under three different design load cases. The two-point loads are affected on beam-to-beam connection nodes of reinforced concrete beams. Thus, while the magnitudes of distributed load and two-points load are remained constant, the distances between two-points loads are taken as 2m, 3m and 4m, respectively. The width and height of the rectangular cross-section of the concrete beam, and the diameters of the longitudinal and confinement steel rebars are treated as design variables of the optimum design problem. The design constraints of the optimization problem consist of the geometric constraints and necessities of the Turkish Requirements for Design and Construction of Reinforced Concrete Structures (TS500), and Turkish Building Earthquake Code (TBEC). As two novel metaheuristics, grey wolf (GW) and backtracking search (BS) optimization algorithms are selected as optimizers. Both algorithms are independently operated five times for three different design problems. Thus, the obtained results are examined statistically to compare in accordance with algorithmic performances. The optimal findings from optimization algorithms show that the GW algorithm is a little bit more robust on the exploitation phase, while the BS algorithm is stronger on the exploration phase. Moreover, it can be deducted from optimal beam designs that the GW algorithm is more viable to minimize reinforced concrete beam design.


Posted ContentDOI
10 May 2022
TL;DR: In this paper , a family of local search algorithms for the minimum-weight spanning tree, indexed by a parameter ρ, was considered, where one step of the local search corresponds to replacing a connected induced subgraph of the current candidate graph whose total weight is at most ρ by the minimum spanning tree (MST) on the same vertex set.
Abstract: We consider a family of local search algorithms for the minimum-weight spanning tree, indexed by a parameter $\rho$. One step of the local search corresponds to replacing a connected induced subgraph of the current candidate graph whose total weight is at most $\rho$ by the minimum spanning tree (MST) on the same vertex set. Fix a non-negative random variable $X$, and consider this local search problem on the complete graph $K_n$ with independent $X$-distributed edge weights. Under rather weak conditions on the distribution of $X$, we determine a threshold value $\rho^*$ such that the following holds. If the starting graph (the "initial candidate MST") is independent of the edge weights, then if $\rho > \rho^*$ local search can construct the MST with high probability (tending to $1$ as $n \to \infty$), whereas if $\rho < \rho^*$ it cannot with high probability.

Journal ArticleDOI
TL;DR: In this article , three formulations of numerical layout optimization for long-span structures are presented, and an approach that combines formulations is proposed to more closely model real-world behaviour and to reduce computational expense.
Abstract: Abstract Layout optimization provides a powerful means of identifying materially efficient structures. It has the potential to be particularly valuable when long-span structures are involved, since self-weight represents a significant proportion of the overall loading. However, previously proposed numerical layout optimization methods neglect or make non-conservative approximations in their modelling of self-weight and/or multiple load-cases. Combining these effects presents challenges that are not encountered when they are considered separately. In this paper, three formulations are presented to address this. One formulation makes use of equal stress catenary elements, whilst the other two make use of elements with bending resistance. Strengths and weaknesses of each formulation are discussed. Finally, an approach that combines formulations is proposed to more closely model real-world behaviour and to reduce computational expense. The efficacy of this approach is demonstrated through application to a number of 2D- and 3D-structural design problems.


Journal ArticleDOI
TL;DR: In this paper , a grillage structure design system under the constraint of high natural frequency is introduced and the design system adopted genetic algorithm to realize optimization procedure and can be used at the design of the experimental facilities of marine field such as a towing carriage, PMM, test frame, measuring frame and rotating arm.
Abstract: Normal strategy of structure optimization procedure has been minimum cost or weight design. Minimum weight design satisfying an allowable stress has been used for the ship and offshore structure, but minimum cost design could be used for the case of high human cost. Natural frequency analysis and forced vibration one have been used for the strength estimation of marine structures. For the case of high precision experiment facilities in marine field, the structure has normally enough margin in allowable stress aspect and sometimes needs high natural frequency of structure to obtain very high precise experiment results. It is not easy to obtain a structure design with high natural frequency, since the natural frequency depend on the stiffness to mass ratio of the structure and increase of structural stiffness ordinary accompanies the increase of mass. It is further difficult at the grillage structure design using the profiles, because the properties of profiles are not continuous but discrete, and resource of profiles are limited at the design of grillage structure. In this paper, the grillage structure design system under the constraint of high natural frequency is introduced. The design system adopted genetic algorithm to realize optimization procedure and can be used at the design of the experimental facilities of marine field such as a towing carriage, PMM, test frame, measuring frame and rotating arm.

Journal ArticleDOI
TL;DR: In this paper , it was shown that the problem is NP-complete for chordal graphs, planar graphs and for two subclasses of bipartite graphs, namely, star convex bipartitite graphs and comb convex-bipartite graph, unless NP ⊆ DTIME(|V | O(log log| V |) ).
Abstract: Let G be a simple, undirected graph. A function g : V ( G ) → {0, 1, 2, 3} having the property that ∑ v∈NG(u) g(v)≥3, if g ( u ) = 0, and ∑ v∈NG(u) g(v)≥2, if g ( u ) = 1 for any vertex u ∈ G , where N G ( u ) is the set of vertices adjacent to u in G , is called a Roman {3} -dominating function (R3DF) of G . The weight of a R3DF g is the sum g ( V )=∑ v ∈ V g ( v ). The minimum weight of a R3DF is called the Roman {3} -domination number and is denoted by γ {R3} ( G ). Given a graph G and a positive integer k , the Roman {3}-domination problem (R3DP) is to check whether G has a R3DF of weight at most k . In this paper, first we show that the R3DP is NP-complete for chordal graphs, planar graphs and for two subclasses of bipartite graphs namely, star convex bipartite graphs and comb convex bipartite graphs. The minimum Roman {3}-domination problem (MR3DP) is to find a R3DF of minimum weight in the input graph. We show that MR3DP is linear time solvable for bounded tree-width graphs, chain graphs and threshold graphs, a subclass of split graphs. We propose a 3(1 + ln(Δ − 1))-approximation algorithm for the MR3DP, where Δ is the maximum degree of G and show that the MR3DP problem cannot be approximated within (1 − ε)ln| V | for any ε > 0 unless NP ⊆ DTIME(| V | O(loglog| V |) ). Next, we show that the MR3DP problem is APX-complete for graphs with maximum degree 4. We also show that the domination and Roman {3}-domination problems are not equivalent in computational complexity aspects. Finally, an ILP formulation for MR3DP is proposed.

Journal ArticleDOI
TL;DR: It is shown that these two query problems are equivalent for query ranges that are squares, for data structures having $\Omega(\log n)$ query times, and new data structures for range closest pair queries with squares are obtained.
Abstract: Let S be a set of n weighted points in the plane and let R be a query range in the plane. In the range closest pair problem, we want to report the closest pair in the set R ∩ S . In the range minimum weight problem, we want to report the minimum weight of any point in the set R ∩ S . We show that these two query problems are equivalent for query ranges that are squares, for data structures having Ω ( log ⁡ n ) query times. As a result, we obtain new data structures for range closest pair queries with squares.

Journal ArticleDOI
TL;DR: In the article discussing the minimum range tree, especially kruskal and sollin algorithms, and applied more specifically to the national transmission network of South Sulawesi Province, then the network can be obtained optimally.
Abstract: Graph theory is one part of the branch of mathematics that is now very famous in computer design. The substitution of a graph is an object statement referred to as a noktah, circle or point, and the object relationship is referred to as a line. Graph is applied in various scientific disciplines, for example: economics, genetic psychology, operation research and network optimization (telecommunication network, PLN transmission (electricity network, PDAM water distribution network). Kruskal and Sollin's algorithm have some similarities in their use for solving the problem of trees stretching the minimum from the smallest to the largest amount in each weight. In the article discussing the minimum range tree, especially kruskal and sollin algorithms, and applied more specifically to the national transmission network of South Sulawesi Province, then the network can be obtained optimally.

Journal ArticleDOI
TL;DR: In this paper , the minimum quasi-total Roman domination problem (MQTRDP) was shown to be NP-hard for split graphs, star convex bipartite graphs, and planar graphs.
Abstract: For a simple, undirected, connected graph G=(V,E), a function f : V(G) →{0, 1, 2} which satisfies the following conditions is called a quasi-total Roman dominating function (QTRDF) of G with weight f(V(G))=ΣvEV(G) f(v).C1). Every vertex ueV for which f(u) = 0 must be adjacent to at least one vertex v with f(v) = 2, and C2). Every vertex ueV for which f(u) = 2 must be adjacent to at least one vertex v with f(v)≥1. For a graph G, the smallest possible weight of a QTRDF of G denoted γqtR(G) is known as the quasi-total Roman domination number of G. The problem of determining γqtR(G) of a graph G is called minimum quasi-total Roman domination problem (MQTRDP). In this paper, we show that the problem of determining whether G has a QTRDF of weight at most l is NP-complete for split graphs, star convex bipartite graphs, comb convex bipartite graphs and planar graphs. On the positive side, we show that MQTRDP for threshold graphs, chain graphs and bounded treewidth graphs is linear time solvable. Finally, an integer linear programming formulation for MQTRDP is presented.

Journal ArticleDOI
TL;DR: In this paper , the complexity difference between Min-PIDF and the problem of finding the minimum weight of an Italian dominating function was discussed, and the hardness of approximation of Min-IDF in general graphs was investigated.

Proceedings ArticleDOI
31 Jul 2022
TL;DR: An O(lg W)-approximation of the MAXIMUM WEIGHTED LEAF TREE problem is presented where W is the maximum weight divided by the minimum weight that appears on the vertices.
Abstract: The MAXIMUM WEIGHTED LEAF TREE problem consists of, given a connected graph G and a weight function w: V (G) → Q+, finding a tree in G whose weight on the leaves is maximized. The variant that requires the tree to be spanning is at least as hard to approximate as the maximum independent set problem. If all weights are unitary, it turns into the well-known problem of finding a spanning tree with maximum number of leaves, which is NP-hard, but is in APX. No further innapproximability result is known for MAXIMUM WEIGHTED LEAF TREE, and the best approximation is an O(lg n)-approximation. In this paper, we present an O(lg W)-approximation where W is the maximum weight divided by the minimum weight that appears on the vertices.

Proceedings ArticleDOI
03 Jan 2022
TL;DR: In this paper , the shape and size of a composite tube with a compressible cross-section around a cylinder were optimized using HEEDS and ABAQUS, and three optimization runs from different initial designs were completed using SHERPA and genetic algorithm optimization methods.
Abstract: Deployable structures are used for many different spacecraft applications like solar arrays, antennas, and booms. They allow spacecraft with large structural components to comply with the volume restrictions of launch platforms. This research optimizes the shape and size of these structural components with both the stowed and deployed configurations in mind. HEEDS, a commercial optimization software, and ABAQUS, a commercial finite element analysis software, are used to evaluate and alter the structure using a single simulation. This makes the design process more efficient than running many different simulations individually. The optimization objectives, design variables, and constraints are chosen to fit the mission requirements of the structure. The structure analyzed in this research is a composite tube with a compressible cross-section wrapped around a cylinder. The change in cross-section reduces the bending stiffness of the tube and allows it to be wrapped without damaging the material. The dimensions controlling cross-section shape and the thickness of the composite layers are the design variables for the optimization. The maximum strain energy stored in the wrapped tube, the minimum volume of the structure, and the minimum weight of the tube are the objectives for the optimization. The strain energy is maximized to get the stiffest possible structure and satisfy the minimum natural frequency constraint. The weight and volume of the tube are minimized because reducing weight and volume is important for any spacecraft structure. Constraints are placed on the design variables and objectives and the Hashin damage criteria are used to ensure wrapping does not cause material failure. Three optimization runs from different initial designs are completed using SHERPA and genetic algorithm optimization methods. The results are compared to determine which optimization method performs best and how the different starting points affect the final results. After the optimized design is found, the full wrapping and deployment simulation is completed to analyze the behavior of the optimized design.

Posted ContentDOI
01 Mar 2022
TL;DR: In this article , the minimum weight and smallest weight minimum-size dominating set problems in vertex-weighted graphs and networks are considered, and the corresponding randomized algorithms for finding small-weight dominating sets in graphs are described as well.
Abstract: We consider the minimum weight and smallest weight minimum-size dominating set problems in vertex-weighted graphs and networks. The latter problem is a two-objective optimization problem, which is different from the classic minimum weight dominating set problem that requires finding a dominating set of the smallest weight in a graph without trying to optimize its cardinality. First, we show how to reduce the two-objective optimization problem to the minimum weight dominating set problem by using Integer Linear Programming formulations. Then, under different assumptions, the probabilistic method is developed to obtain upper bounds on the minimum weight dominating sets in graphs. The corresponding randomized algorithms for finding small-weight dominating sets in graphs are described as well. Computational experiments are used to illustrate the results for two different types of random graphs.

Posted ContentDOI
10 Oct 2022
TL;DR: In this article , the authors presented an approach for using minimum-weight surfaces in bounded Voronoi diagrams to generate synthetic 3D images of cracks in a cellular complex with weighted facets.
Abstract: Shortest paths play an important role in mathematical modeling and image processing. Usually, shortest path problems are formulated on planar graphs that consist of vertices and weighted arcs. In this context, one is interested in finding a path of minimum weight from a start vertex to an end vertex. The concept of minimum-weight surfaces extends shortest paths to 3d. The minimum-weight surface problem is formulated on a cellular complex with weighted facets. A cycle on the arcs of the complex serves as input and one is interested in finding a surface of minimum weight bounded by that cycle. In practice, minimum-weight surfaces can be used to segment 3d images. Vice versa, it is possible to use them as a modeling tool for geometric structures such as cracks. In this work, we present an approach for using minimum-weight surfaces in bounded Voronoi diagrams to generate synthetic 3d images of cracks.



Journal ArticleDOI
TL;DR: In this article , the authors formulate discrete mathematical programming models to determine the optimal thicknesses for three different criteria: maximize reliability, minimize weight, and achieve a trade-off between maximizing reliability and minimizing weight.
Abstract: A light and reliable aircraft has been the major goal of aircraft designers. It is imperative to design the aircraft wing skins as efficiently as possible since the wing skins comprise more than fifty percent of the structural weight of the aircraft wing. The aircraft wing skin consists of many different types of material and thickness configurations at various locations. Selecting a thickness for each location is perhaps the most significant design task. In this paper, we formulate discrete mathematical programming models to determine the optimal thicknesses for three different criteria: maximize reliability, minimize weight, and achieve a trade-off between maximizing reliability and minimizing weight. These three model formulations are generalized discrete resource-allocation problems, which lend themselves well to the dynamic programming approach. Consequently, we use the dynamic programming method to solve these model formulations. To illustrate our approach, an example is solved in which dynamic programming yields a minimum weight design as well as a trade-off curve for weight versus reliability for an aircraft wing with thirty locations (or panels) and fourteen thickness choices for each location.

Posted ContentDOI
22 Nov 2022
TL;DR: In this paper , it was shown that the weights of a complete graph are independent copies of a symmetric random variable (satisfying a mild condition on tail probabilities), in particular when the weights are Gaussian.
Abstract: Suppose that the edges of a complete graph are assigned weights independently at random and we ask for the weight of the minimal-weight spanning tree, or perfect matching, or Hamiltonian cycle. For these and several other common optimisation problems, we establish asymptotically tight bounds when the weights are independent copies of a symmetric random variable (satisfying a mild condition on tail probabilities), in particular when the weights are Gaussian.