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This paper presents a practical optimum design solution of prismatic simply supported prestressed concrete girders that are subjected to uniformly distributed static loads. While assuming linear elastic behaviour and employing working stresses method, the optimum values of two design variables, namely the cross-sectional dimensions and the prestressing force, are formulated as a nonlinear optimization model. Optimum values of the design variables are computed to satisfy either a minimum weight or a minimum cost objective function. To solve the nonlinear programming models, a program named Non-Linear Programming Prestressed Concrete Optimizer (NLPRECO) was coded in MATLAB® programming environment. Some illustrative design problems were solved using NLPRECO and their results are demonstrated herein. Sensitivity analysis of the optimized design variables, to variations in design parameters, was also investigated and the results are presented. Results show substantial improvement over the regular un-optimized solutions and moderate improvement over a linear programming optimization solutions.

The minimum weight of the code generated by the incidence matrix of points versus lines in a projective plane has been known for over 50 years. Surprisingly, finding the minimum weight of the dual code of projective planes of non-prime order is still an open problem, even in the Desarguesian case. In this paper, we focus on the case of projective planes of order $$p^2$$ p 2 , where p is prime, and we link the existence of small weight code words in the dual code to the existence of embedded subplanes and antipodal planes. In the Desarguesian case, we can exclude such code words by showing a more general result that no antipodal plane of order at least 3 can be embedded in a Desarguesian projective plane. Furthermore, we use combinatorial arguments to rule out the existence of code words in the dual code of points and lines of an arbitrary projective plane of order $$p^2$$ p 2 , p prime, of weight at most $$2p^2-2p+4$$ 2 p 2 - 2 p + 4 using more than two symbols. In particular, this leads to the result that the dual code of the Desarguesian projective plane $${{\,\textrm{PG}\,}}(2,p^2)$$ PG ( 2 , p 2 ) , $$p\ge 5$$ p ≥ 5 , has minimum weight at least $$2p^2-2p+5$$ 2 p 2 - 2 p + 5 .

An Italian dominating function on a simple undirected graph G is a function f : V ( G ) ⟶ { 0 , 1 , 2 } satisfying the condition that for each vertex v with f ( v ) = 0 , ∑ u ∈ N G ( v ) f ( u ) ≥ 2 . An Italian dominating function f on G is called a perfect Italian dominating function on G if for each vertex v with f ( v ) = 0 , ∑ u ∈ N G ( v ) f ( u ) = 2 . The weight of a function f on a graph G , denoted by w ( f ) , is the sum ∑ v ∈ V ( G ) f ( v ) . For a simple undirected graph G , Min-PIDF is the problem of finding the minimum weight of a perfect Italian dominating function on G . First, we discuss the complexity difference between Min-PIDF and the problem of finding the minimum weight of an Italian dominating function. We then establish the NP -completeness of the decision version of Min-PIDF in chordal graphs and investigate the hardness of approximation of Min-PIDF in general graphs. Finally, we present linear time algorithms for computing the minimum weight of a perfect Italian dominating function in block graphs and series-parallel graphs.

There has been a growing interest in the use of free-form structures with irregularly curved yet aesthetically pleasing configurations in the recent decades. Although design optimization of regular steel grids has been well addressed in the literature of structural optimization, still limited work has been devoted to optimum design of real-size free-form grid structures. On the one hand, a main obstacle when dealing with real-size free-form steel grids is the excessive computational effort associated with contemporary evolutionary optimization algorithms. On the other hand, it is generally perceived that the obtained final designs using conventional optimization algorithms may not necessarily be favored in practice if certain provisions are not stipulated by the algorithm to preclude an abundance of distinct steel section sizes in the final design. Hence, instead of offering a single optimum or near optimum design, it would be more desirable to provide the designer or decision maker with a Pareto front set of non-dominated design alternatives taking into account both the minimum weight as well as the assortment of available steel section sizes in the final design. Accordingly, in this paper, a computationally efficient multi-stage guided stochastic search algorithm is proposed for optimization and standardization of real-size free-form steel double-layer grids. A gradual design-oriented section elimination approach is followed where in the first optimization stage, a complete set of commercially available steel sections is introduced to the algorithm and in the succeeding stages, the size of section list is reduced by eliminating the redundant sizes. Two variants of the algorithm are employed to demonstrate the usefulness of the proposed technique in challenging test examples of free-form steel double-layer grids, and the obtained Pareto fronts are plotted to illustrate the trade-off between minimum weight and assortment of steel section sizes in the final design.

In this paper, we propose several algorithms for determining an optimal length tree-like refutation of linear feasibility in systems of Unit Two Variable Per Inequality (UTVPI) constraints. Given an infeasible UTVPI constraint system (UCS), a refutation certifies its infeasibility. The problem of finding refutations in a UCS finds applications in domains such as program verification and operations research. In general, there exist several types of refutations of feasibility in constraint systems. In this paper, we focus on a specific type of refutation called a tree-like refutation. Tree-like refutations are complete, in the sense that if a system of linear constraints is infeasible, then it must have a tree-like refutation. Associated with a refutation is its length, which equals the total number of constraints (accounting for the reuse of constraints) that are used to establish the infeasibility of the corresponding linear constraint system. Our goal in this paper is to find an optimal length tree-like refutation (OTLR) of an infeasible UCS. We describe two deterministic algorithms that find an OTLR of a UCS. If m is the number of constraints, n is the number of variables in the system, and k is the length of an OTLR, then our two algorithms run in O ( n 3 ⋅ log k ) time and O ( m ⋅ n ⋅ k ) time respectively. We also propose a true-biased, randomized algorithm for this problem. This algorithm runs in O ( m ⋅ n ⋅ log n ) time, and returns the length of an OTLR with probability ( 1 − 1 e ) . We extend our work to weighted UTVPI constraint systems (WUCS), where a positive weight is associated with each UTVPI constraint. The weight of a tree-like refutation is defined as the sum of the weights of the constraints used by the refutation. The problem of finding a minimum weight refutation in a WUCS is called the weighted optimal length tree-like refutation (WOTLR) problem and is known to be NP-hard. We propose a pseudo-polynomial time algorithm for the WOTLR problem and convert it into a fully polynomial time approximation scheme (FPTAS).

We investigate the total number of edge crossings (i.e., the crossing number) of the Euclidean minimum weight Laman graph \(\mathsf {MLG}(P)\) on a planar point set P. Bereg et al. (2016) showed that the upper and lower bounds for the crossing number of \(\mathsf {MLG}(P)\) are \(6|P|-9\) and \(|P|-3\), respectively. In this paper, we improve these upper and lower bounds given by Bereg et al. (2016) to \(2.5|P|-5\) and \((1.25-\varepsilon )|P|\) for any \(\varepsilon > 0\), respectively. Especially, for improving the upper bound, we introduce a novel counting scheme based on some geometric observations.

Given a bipartite graph G = ( V 1 , V 2 , E ) , a biclique of G is a complete bipartite subgraph of G , and a biclique partitioning of G is a set A ⊆ E such that the bipartite graph G ′ = ( V 1 , V 2 , A ) is a vertex-disjoint union of bicliques. The biclique partitioning problem (BPP) consists of, given a complete bipartite graph G = ( V 1 , V 2 , E ) with edge weights w e ∈ R for all e ∈ E (thus, negative weights are allowed), finding a biclique partitioning A ⊆ E of minimum weight. The bicluster editing problem (BEP) is a variant of the BPP and consists of editing a minimum number of edges of an input bipartite graph G in order to transform its edge set into a biclique partitioning. Editing an edge consists of either adding it to the graph or deleting it from the graph. In addition to the BPP and the BEP, other problems in the literature aim at finding biclique partitionings, and this motivates the study of the biclique partitioning polytope P n m of the complete bipartite graph K n m (i.e., P n m is the convex hull of the incidence vectors of the biclique partitionings of K n m ). In this paper we develop such a polyhedral study and show that ladder, bellows, and grid inequalities induce facets of P n m . Our computational results show that these inequalities are very effective in solving the BEP. In particular, they are able to improve the value of the relaxed solution by up to 20%.

Composites have proved their usefulness in the automotive industry during recent years. Many automobile companies use them in different parts to reduce weight without hampering strength. In a composite material, Lay-up sequence and orientation highly affects the properties of the laminate. Therefore, it is important to perform design optimization on a component to achieve high strength in minimum weight. This paper deals with the optimization of lay-up for composite Racing Seat using finite element analysis. Different lay-up sequences for laminates including, cross-ply [0/90]n, angle-ply [±α]n, and [0/90/±α]n are analysed. The lay-up sequence, orientation and ply number are optimized using composite material carbon fibre/Epoxy. Driver’s ergonomics and impact sustainability are considered constraints for weight optimization. Driver’s ergonomics were based on 95th percentile male and 5th percentile female rule. Force analysis is performed on the seat according to SFI 39.2 to evaluate the strength requirement. Finite element analysis of composite racing seat is performed via commercial finite element code ANSYS and using the capabilities of ANSYS Composite PrepPost (ACP) to form desired composite lay-up. A finite element code is based on classical lamination theory; including Puck’s failure criterion for first-ply failure. The seat is divided into three portions with a different number of layers considering the values and specific nature of acting forces; which resulted in different thicknesses in different regions. The optimization results show that for all the angles of Angle-ply laminate considered, Angle-ply laminates with an angle of 45⁰ provides a more optimum design. The minimum weight obtained is 10.15 kg.

Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. These codes were first introduced by Massey in 1964. Nowadays, LCD codes are extensively studied in the literature and widely applied in data storage, cryptography, etc. In this paper, we prove some properties of binary LCD codes using their shortened and punctured codes. We also present some inequalities for the largest minimum weight $d_{LCD}(n,k)$ of binary LCD [n,k] codes for given length n and dimension k. Furthermore, we give two tables with the values of $d_{LCD}(n,k)$ for $k\le 32$ and $n\le 40$, and two tables with classification results., 19 pages

This work addresses the balanced connected k -partition problem ( BCP k ), which is formally defined as follows. Given a connected graph G = ( V , E ) with nonnegative weights on the vertices, find a partition { V i } i = 1 k of V such that each class V i induces a connected subgraph of G , and the weight of a class with the minimum weight is as large as possible. This problem, known to be NP -hard, has been largely investigated under different approaches and perspectives: exact algorithms, approximation algorithms for some values of k or special classes of graphs, and inapproximability results. On the practical side, BCP k is used to model many applications arising in image processing, cluster analysis, operating systems and robotics. We propose three linear programming formulations for BCP k . The first one contains only binary variables and a potentially large number of constraints that can be separated in polynomial time in the corresponding linear relaxation. We introduce new valid inequalities and design polynomial-time separation algorithms for them. The other two formulations are based on flows and have a polynomial number of constraints and variables. Our computational experiments show that the exact algorithms based on the proposed formulations outperform the other exact approaches presented in the literature.

An outer independent (double) Roman dominating function is a (double) Roman dominating function f for which the set of vertices assigned 0 under f is independent. The outer independent (double) Roman domination number ( $$\gamma _{oidR}(G)$$ ) $$\gamma _{oiR}(G)$$ is the minimum weight taken over all outer independent (double) Roman dominating functions of G. A vertex cover number $$\beta (G)$$ is the minimum size of any vertex cover sets of a graph G. In this work, we present some contributions to the study of outer independent double Roman domination in graphs. Characterizations of the families of all connected graphs with small outer independent double Roman domination numbers, and tight lower and upper bounds on this parameter are given. We also prove that the decision problem associated with $$\gamma _{oidR}(G)$$ is NP-complete even when restricted to planar graphs with maximum degree at most four. We moreover prove that $$2\beta (T)+1\le \gamma _{oidR}(T)\le 3\beta (T)$$ for any tree T, and show that each integer between the lower and upper bounds is realizable. Finally, we give an exact formula for this parameter concerning the corona graphs.

We show that the minimum weight of a weighted blow-up of $\mathbf A^d$ with $\varepsilon$-log canonical singularities is bounded by a constant depending only on $\varepsilon $ and $d$. This was conjectured by Birkar. Using the recent classification of $4$-dimensional empty simplices by Iglesias-Vali\~no and Santos, we work out an explicit bound for blowups of $\mathbf A^4$ with terminal singularities: the smallest weight is always at most $32$, and at most $6$ in all but finitely many cases., Comment: Sections 3.3 and 3.4 are completely new, and give a proof of Conjecture 1.2 (Birkar) in the general case. Title changed to reflect the increased generality. Minor changes and restructuring in other places

The bounded diameter minimum spanning tree (BD-MST) problem seeks a spanning tree (T) of minimum weight on a given connected, undirected and edge-weighted graph subject to the diameter of T does not exceed $$D \ge 2$$ , where D is a given positive integer. The BD-MST problem is $${\mathcal {N}}{\mathcal {P}}$$ -hard problem and finds many real-world applications. In this paper, we propose an artificial bee colony (ABC) algorithm for the BD-MST problem. ABC algorithm is a swarm-based metaheuristic technique based on the intelligent foraging behavior of honeybees. The proposed ABC algorithm employs permutation encoding. To exploit this encoding structure, two neighborhood strategies that help ABC algorithm in faster convergence towards finding high quality solutions are applied. On a set of Euclidean and non-Euclidean benchmark instances for various diameter bounds, the proposed approach has been compared with state-of-the-art approaches. Computational results demonstrate the effectiveness of the proposed approach to the other extant approaches in the literature.

Given an edge-weighted graph and a subset of the vertices called terminals, the multiway cut problem aims to find a minimum weight set of edges that separates each terminal from all the others. This problem is known to be NP-hard even for $$k=3$$ . Computational experiments on social networks obtained from the Indian e-commerce company Flipkart show that an integer programming formulation (referred to as EF2) of the problem introduced by Chopra and Owen (1996) provides a very strong LP-relaxation that allows us to solve large problems in a reasonable amount of time. We show that the cardinality EF2 (where all edge weights are 1) on a wheel graph has a primal integer solution and a dual integer solution of the same value. We consider a hub-spoke network of wheel graphs constructed by adding edges connecting the hub vertices of a collection of wheel graphs. We assume that every wheel has a terminal hub or a terminal vertex with three non-terminal neighbors, and show that if the graph connecting the hub vertices is planar, the cardinality EF2 on the hub-spoke network of the wheel graphs has a primal integer solution and a dual integer solution of the same value. Given the prevalence of such structures in our social networks, our results provide some theoretical justification for the strong empirical performance of the EF2 formulation.

Purpose This paper aims to focus on studying the influence of gradient parameters, namely, thickness coefficient, length coefficient and height ratio of auxetic structure on responses such as strength, stiffness and specific energy absorption (SEA) under compressive loading. Optimization of significant parameters is also performed to maximize responses. Further, efforts have also been made to develop regression models for strength, stiffness and SEA of auxetic structure. Design/methodology/approach Central composite design of response surface methodology is used for planning experiments. Auxetic structures of acrylonitrile butadiene styrene (ABS) and poly-lactic acid (PLA) materials are fabricated by the material extrusion (ME) technique of additive manufacturing. Fabricated structures are tested under in-plane uniaxial compressive loading. Grey relational analysis is used for the optimization of gradient parameters of the unit cell of auxetic structure to maximize responses and minimize weight and time of fabrication. Findings From the analysis of variance of experimental data, it is found that the compressive strength of auxetic structures increases with a decrease in length coefficient and height ratio. In the case of ABS structures, stiffness increases with a decrease in thickness coefficient and length coefficient, while in the case of PLA structures, stiffness increases with a decrease in length coefficient and height ratio. SEA is influenced by length coefficient and thickness coefficient in ABS and PLA structures, respectively. Based on the analysis, statistical non-linear quadratic models are developed to predict strength, stiffness and SEA. Optimal configuration of auxetic structure is determined to maximize strength, stiffness, SEA and minimize weight and time of fabrication. Research limitations/implications The present study is limited to re-entrant type of auxetic structures made of ABS and PLA materials only under compressive loading. Also, results from the current study are valid within a selected range of gradient parameters. The findings of the present study are useful in the optimal selection of gradient parameters for the fabrication of auxetic structures of maximum strength, stiffness and SEA with minimum weight and time of fabrication. These outcomes have wide applications in domains such as automotive, aerospace, sports and marine sectors. Originality/value Limited literature is available on studying the influence of gradient parameters of ME manufactured auxetic structure of ABS and PLA materials on responses, namely, strength, stiffness and SEA under compressive loading. Also, no work has been reported on studying the influence of gradient parameters on mechanical properties, weight and time of fabrication of auxetic structures. The present study is an attempt to fulfil the above research gaps.

The optimum elastic design of p itched roof frames has been studied. An iterative method which uses Taylor's first order series expansion to express the various required constraints is employed. The function of the problem is linear in the design variables, which enables the simp lex line ar programming algorithm to be used to solve the problem, An example of rectangular hall has been investigated. The hall is cove red by pitched roof frames with different sp ans, spacing and slop es. Stress and deflection limitations are taken into consideration and the optimum cross-sectional area of the various members of the structure has been obtained. Design charts to determine the minimum weight of p itched roof frames, with different sp ans, spacing and slopes, covering a rectangular hall are given.

The integral shrouded blisk provides better performance with minimum weight, but its semi-open structure presents problems for its production. Manufacturing processes of these components require a removal of about 70%-90% of material from their blanks. Multi-axis electrical discharge machining (EDM) is commonly used for these processes, but its poor efficiency cannot meet the requirements of mass production. Strong flushing assisted high-current discharge is able to improve the machining efficiency. In this paper, this method was applied to manufacture the integral shrouded blisk. An electrode design method was proposed. Taking the largest revolving entity inside the flow channel as the base geometry, this laminated arc-shaped hollow electrode meets the requirements such as high pressure flushing, tool wear compensation, and easy to be made. A 4-axis linkage machining tool path with planetary motion was proposed. Taking an integral guide vane ring as an example, it has been experimentally verified that the time consumption for each channel using this method was reduced to a half of the ordinary EDM method, while the finished surface quality remains same.

This research aims to minimize the weight of truss structures using force method formulation as a structural analyzer and Jaya algorithm as an optimizer tool. Constraints considered herein include stress limitations, displacement limitations, and size limitations. Design variables include the cross-sectional area of each element. They may easily be related to each other which will lead to decrease of design variables. Jaya algorithm is a meta-heuristic random search method recently developed for constrained and unconstrained problems. The main superiority of Jaya algorithm to other random search methods is that it does not need any specific tuning parameter to generate next population. This algorithm consists of two steps in each cycle. First, a new population is generated using a simple random formula. Second, each new point is compared to its corresponding previous one while penalty function method is implemented. If the new point is in a better condition than the old one, the old one is replaced by the new one. All points are tested similarly till the population is updated. The procedure is repeated so as to achieve the desired convergence. Several landmark examples appearing in the literature have been solved by the proposed method, thus showing the efficacy of the developed procedure. A perusal of results shows that procedure is not sensitive to the starting points and it should just be selected large enough to lie in feasible-usable design space. Moreover, rapid reduction of weight is obtained in the first few steps and the tendency of decreasing of the weight appears to be monotonic and uniform in all examples. Unlike other metaheuristic methods that need a large number of optimization cycles to settle near the optimum point, combination of force method and Jaya algorithm provides higher computational efficiency and rapid convergence ability achieved by the above match. This is owing to the forced method formulation that makes the stress constraints to be linear, resulting in facilitating the procedure and enhancing its efficiency.

The automatic optimal design of feeding system in the shape casting process is considered in the present work. In fact, the goal is to find the optimal position, size, shape, and topology of risers in the shape casting process. This problem is formulated as a minimum weight topology optimization problem subjected to a non-linear transient PDE and space-time state dependent pointwise constraints. An elegant bi-level reformulation of the optimization problem is introduced which makes it possible to manage the infinite number of design parameters and state constraints efficiently. The computational cost of this algorithm is independent of the number of constraints. The validity and efficiency of the presented method are supported by several examples, from simple benchmarks to complex industrial castings. According to numerical results, the presented approach makes a complete solution to the problem of automatic optimal riser design in the shape casting process.

We consider multiway cut, a basic graph partitioning problem in which the goal is to find the minimum weight collection of edges disconnecting a given set of special vertices called terminals. Multiway cut admits a well-known simplex embedding relaxation, where rounding this embedding is equivalent to partitioning the simplex. Current best-known solutions to the problem are comprised of a mix of several different ingredients, resulting in intricate algorithms. Moreover, the best of these algorithms is too complex to fully analyze analytically, and a computer was partly used in verifying its approximation factor. We propose a new approach to simplex partitioning and the multiway cut problem based on general transformations of the simplex that allow dependencies between the different variables. Our approach admits much simpler algorithms and, in addition, yields an approximation guarantee for the multiway cut problem that (roughly) matches the current best computer-verified approximation factor.

It is well-known that each left ideal in a matrix rings over a finite field is generated by an idempotent matrix. In this work we compute the number of left ideals in these rings, the number of different idempotents generating each left ideal, and give explicitly a set of idempotent generators of all left ideals of a given rank. We then apply these results to give examples of left group codes that have best possible minimum weight.

Consider $$n$$ nodes $$\{X_i\}_{1 \le i \le n}$$ independently distributed in the unit square $$S,$$ each according to a density $$f$$ , and let $$K_n$$ be the complete graph formed by joining each pair of nodes by a straight line segment. For every edge $$e$$ in $$K_n$$ , we associate a weight $$w(e)$$ that may depend on the individual locations of the endvertices of $$e$$ and is not necessarily a power of the Euclidean length of $$e.$$ Denoting $$\mathrm{TSP}_n$$ to be the minimum weight of a spanning cycle of $$K_n$$ corresponding to the travelling salesman problem (TSP) and assuming an equivalence condition on the weight function $$w(\cdot ),$$ we prove that $$\mathrm{TSP}_n$$ appropriately scaled and centred converges to zero almost surely and in mean as $$n \rightarrow \infty .$$ We also obtain upper and lower bound deviation estimates for $$\mathrm{TSP}_n.$$

The Steiner tree problem asks for a minimum weight subtree of an undirected graph spanning distinct terminal nodes. As one of the most fundamental network design problems, it has received much attention from both the mathematical programming and the algorithmic community and indeed, many integer linear programming (ILP) formulations of varying strength are known. The practical usefulness of the formulations can be enhanced with additional valid inequalities that reduce the gap between the efficiently computable continuous relaxation and the computationally difficult integer linear program. We aim to better understand the structure of these inequalities. In particular, we want to know how the inequalities can be obtained through Chvatal–Gomory cuts; a general procedure that is implemented in state-of-the-art ILP solver software. We start with the most basic ILP formulation for the Steiner tree problem and analyze how two known classes of strengthening inequalities – partition inequalities and odd-hole inequalities – can be derived systematically as Chvatal–Gomory cuts and how these inequalities themselves can be used to derive Chvatal–Gomory cuts. Along the way, we prove that the Chvatal rank of k -partition and k -odd-hole inequalities is at most k − 2 and k − 1 , respectively. In particular, this proves that k iterations of the Chvatal–Gomory cut procedure suffice to obtain a given k + 2 -partition or a given k + 1 -odd-hole inequality.

This paper presents the findings of a comparative study on minimum weight design and sensitivity evaluation using different experimental design methods for the structural design of an active-type deck support frame (DSF) developed for the float-over installation of an offshore plant topside. The thickness sizing variables of the structural members of a passive-type DSF were considered the design factors, and the output responses were defined using the weight and strength performances. The design of the experimental methods applied in the comparative study of the minimum weight design and the sensitivity evaluation were the orthogonal array design, Box– Behnken design, and Latin hypercube design. A response surface method was generated for each design of the experiment to evaluate the approximation performance of the design space exploration according to the experimental design, and the accuracy characteristics of the approximation were reviewed. Regarding the minimum weight design, the design results, such as numerical costs and weight minimization, of the experimental design for the best design case, were evaluated. The Box– Behnken design method showed the optimum design results for the structural design of the passive-type DSF.

This paper is devoted to the affine-invariant ternary codes defined by Hermitian functions. We first compute the incidence matrices of the 2-designs supported by the minimum weight codewords of these ternary codes. Then we show that the linear codes spanned by the rows of these incidence matrices are subcodes of the 4-th order generalized Reed-Muller codes and also hold 2-designs. Finally, we determine the dimension and develop a lower bound on the minimum distance of the ternary linear codes.

In the present paper, we give Assmus–Mattson type theorems for codes and lattices. We show that a binary doubly even self-dual code of length 24m with minimum weight 4m provides a combinatorial 1-design and an even unimodular lattice of rank 24m with minimum norm 2m provides a spherical 3-design. We remark that some of such codes and lattices give t-designs for higher t. As a corollary, we give some restrictions on the weight enumerators of binary doubly even self-dual codes of length 24m with minimum weight 4m. Ternary and quaternary analogues are also given.

The reliability-based design optimization (RBDO) problem involving discrete design variables and multi-working constraints is tackled with the consideration of the uncertainty factors in the optimal design of crawler crane’s lattice boom. In the optimization model, the uncertainties of material property, geometric parameters and loads are represented by random variables. The geometrical dimensions, performance functions’ reliability indexes and the minimum weight of lattice boom are defined respectively as the random design variables, probabilistic constraints and objective function. Integrating the reliability analysis method based on response surface method (RSM) with multi-island genetic algorithm (MIGA), an efficient reliability-based design optimization process for the lattice boom is developed under the typical constrained working conditions. Several verification cases are presented to demonstrate the effectiveness of optimization results. It is shown that the reliability-based design optimization method can not only satisfy the reliability constraints of the lattice boom, but also ensure the safety and economy of crawler crane boom as well as minimize the structure weight. The developed method is capable to be extended to the reliability-based design optimization of other large and complex construction machinery structures.

Building on classical theorems of Sperner and Kruskal-Katona, we investigate antichains $\mathcal {F}$ in the Boolean lattice Bn of all subsets of $[n]:=\{1,2,\dots ,n\}$ , where $\mathcal {F}$ is flat, meaning that it contains sets of at most two consecutive sizes, say $\mathcal {F}=\mathcal {A}\cup {\mathscr{B}}$ , where $\mathcal {A}$ contains only k-subsets, while ${\mathscr{B}}$ contains only (k − 1)-subsets. Moreover, we assume $\mathcal {A}$ consists of the first m k-subsets in squashed (colexicographic) order, while ${\mathscr{B}}$ consists of all (k − 1)-subsets not contained in the subsets in $\mathcal {A}$ . Given reals α, β > 0, we say the weight of $\mathcal {F}$ is $\alpha \cdot |\mathcal {A}|+\beta \cdot |{\mathscr{B}}|$ . We characterize the minimum weight antichains $\mathcal {F}$ for any given n,k,α,β, and we do the same when in addition $\mathcal {F}$ is a maximal antichain. We can then derive asymptotic results on both the minimum size and the minimum Lubell function.

Given a weighted graph $$G=(V,E)$$ with weight $$w: E\rightarrow \mathbb {Z}^+$$ , a k-cycle transversal is an edge subset A of E such that $$G-A$$ has no k-cycle. The minimum weight of k-cycle transversal is the weighted transversal number on k-cycle, denoted by $$\tau _{k}(G_{w})$$ . In this paper, we design a $$(k-1/2)$$ -approximation algorithm for the weighted transversal number on k-cycle when k is odd. Given a weighted graph $$G=(V,E)$$ with weight $$w: E\rightarrow \mathbb {Z}^+$$ , a k-clique transversal is an edge subset A of E such that $$G-A$$ has no k-clique. The minimum weight of k-clique transversal is the weighted transversal number on k-clique, denoted by $$\widetilde{\tau _{k}}(G_{w})$$ . In this paper, we design a $$(k^2-k-1)/2$$ -approximation algorithm for the weighted transversal number on k-clique. Last, we discuss the relationship between k-clique covering and k-clique packing in complete graph $$K_n$$ .

Due to their practical applications, hulls of linear codes have been of interest and extensively studied. In this paper, we focus on constructions and bounds on quaternary linear codes with Hermitian hull dimension one. Optimal $$[n,2]_4$$ [ n , 2 ] 4 codes with Hermitian hull dimension one are constructed for all lengths $$n\ge 3$$ n ≥ 3 , such that $$n \equiv 1,2,4 \ (\mathrm{mod}\ 5)$$ n ≡ 1 , 2 , 4 ( mod 5 ) . For positive integers $$n \equiv 0,3 \ (\mathrm{mod}\ 5)$$ n ≡ 0 , 3 ( mod 5 ) , good lower and upper bounds on the minimum weight of quaternary $$[n,2]_4$$ [ n , 2 ] 4 codes with Hermitian hull dimension one are given.

In this paper, structural design optimization of box-type double-girder overhead crane was performed using weighted decision matrix and finite element analysis (FEA). Primarily, structural design calculations were achieved for 280 proposed crane case studies, then crane design parameters values were optimized using the weighted decision matrix technique based on three concepts, and these are minimum weight, minimum deflection, and minimum stress. This was followed by building and modeling the optimum crane design related to each concept using solid works software, and FEA was performed. The results showed that minimum weight concept led to the optimum crane design with minimum weight and minimum cost but with mean deflection and mean stress values. However, minimum deflection concept led to the optimum crane design with minimum deflection and minimum stress but with much higher weight, while minimum stress concept led to small deflection and small stress values but with high weight as well. Crane design was also verified by manufacturing and testing a real crane case study.

Given an assignment of real weights to the ground elements of a matroid, the min–max weight of a ground element e is the minimum, over all circuits containing e , of the maximum weight of an element in that circuit with the element e removed. We use this concept to answer the following structural questions for the minimum weight basis problem. Which elements are persistent under a given weighting (belong to all or to none of the optimal bases)? What changes of the weights are allowed while preserving optimality of optimal bases? How does the minimum weight of a basis change when the weight of a single ground element is changed, or when a ground element is contracted or deleted? Our answer to this latter question gives the tropical ( min , + , − ) analogue of Kirchhoff’s arithmetic ( + , × , ∕ ) effective conductance formula for electrical networks.

The minimum weight vertex cover problem (MWVCP) is a fundamental combinatorial optimization problem with various real-world applications. The MWVCP seeks a vertex cover of an undirected graph such that the sum of the weights of the selected vertices is as small as possible. In this paper, we present an effective algorithm to solve the MWVCP. First, a master-apprentice evolutionary algorithm based on two individuals is conducted to enhance the diversity of solutions. Second, a hybrid tabu search combined configuration checking and solution-based tabu search is introduced to intensify local search procedure. Harnessing the power of the evolutionary strategy and a novel variant of hybrid tabu search, Master-Apprentice Evolutionary Algorithm with Hybrid Tabu Search, MAE-HTS, is presented. Results of extensive computational experiments using standard benchmark instances and other large-scale instances demonstrate the efficacy of our algorithm in terms of solution quality, running time, and robustness compared to state-of-the-art heuristics from the literature and the commercial MIP solver Gurobi. We also systematically analyze the role of each individual component of the algorithm which when worked in unison produced superior outcomes. In particular, MAE-HTS produced improved solutions for 2 out of 126 public benchmark instances with better running time. In addition, our MAE-HTS outperforms other state-of-the-art algorithms DLSWCC and NuMWVC for 72 large scale MWVCP instances by obtaining the best results for 64 ones, while other two reference algorithms can only obtain 27 best results at most.

Container ships has a transverse section in the form of an open profile, making it very sensitive to torsion phenomena. To minimize this effect, a structure known as a torsion box exists, which is subject to high stresses influenced by the fatigue phenomenon and the existence of cut-outs, for the passage of the longitudinal stiffeners, acting as stress concentrators. The aim of this study is to propose a two-stage design methodology to aid designers in satisfying the structural requirements and contribute with to a better understanding of the considered structure. The transverse webs of a torsional box structure are examined by comparing different cut-out geometries from numerical models with different regular load conditions to obtain the variables of the fatigue safety factor through linear regression models. The most appropriate geometry of the torsion box is established in terms of minimum weight, from nonlinear multivariable optimization models.

The Roman domination in a graph $G$ is a variant of the classical domination, defined by means of a so-called Roman domination function $f\colon V(G)\to \{0,1,2\}$ such that if $f(v)=0$ then, the vertex $v$ is adjacent to at least one vertex $w$ with $f(w)=2$ . The weight $f(G)$ of a Roman dominating function of $G$ is the sum of the weights of all vertices of $G$ , that is, $f(G)=\sum _{u\in V(G)}f(u)$ . The Roman domination number $\gamma _{R}(G)$ is the minimum weight of a Roman dominating function of $G$ . In this paper we propose algorithms to compute this parameter involving the $(\min,+)$ powers of large matrices with high computational requirements and the GPU (Graphics Processing Unit) allows us to accelerate such operations. Specific routines have been developed to efficiently compute the $(\min,+)$ product on GPU architecture, taking advantage of its computational power. These algorithms allow us to compute the Roman domination number of cylindrical graphs $P_{m}\Box ~C_{n}$ i.e., the Cartesian product of a path and a cycle, in cases $m=7,8$ ,9 $n\geq 3$ and $m\geq $ 10 $, n\equiv 0\pmod 5$ . Moreover, we provide a lower bound for the remaining cases $m\geq $ 10 $, n\not \equiv 0\pmod 5$ .

In the present work, three different armor materials such as Carbon fiber reinforced polymer (CFRP), Kevlar and Steel were studied and simulated using Software ANSYS by considering bullet made of brass. Kevlar of 5 mm and 10 mm were taken to study the influence of layer on ballistic impact of armor materials. The study was performed on four different performance defining attributes (PDAs) such as maximum Directional Deformation, Maximum Stress, Energy Absorption and Weight. The attributes were taken as per the standard of NIJ Standard 0101.02, USA. Finally, Gray Relational Analysis was applied to rank the materials. The finding of result indicated that the best material for the given conditions of minimum deformation is steel, maximum energy absorption is CFRP, maximum stress is CFRP and minimum weight is Kevlar 10 mm thick. However none of materials crashes or deforms permanently and are within the limit specified by NIJ Standard 0101.02, USA. Kevlar is the lightest and second in maximum deformation, being the best in usability due to the economy in energy spent for the user or the vehicle armor. The thickness of Kevlar affects the deformation and energy absorption significantly. Kevlar has shown as the best material followed by CFRP and Steel on the basis of given attributes.

Along with the recent developments and innovations in the automotive and heavy vehicle industry, the performance requirements such as fuel efficiency, emissions reduction, low manufacturing cost, etc., keep in-creasing day by day. In order to have a place in the world market, it is es-sential to meet these requirements. Along with the other strategies, vehi-cle weight reduction is one of the most critical strategies in the heavy ve-hicle industry. This paper aims to obtain an optimal design of a truck brake pedal by employing topology and shape optimization. To accom-plish this goal, the material used for an existing brake pedal is unchanged as this study focuses on reducing the weight of the existing brake pedal without material substitution. The rough dimensions of the brake pedal are designed by inspiring the results of the topology optimization. To de-termine the precise dimensions of the brake pedal design of experiment (DOE) and shape optimization studies are conducted respectively. Wall and flange thickness are defined as variable parameters for the DOE. Three different values are selected for each design parameter. Stress analyses are conducted by using the finite element method for nine cases. As a result of the studies mentioned so far, two responses are obtained. In order to obtain minimum weight value, which is possible shape optimiza-tion is performed by using fmincon function in MATLAB®. As a result of the study, the mass reduction of the brake pedal is %50, and it is shown that the developed method can be used to design a lightweight truck brake pedal.

The use of steel in building or construction manufacture continues to decrease, owing in part to the sustainability and mechanical properties of fibers which have higher strength in minimum weight than steel. This preliminary study was defined to evaluate the mechanical properties of high-performance fibers, especially ultrahigh molecular weight polyethylene (UHMWPE), in terms of the composite to be the main material of windmill turbines. It was UHMWPE as reinforcement and high-density polyethylene (HDPE) as a matrix in this composite system. The composites were processed in a variety of pressure and duration (50 to 165 bar and 10 minutes to 48 hours). The mechanical strength was tested by 3-point bending tests to measure the interlaminar shear strength, shear modulus, and bending strength. The result showed a significant difference in properties of the composite which is higher pressure and longer duration obtained a higher value of mechanical strength.

A vertex-edge Roman dominating function (or just ve-RDF) of a graph G = (V, E) is a function f : V (G) → {0, 1, 2} such that for each edge e = uv either max{f (u), f (v)} ≠ 0 or there exists a vertex w such that either wu ∈ E or wv ∈ E and f (w) = 2. The weight of a ve-RDF is the sum of its function values over all vertices. The vertex-edge Roman domination number of a graph G, denoted by γ veR (G), is the minimum weight of a ve-RDF G. We characterize trees with vertexedge roman domination number equal to twice domination number minus one.

For a simple, undirected graph $$G = (V,$$ E), an independent Roman dominating function (IRDF) $$f : V \rightarrow \lbrace 0, 1, 2 \rbrace $$ has the property that every vertex $$v \in V$$ with $$f(v) = 0$$ is adjacent to at least one vertex u, with $$f(u) = 2$$ , and no two vertices assigned positive values are adjacent. An independent Roman $$\lbrace 2 \rbrace $$ -dominating function (IR2DF) is an IRDF f with an additional property that, for every vertex $$v \in V$$ with $$f(v) = 0$$ , there exists at least two vertices $$x, y \in N_G(v)$$ with $$f(x) = f(y) = 1$$ . An independent double Roman dominating function (IDRDF) on G is a function $$f : V \rightarrow \lbrace 0, 1, 2, 3 \rbrace $$ , such that for every vertex $$v \in V$$ , if $$f(v) = 0$$ , then v has at least two neighbors x, y with $$f(x) = f(y) = 2$$ or one neighbor w with $$f(w) = 3$$ , and if $$f(v) = 1$$ , then v must have at least one neighbor w with $$f(w) \ge 2$$ , and no two vertices assigned positive values are adjacent. The weight of an IRDF (IR2DF, IDRDF) f is the sum $$f(V) = \sum _{v \in V}f(v)$$ . Given a graph G and a positive integer k, the independent Roman domination problem (IRDP), independent Roman $$\lbrace 2 \rbrace $$ -domination problem (IR2DP) and independent double Roman domination problem (IDRDP), respectively, is to check whether G has an IRDF, IR2DF, and IDRDF of weight at most k. The IRDP, IR2DP and IDRDP are known to be NP-complete for bipartite graphs. We investigate the complexity of these problems for dually chordal graphs and some subclasses of bipartite graphs, namely, star convex bipartite graphs and comb convex bipartite graphs. We also investigate the complexity of IR2DP and IDRDP for chordal graphs. The minimum independent Roman domination problem (MIRDP), minimum independent Roman $$\lbrace 2 \rbrace $$ -domination problem (MIR2DP), and minimum independent double Roman domination problem (MIDRDP), respectively, are to find an IRDF, IR2DF, and IDRDF of minimum weight in the input graph. We show that MIRDP, MIR2DP, and MIDRDP are linear time solvable for bounded tree-width graphs, chain graphs, and threshold graphs, a subclass of split graphs. We also show that the MIRDP, MIR2DP, and MIDRDP are APX-hard for graphs with bounded degree 4. Finally, we show that the domination problem and IRDP (IR2DP, IDRDP) are not equivalent in computational complexity aspects.

We address the problem of finding an arborescence of minimum total edge weight rooted at a given vertex in a directed, edge-weighted graph. If the arborescence must span all vertices the problem is solvable in polynomial time, but the non-spanning version is NP-hard. We propose reduction rules which determine vertices that are required or can be excluded from optimal solutions, a modification of Edmonds algorithm to construct arborescences that span a given set of selected vertices, and embed this procedure into an iterated local search for good vertex selections. Moreover, we propose a cutset-based integer linear programming formulation, provide different linear relaxations to reduce the number of variables in the model and solve the reduced model using a branch-and-cut approach. We give extensive computational results showing that both the heuristic and the exact methods are effective and obtain better solutions on instances from the literature than existing approaches, often in much less time.

This article deals with problems of detecting abrupt changes in time series ba Change Point Model (CPM) framework. We propose a fuzzification in a Fuzzy Time Series (FTS) model to eliminate a trend in a contaminated dependent series. The independent residuals are then inputed on the CPM method. In simulating an abrupt change, an ARIMA(1,1,1) and variance of the model are considered. The abrupt change is modelled as an AO (Additive Outlier) type of outliers. The minimum weight or breaksize of the abrupt change is defined based on the ARIMA variance formulated in this article. The percentage of uncorrelated residuals obtained by the FTS model and the percentage of correct detection of the proposed procedure are shown by simulation. The proposed detecting algorithm is implemented to detect abrupt changes in monthly tourism series in literature, i.e., in Taiwan and in Bali. The first series shows a slowly increasing trend with one abrupt change while the second series exhibits not only a slowly increasing trend but also a strong seasonal pattern with two abrupt changes. For comparison, we detect the changes in the empirical examples on an existing automatic detection procedure using tso package in R. For the first example, the results show that both detecting procedures give exactly a similar location of one change point where the package recognises it as an AO type of outliers. The abrupt change is related to the period of SARS outbreak in Taiwan. On the second example, the proposed procedure locates 4 change points which form two locations of changes, i.e., the first two change points are within 2 time points so do the last two change points. The locations are closed to times of Bali Bombing events. Meanwhile, the automatic procedure recognizes only one AO outlier on the series.

A set S of vertices is a perfect dominating set of a graph G if every vertex not in S is adjacent to exactly one vertex of S . The minimum cardinality of a perfect dominating set is the perfect domination number γ p ( G ) . A perfect Roman dominating function (PRDF) on a graph G = ( V , E ) is a function f : V → { 0 , 1 , 2 } satisfying the condition that every vertex u with f ( u ) = 0 is adjacent to exactly one vertex v for which f ( v ) = 2 . The weight of a PRDF is the sum of its function values over all vertices, and the minimum weight of a PRDF of G is the perfect Roman domination number γ R p ( G ) . Obviously, for every graph G , γ R p ( G ) ≤ 2 γ p ( G ) , and those graphs attaining the equality are called perfect Roman graphs. In this paper, we provide a characterization of perfect Roman trees.

For a given graph G, the minimum weight connected-k-subgraph cover problem (MinWCkSC) is to find a minimum weight vertex subset C of G such that each connected subgraph of G on k vertices contains at least one vertex of C. Previously, Zhang et al. [37] presented a ( k − 1 ) -approximation algorithm for MinWCkSC under the assumption that the girth of G, which is the length of a shortest cycle of G, is at least k. In this paper, we improve this result by showing that ( k − 1 ) -approximation can be achieved when the girth requirement is relaxed from k to 2 k / 3 .

A double Roman dominating function (DRDF) on a graph G = ( V , E ) is a function f : V ⟶ { 0 , 1 , 2 , 3 } such that every vertex v ∈ V with f ( v ) = 0 is either adjacent to a vertex u with f ( u ) = 3 or two distinct vertices x and y with f ( x ) = f ( y ) = 2 , and every vertex v ∈ V with f ( v ) = 1 is adjacent to a vertex u with f ( u ) ≥ 2 . The weight of f is the sum f ( V ) = ∑ v ∈ V f ( v ) . The minimum weight of a DRDF on G is the double Roman domination number of G , denoted by γ d R ( G ) . A graph G is a double Roman Graph if γ d R ( G ) = 3 γ ( G ) , where γ ( G ) is the domination number of G . In this paper, we first show that the decision problem associated to double Roman domination is NP-complete even when restricted to planar graphs. Then, we study the complexity issue of a problem posed in [R.A. Beeler, T.W. Haynesa and S.T. Hedetniemi, Double Roman domination, Discrete Appl. Math. 211 (2016), 23–29], and show that the problem of deciding whether a given graph is double Roman is NP-hard even when restricted to bipartite or chordal graphs. Then, we give linear algorithms that compute the domination number and the double Roman domination number of a given unicyclic graph. Finally, we give a linear algorithm that decides whether a given unicyclic graph is double Roman.

In this paper, we study the minimum (connected) k-bounded-degree node deletion problem (Min(C)kBDND). For a connected graph G, a constant k and a weight function w : V → R + , a vertex set C ⊆ V ( G ) is a kBDND-set if the maximum degree of graph G − C is at most k. If furthermore, the subgraph of G induced by C is connected, then C is a CkBDND-set. The goal of MinWkBDND (resp. MinWCkBDND) is to find a kBDND-set (resp. CkBDND-set) with the minimum weight. In this paper, we focus on their cardinality versions with w ( v ) ≡ 1 , v ∈ V , which are denoted as MinkBDND and MinCkBDND. This paper presents a ( 1 + e ) and a 3.76-approximation algorithm for MinkBDND and MinCkBDND on unit disk graphs, respectively, where 0 e 1 is an arbitrary constant.

A perfect Italian dominating function of a graph $G=(V,E)$ is a function $f : V \to \{0,1,2\}$ such that for every vertex $f(v) = 0$, it holds that $\sum_{u \in N(v)} f(u) = 2$, i.e., the weight of the labels assigned by $f$ to the neighbors of $v$ is exactly two. The weight of a perfect Italian function is the sum of the weights of the vertices. The perfect Italian domination number of $G$, denoted by $\gamma^p_I(G)$, is the minimum weight of any perfect Italian dominating function of $G$. While introducing the parameter, Haynes and Henning (Discrete Appl. Math. (2019), 164--177) also proposed the problem of determining the best possible constants $c_\mathcal{G}$ such that $\gamma^p_I(G) \leq c_\mathcal{G} \times n$ for all graphs of order $n$ when $G$ is in a particular class $\mathcal{G}$ of graphs. They proved that $c_\mathcal{G} = 1$ when $\mathcal{G}$ is the class of bipartite graphs, and raised the question for planar graphs and regular graphs. We settle their question precisely for planar graphs by proving that $c_\mathcal{G} = 1$ and for cubic graphs by proving that $c_\mathcal{G} = 2/3$. For split graphs, we also show that $c_\mathcal{G} = 1$. In addition, we characterize the graphs $G$ with $\gamma^p_I(G)$ equal to 2 and 3 and determine the exact value of the parameter for several simple structured graphs. We conclude by proving that it is NP-complete to decide whether a given bipartite planar graph admits a perfect Italian dominating function of weight $k$., Comment: To appear in Discrete Applied Mathematics

This article deals with structural controllability of a linear time invariant (LTI) composite system consisting of several circuits/subsystems. We consider subsystems with structurally similar state matrices, i.e., the zero/nonzero pattern of the state matrices of the subsystems are the same, but dynamics can be different due to different numerical values. Structurally similar subsystems arise in large circuits implemented using many similar smaller circuits and agent-based networks consisting of homogeneous agents. The subsystems may not be structurally controllable individually; however, structural controllability of the composite system can be achieved by sharing state information. Sharing of information among subsystems incurs cost and our aim is to design a structurally controllable composite system with minimum information sharing. Minimizing information sharing is the same as minimizing the number of interaction links between subsystems, referred to as interconnections . An optimal network topology is one with a minimum number of interconnections. This article presents a closed-form expression for the minimum number of interconnections for structural controllability and derives a polynomial time algorithm to find an optimal network topology. The algorithm is based on a minimum weight perfect matching algorithm and a so-called edge reconstruction process. The minimum number of interconnections required is formulated in terms of two indices we define in the article: maximum commonality index ( $\alpha _{{{\mathscr N}}}$ ) and dilation index ( $\beta _{{\mathcal {I}}}$ ). Loosely speaking, more connectedness of subsystems leads to a lower total value of $\alpha _{{{\mathscr N}}}$ and $\beta _{{\mathcal {I}}}$ . Further, $\alpha _{{{\mathscr N}}}$ decreases if the subsystems have fewer numbers of connected components. We apply and verify our general result to special cases that arise in control, where the minimum number can be more directly obtained. The special cases considered are structurally cyclic subsystems, irreducible subsystems, and subsystems in controller canonical form.

Correlation immunity (CI) of Boolean functions is an important concept relevant both in the design of nonlinear combiners and for the protection against side-channel cryptanalysis to name a few applications. In this article we give further simplification of the proofs of some known characterizations of these functions, including some new results related to certain properties of the algebraic normal form of these functions. We also provide two efficient constructions of CI functions, thus extending the known construction methods. In particular, a special case of our first construction method is well suited for construction of low-weight CI functions. It is shown that Carlet and Chen conjecture (Carlet and Chen, 2018) on the minimum weight of 3-CI functions (equivalent to the existence of Hadamard matrices of order n = 4 k ) is valid for a great variety of input sizes n , thus apart from the case n = 2 k which was already proved in Carlet and Chen (2018). This further confirms that the conjecture might be correct for any input size n .