Incremental Problem Research Articles

Modelling 3-Coloring of Outerplanar Graphs via Incremental Satisfiability

A novel method to model the problem of 3-coloring on outerplanar graphs is presented. The proposal is based on the specification of the logical constraints for the 3-coloring of an outerplanar graph in a dinaymic way, resulting in a polynomial-time instance of the incremental satisfiability problem. This proposal can be extended to consider other polynomial-time instances of the 3-coloring problem.

An energetic formulation of a gradient damage model for concrete and its numerical implementation

The energetic formulation of a rate-independent system assumes that the evolution of the system is driven by two scalar-valued functions: the storage energy functional and the dissipation pseudo-potential. The evolution of the material system is then characterized by two energetic principles: the global stability condition and the energy balance between stored and dissipated energies with the work of external loading. Rate-independent generalized standard materials are endowed with such structure, whereas the existence of such energetic structure is not so apparent in materials with non-associated flow rule. In this paper, we consider a rate-independent gradient damage model for concrete where the evolution of the damage does not follow the normality rule. We will show that such model can be nevertheless derived by a dissipation potential at the expense of having a state variable-dependent potential, and therefore the energetic formulation can be obtained also in this case. After introducing the incremental minimization problem consistent with such formulation, we obtain a discrete version of the stability condition and establish lower and upper a-priori energy bounds met by the energetic solution. These are fundamental results for the analysis of the formulation.The actual numerical solution of the incremental minimization problem is realized by considering first a variable splitting in order to treat the gradient of the damage field as an independent variable, and then by applying the augmented Lagrangian method to tackle with the resulting constrained optimization problem. We solve the first order stationarity conditions of the augmented Lagrangian functional by a path-following Newton’s method based on the energy dissipation rate control.We show that we are able to describe highly non-linear responses of the material, such as softening branches and snap-back responses. Several numerical tests are performed to verify the objectivity of the formulation and of the proposed numerical method. Details of the numerical implementation are also given.

Wrinkles in soft dielectric plates

We show that a smooth giant voltage actuation of soft dielectric plates is not easily obtained in practice. In principle one can exploit, through pre-deformation, the snap-through behavior of their loading curve to deliver a large stretch prior to electric breakdown. However, we demonstrate here that even in this favorable scenario, the soft dielectric is likely to first encounter the plate wrinkling phenomenon, as modeled by the onset of small-amplitude sinusoidal perturbations on its faces. We provide an explicit treatment of this incremental boundary value problem. We also derive closed-form expressions for the two limit cases of very thin membranes (with vanishing thickness) and of thick plates (with thickness comparable to or greater than the wavelength of the perturbation). We treat explicitly examples of ideal dielectric free energy functions (where the mechanical part is of the neo-Hookean, Mooney–Rivlin or Gent form) and of dielectrics exhibiting polarization saturation. In addition to the expected buckling mode coming from the purely elastic case, we discover a second mode occurring at large voltages in extension. We find that plates always wrinkle anti-symmetrically, before the symmetric modes can be reached. Finally, we make the link with the classical results of the Hessian electro-mechanical instability criterion and of Euler buckling for an elastic column.

Portfolio selection with consumption ratcheting

In this paper we study the portfolio selection problem of a finite-lived agent who does not tolerate a decline in standard of living. The preference can be regarded as exhibiting extreme-form of habit formation and also related to loss aversion in the prospect theory. We show that the agent’s optimal portfolio exhibits a trend chasing behavior and the portfolio share of the risky asset fluctuates between 0 and the value of an unconstrained individual; the fluctuations do not attenuate as time gets near the end of the planning horizon. We also explore implications of the model for asset pricing and show that the model has a potential to match better the recent US data than traditional habit models. We provide a complete solution to the problem by considering a transformed problem, which is similar in its formal structure to an irreversible incremental investment problem and equivalent to an infinite series of optimal stopping problems.

Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue

In this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the fracture process depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e. a complete fracture may be produced by oscillation of small jumps. The first step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main difficulty in the passage to the continuous-time limit is that we lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. Eventually, after proving the existence in this weak formulation, we improve the result by showing that the Young measure is concentrated on a function and coincides with the variation of the jump of the displacement.

Waveform covariance matrix design for robust signal-dependent interference suppression in colocated MIMO radars

Abstract In multiple-input multiple-output (MIMO) radars, interference can be properly suppressed by designing transmit waveforms. However, having an error in initial estimation of interferers’ locations can result in degradation of signal-to-interference-plus-noise ratio (SINR), significantly. In this paper we consider the problem of robust interference suppression and SINR increment in collocated MIMO radars, in the presence of signal-dependent interference resources. We propose an efficient method to generate transmit waveform covariance matrix with the following properties: (a) robustness in interference suppression, (b) high SINR at the receiver, c) using the same power level for all transmit antennas and (d) suitable for generating BPSK waveforms in a closed-form. We solve the resulted optimization problems with numerical approaches in a short period of time. The proposed covariance matrix, by exploiting the correlated MIMO radar concept and a technique we use in the transmitter, yields to a better SINR level compared to conventional MIMO radars, phased array method and the recent introduced schemes. Simulation results validate our claims and show the advantages of our work .

Research of Adaptive Neighborhood Incremental Principal Component Analysis and Locality Preserving Projection Manifold Learning Algorithm

In view of the incremental learning problem of manifold learning algorithm, an adaptive neighborhood incremental principal component analysis (PCA) and locality preserving projection (LPP) manifold learning algorithm is presented, and the incremental learning principle of algorithm is introduced. For incremental sample data, the adjacency and covariance matrices are incrementally updated by the existing samples; then the dimensionality reduction results of the incremental samples are estimated by the dimensionality reduction results of the existing samples; finally, the dimensionality reduction results of the incremental and existing samples are updated by subspace iteration method. The adaptive neighborhood incremental PCA-LPP manifold learning algorithm is applied to processing of gearbox fault signals. The dimensionality reduction results by incremental learning have very small error, compared with those by batch learning. Spatial aggregation of the incremental samples is basically stable, and fault identification rate is increased.

Rate-independent dissipation in phase-field modelling of displacive transformations

In this paper, rate-independent dissipation is introduced into the phase-field framework for modelling of displacive transformations, such as martensitic phase transformation and twinning. The finite-strain phase-field model developed recently by the present authors is here extended beyond the limitations of purely viscous dissipation. The variational formulation, in which the evolution problem is formulated as a constrained minimization problem for a global rate-potential, is enhanced by including a mixed-type dissipation potential that combines viscous and rate-independent contributions. Effective computational treatment of the resulting incremental problem of non-smooth optimization is developed by employing the augmented Lagrangian method. It is demonstrated that a single Lagrange multiplier field suffices to handle the dissipation potential vertex and simultaneously to enforce physical constraints on the order parameter. In this way, the initially non-smooth problem of evolution is converted into a smooth stationarity problem. The model is implemented in a finite-element code and applied to solve two- and three-dimensional boundary value problems representative for shape memory alloys.

Intrusion Detection and Prevention Systems as a Service in Could-based Environment

Intrusion Detection and Prevention Systems (IDPSs) are standalone complex hardware, expensive to purchase, change and manage. The emergence of Network Function Virtualization (NFV) and Software Defined Networking (SDN) mitigates these challenges and delivers middlebox functions as virtual instances. Moreover, cloud computing has become a very cost-effective model for sharing large-scale services in recent years. Features such as portability, isolation, live migration, and customizabil-ity of virtual machines for high-performance computing have attracted enterprise customers to move their in-house IT data center to the cloud. In this paper, we formulate the placement of Intrusion Detection and Prevention Systems (IDPS) and introduce a model called Incremental Mobile Facility Location Problem (IMFLP) to study the IDPP problem. Moreover, we propose a novel and efficient solution called Adaptive Facility Location (AFL) to efficiently solve the optimization problem introduced in the IMFLP model. The effectiveness of our solution is evaluated through realistic simulation studies compared with other popular online facility location algorithms.

Deterministic construction of sparse binary matrices via incremental integer optimization

A central problem in compressed sensing (CS) is the design of measurement matrices. Compared with the conventional random matrices, sparse binary matrices have some attractive properties, such as lower storage/encoding cost and easy hardware implementation. In this paper, we formulate the construction of sparse binary measurement matrices from an optimization standpoint. A new algorithm is presented to construct arbitrary-size sparse binary measurement matrices through relaxing the resultant optimization model to an incremental integer programming problem. The proposed method in general outputs sparse binary matrices with optimal mutual coherence. In addition, we prove that the constructed matrices can be almost completely incoherent with the conventional wavelet dictionary. Extensive simulation results show that the sparse binary matrices constructed by the proposed algorithm significantly outperform Gaussian random matrices, random sparse binary matrices and two well-performing deterministic sparse binary matrices.

Accelerated proximal gradient method for elastoplastic analysis with von Mises yield criterion

It is known that, under certain conditions, the quasi-static incremental analysis problem of elastoplastic structures with the von Mises yield criterion can be formulated as a second-order cone programming (SOCP) problem, which can be solved with a primal-dual interior-point method. Alternatively, this paper proposes to solve an equivalent unconstrained nonsmooth convex optimization problem, which has a form similar to a class of regularized least-square problems, known as group LASSO. We propose an accelerated proximal gradient method with an adaptive restart scheme for solving this unconstrained optimization problem. The algorithm is easy to implement, and free from numerical solution of linear equations unlike conventional methods in computational mechanics. Numerical experiments suggest that the presented algorithm outperforms a standard solver that implements a primal-dual interior-point method for conic optimization.

E-Commerce Decision Model Based on Auto-Learning

The proposed model utilizes the information implied in the history of E-commerce negotiation to automatically mark the data to form the training samples, and apply the clues binary decision tree to automatically learn the samples to obtain the estimate of the opponent difference function. Then, an incremental decision-making problem is constituted through the combination of its own and the opponent's difference functions; and the dispersion algorithm is adopted to solve the optimization problem. The experimental results show that, the model still demonstrates relatively high efficiency and effectiveness under the condition of information confidentiality and no priori knowledge.

On recoverable and two-stage robust selection problems with budgeted uncertainty

In this paper, the problem of selecting p out of n available items is discussed, such that their total cost is minimized. We assume that the item costs are not known exactly, but stem from a set of possible outcomes modeled through budgeted uncertainty sets, i.e., the interval uncertainty sets with an additional linear (budget) constraint, in their discrete and continuous variants. Robust recoverable and two-stage models of this selection problem are analyzed through an in-depth discussion of variables at their optimal values. Polynomial algorithms for both models under continuous budgeted uncertainty are proposed. In the case of discrete budgeted uncertainty, compact mixed integer formulations are constructed and some approximation algorithms are proposed. Polynomial combinatorial algorithms for the adversarial and incremental problems (the special cases of the considered robust models) under both discrete and continuous budgeted uncertainty are constructed.

Variable neighborhood scatter search for the incremental graph drawing problem

Automated graph-drawing systems utilize procedures to place vertices and arcs in order to produce graphs with desired properties. Incremental or dynamic procedures are those that preserve key characteristics when updating an existing drawing. These methods are particularly useful in areas such as planning and logistics, where updates are frequent. We propose a procedure based on the scatter search methodology that is adapted to the incremental drawing problem in hierarchical graphs. These drawings can be used to represent any acyclic graph. Comprehensive computational experiments are used to test the efficiency and effectiveness of the proposed procedure.

Subdifferential‐based implicit return‐mapping operators in Mohr‐Coulomb plasticity

AbstractThe paper is devoted to constitutive solution, limit load analysis and Newton‐like methods in elastoplastic problems containing the Mohr‐Coulomb yield criterion. Within the constitutive problem, we introduce a self‐contained derivation of the implicit return‐mapping solution scheme using a recent subdifferential‐based treatment. Unlike conventional techniques based on Koiter's rules, the presented scheme a priori detects a position of the unknown stress tensor on the yield surface even if the constitutive solution cannot be found in a closed form. This eliminates blind guesswork from the scheme and enables to analyze properties of the constitutive operator. It also simplifies the construction of the consistent tangent operator, which is important for the semismooth Newton method when applied to the incremental boundary‐value elastoplastic problem. The incremental problem in Mohr‐Coulomb plasticity is combined with limit load analysis. Beside a conventional direct method of incremental limit analysis, a recent indirect one is introduced and its advantages are described. The paper contains 2D and 3D numerical experiments on slope stability with publicly available Matlab implementations.

Bond Behavior of FRCM Carbon Yarns Embedded in a Cementitious Matrix: Experimental and Numerical Results

The use of inorganic cement based composite systems, known as Fiber Reinforced Cementitious Matrix (FRCM), is a very promising technique for retrofitting and strengthening the existing masonry or concrete structures. The effectiveness of FRCM systems is strongly related to the interface bond between inorganic matrix and fabric reinforcement, and, since the major weakness is often located on this interface, the study of stress-transfer mechanisms between fibers and matrix becomes of fundamental importance.FRCM are usually reinforced with uni-directional or bi-directional fabrics consisting of multifilament yarns made of carbon, glass, basalt or PBO fibers, disposed along two orthogonal directions. The difficulty of the mortar to penetrate within the filaments that constitute the fabric yarns and the consequent non-homogeneous stress distribution through the yarn cross section makes difficult to access the characterization of the composite material. The use of polymer coatings on the fibers surface showed to enhance the bond strength of the interface between fibers and mortar and, as a consequence, to improve the mechanical performance of the composite. The coating does not allow the mortar to penetrate within the filaments while is able to improve the bond between the two materials and to increase the shear stress transfer capacity at the interface.An experimental session of several pull out tests on carbon yarns embedded in a cementitious matrix was carried out. Different embedded lengths have been analyzed, equal to 20, 30 and 50 mm. The carbon yarns object of this study were pre-impregnated with a flexible epoxy resin enhanced with a thin layer of quartz sand applied on the surface.A variational model was proposed to evaluate the pull-out behaviour and failure mechanisms of the system and to compare numerical results to the experimental outcomes. Evolution of fracture in the yarn-matrix system is determined by solving an incremental energy minimization problem, acting on an energy functional which account for brittle failure of matrix and yarn, and for debonding at the yarn-matrix interface. The model was able to accurately describe the three phases of the pull-out mechanism, depending on the embedded length.

Prospects of pyrolysis oil from plastic waste as fuel for diesel engines: A review

The purpose ofthis study is to review the existing literature about chemical recycling of plastic waste and its potential as fuel for diesel engines. This is a review covering on the field of converting waste plastics into liquid hydrocarbon fuels for diesel engines. Disposal and recycling of waste plastics have become an incremental problem and environmental threat with increasing demand for plastics. One of the effective measures is by converting waste plastic into combustible hydrocarbon liquid as an alternative fuel for running diesel engines. Continued research efforts have been taken by researchers to convert waste plastic in to combustible pyrolysis oil as alternate fuel for diesel engines. An existing literature focuses on the study of chemical structure of the waste plastic pyrolysis compared with diesel oil. Converting waste plastics into fuel oil by different catalysts in catalytic pyrolysis process also reviewed in this paper. The methodology with subsequent hydro treating and hydrocracking of waste plastic pyrolysis oil can reduce unsaturated hydrocarbon bonds which would improve the combustion performance in diesel engines as an alternate fuel.

Efficient Spectrum Utilization in Large Scale RWA Problems

While the routing and wavelength assignment (RWA) has been widely studied, a very few studies attempt to solve realistic size instances, namely, with 100 wavelengths per fiber and a few hundred nodes. Indeed, state of the art is closer to around 20 nodes and 30 wavelengths, regardless of what the authors consider, heuristics or exact methods with a very few exceptions. In this paper, we are interested in reducing the gap between realistic data sets and test bed instances that are often used, using exact methods. Even if exact methods may fail to solve in reasonable time very large instances, they can, however, output $\varepsilon $ -solutions with a very good and proven accuracy. The novelty of this paper is to exploit the observations that optimal solutions contain a very large number of light paths associated with shortest paths or $k$ -shortest paths with a small $k$ . We propose different RWA algorithms that lead to solve exactly or near exactly much larger instances than in the literature, i.e., with up to 150 wavelengths and 90 nodes. Extensive numerical experiments are conducted on both the static and dynamic incremental planning RWA problem.

OPTIMAL PLACEMENT OF HYSTERETIC OR VISCOUS DAMPER BASED ON THE INCREMENTAL INVERSE PROBLEM

Abstract. Structural control system aims to improve the protection of buildings and civil structures, occupants and contents from the destructive forces of nature due to earthquakes, wind and waves. Control techniques can be classified according to how the system manipulates, absorbs and dissipates the imposed energy. Passive damping system absorbs or consumes a portion of the input energy, reducing energy dissipation on primary structural members and does not require an external power source. In this work the efficiency of four Matlab programmed routines in terms of time or computational cost and flexibility according to the type of damper will be assessed. Two techniques were evaluated: (a) An analytical procedure known as incremental inverse problem for redesign of structural system with a hysteretic damping system for target transfer functions and (b) to apply an efficient and systematic procedure for to find the optimal damper placement to minimize the sum of amplitudes of the transfer functions evaluated at the undamped fundamental natural frequency of a structural system subject to a constraint on the sum of the damping coefficients of added dampers. Keywords: Optimal placement of dampers, Hysteretic and viscous devices, Incremental inverse problem, Transfer function, Passive control

On the Uniqueness Conditions and Bifurcation Criteria in Coupled Thermo-Elasto-Plasticity

The global and local conditions of uniqueness and the criteria excluding a possibility of bifurcation of the equilibrium state for small strains are derived. The conditions and criteria are derived analyzing the problem of uniqueness of solution of the basic incremental boundary problem of coupled generalized thermo-elasto-plasticity. This paper is a continuation of some previous works by the author, but contains new derivation of the global and local criteria excluding a possibility of bifurcation of the equilibrium state for a comparison body dependent on statically admissible fields of stress velocity. All the thermal elastoplastic coupling effects, non-associated laws of plastic flow and influence of plastic strains on thermoplastic properties of a body were taken into account in this work. Thus, the mathematical problem considered here is not a self-conjugated problem. The paper contains four Appendices A, B, C and D where the local necessery and sufficient conditions of uniqueness have been derived.