Full Constraints Research Articles

Optimal switching with minimum dwell time constraint

The problem of optimal switching between different subsystems/configurations with minimum dwell time constraints is investigated in this study and a feedback solution, using the framework of approximate dynamic programming, is proposed. The method calls for a tuning stage in which parameters of a function approximator are tuned. Online control will then be conducted with a computational load as low as evaluating a few scalar-valued functions. Finite-horizon and infinite-horizon cost functions are investigated and convergence and stability are analyzed considering the presence of approximation errors. Moreover, the case of applying a full or partial constraint on the mode sequence, as well as having a mode-dependent minimum dwell time are investigated. Finally, performance of the scheme in handling different challenges is numerically evaluated through different examples.

Isolating the Lyman alpha forest BAO anomaly

A 2.5-3σ discrepancy has been reported between the baryonic acoustic oscillation peak (BAO) in the Lyman α forest at z∼ 2.34 and the best fit Planck ΛCDM cosmology. To isolate the origin of the tension, we consider unanchored BAO, in which the standard BAO ruler is not calibrated, eliminating any dependence on cosmology before redshift z∼ 2.34. We consider BOSS BAO measurements at z∼ 0.32, 0.57 and 2.34, using the full 2-dimensional constraints on the angular and line of sight BAO scale, as well as isotropic BAO measurements by 6dF and SDSS at z∼ 0.106 and z∼ 0.15. We find that the z>0.43 data alone is in 2.9σ of tension with ΛCDM with or without the Planck best fit values of the mass fraction Ωm and the BAO scale rd H0, indicating that the tension arises not from the ΛCDM parameters but from the dark energy evolution itself at 0.57<z<2.34. This conclusion is supported when the acoustic scale measured by the CMB is included, which further increases the tension and excludes a solution with a constant dark energy equation of state. Including the low z BAO data, which is itself consistent with ΛCDM, reduces the tension to just over 2σ, however in this case a CPL parametrization of the dark energy evolution yields only a modest improvement.

Hybrid metaheuristic to solve the “one-to-many-to-one” problem

PurposeThe purpose of this paper is to present a specific variant of vehicle routing problem with simultaneous full pickup and delivery problem (VRPSFPD) known as one-to-many-to-one (1-M-1) problem with several vehicles, where every customer can receive and send goods simultaneously, which has added the notion of the totality for the pickup goods. Currently, hybrid metaheuristics have become more popular because they offer the best solutions to several combinatorial optimization problems. Therefore, due to the complexity of 1-M-1 a hybrid genetic algorithm with variable neighborhood descent (HGAVND) local search is proposed. To improve the solution provided by the HGAVND the authors suggest applying a structure OR-Opt. To test the performance of the algorithm the authors have used a set of benchmarks from the literature and apply the HGAVND algorithm to solve the real case of distribution of soft drink in Tunisia. The experimental results indicate that the algorithm can outperform all other algorithms proposed in literature with regard to solution quality and processing time. Moreover, the authors improve the best known solution of the majority of benchmark instances taken from the literature.Design/methodology/approachDue to the complexity of 1-M-1 a HGAVND local search is proposed.Originality/valueFirst, in the presence of full pickup constraints, the problem becomes more complex, this implies that the choice of a good metaheuristic can provide good results. Second, the best contribution consists in a specific variant of VRPSFPD problem as 1-M-1 which the paper present the first application of metaheuristics to solve the specific 1-M-1 and to apply it in real case of distribution of soft drink.

A Biologically Inspired Energy-Efficient Duty Cycle Design Method for Wireless Sensor Networks

The recent success of emerging wireless sensor networks technology has encouraged researchers to develop new energy-efficient duty cycle design algorithm in this field. The energy-efficient duty cycle design problem is a typical NP-hard combinatorial optimization problem. In this paper, we investigate an improved elite immune evolutionary algorithm (IEIEA) strategy to optimize energy-efficient duty cycle design scheme and monitored area jointly to enhance the network lifetimes. Simulation results show that the network lifetime of the proposed IEIEA method increased compared to the other two methods, which means that the proposed method improves the full coverage constraints.

Effects of Lawn Tennis Association mini tennis as task constraints on children’s match-play characteristics

ABSTRACTThe Lawn Tennis Association’s mini tennis (MT) is a modified version of tennis consisting of progressive stages; however, there have been few attempts to evaluate how MT might shape performance behaviours. Here, we examine effects of playing MT on the emergence of children’s match-play behaviours in 48 junior tennis players. Performance in 1010 match-play points were filmed and coded across 4 tennis stages (MT Red, MT Orange, MT Green and Full Ball), using a notational analysis system. Recorded performance variables included rally length, first serve percentage and shot type, for the purpose of analysing inter-stage comparisons. Results showed a series of specific adaptations to playing characteristics across the stages, including rally length, shot variety and serve success. MT Red rallies (7.36 ± 6.06) were longer than Full Ball rallies (3.83 ± 2.40), and a higher percentage of forehands were played at MT Red (66.40 ± 8.49%) than at Full Ball stage (45.96 ± 6.47%). Findings suggested that MT stages can afford children more opportunities to develop their skills and elicit different match-play characteristics than Full Ball task constraints. Coaches, therefore, should consider the nature of emergent adaptations when designing practice environments to facilitate learning in young tennis players.

Evolution of microstructure and texture in commercial pure aluminum subjected to high pressure torsion processing

Commercially pure aluminum was chosen as a model face-centered cubic material for a detailed investigation of microstructural and textural evolution during processing by high pressure torsion. Severe grain refinement was observed as the average grain size decreased from ~85μm to ~1.22μm at an equivalent strain of ɛ=99. It is observed that at early stages of deformation an accumulation of dislocations inside grains occurs. More straining results in an increase of misorientation and eventually gives rise to fragmentation of parent grains to new smaller grains. A near saturation of grain refinement is observed after a strain of ɛ=15. Kernel average misorienation maps suggest the occurrence of a weak recovery process at relatively large strains, resulting in annihilation of dislocations inside the grains. The texture results show that a simple shear type texture develops during deformation, although it is a relatively weak texture due to the nature of simple shear strain mode and the occurrence of grain fragmentation. The full constraint Taylor model and the viscoplastic self-consistent crystal plasticity model were employed to reproduce the experimental textures at relatively large strains. It is shown that the Taylor model leads to a better agreement between simulated and experimental data. It is observed that a satisfactory simulation of the texture evolution at severe strain amplitudes cannot be obtained with models that ignore the effect of grain fragmentation.

Sequential Randomized Algorithms for Convex Optimization in the Presence of Uncertainty

In this technical note, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full constraint satisfaction and partial constraint satisfaction, respectively, is given. The proposed methods allow to enlarge the applicability of the existing randomized methods to real-world applications involving a large number of design variables. Since the proposed approach does not provide a priori bounds on the sample complexity, extensive numerical simulations, dealing with an application to hard-disk drive servo design, are provided. These simulations testify the goodness of the proposed solution.

A container loading algorithm with static mechanical equilibrium stability constraints

The Container Loading Problem (CLP) literature has traditionally guaranteed cargo static stability by imposing the full support constraint for the base of the box. Used as a proxy for real-world static stability, this constraint excessively restricts the container space utilization and has conditioned the algorithms developed for this problem. In this paper we propose a container loading algorithm with static stability constraints based on the static mechanical equilibrium conditions applied to rigid bodies, which derive from Newton’s laws of motion. The algorithm is a multi-population biased random-key genetic algorithm, with a new placement procedure that uses the maximal-spaces representation to manage empty spaces, and a layer building strategy to fill the maximal-spaces. The new static stability criterion is embedded in the placement procedure and in the evaluation function of the algorithm. The new algorithm is extensively tested on well-known literature benchmark instances using three variants: no stability constraint, the classical full base support constraint and with the new static stability constraint—a comparison is then made with the state-of-the-art algorithms for the CLP. The computational experiments show that by using the new stability criterion it is always possible to achieve a higher percentage of space utilization than with the classical full base support constraint, for all classes of problems, while still guaranteeing static stability. Moreover, for highly heterogeneous cargo the new algorithm with full base support constraint outperforms the other literature approaches, improving the best solutions known for these classes of problems.

CLASH: JOINT ANALYSIS OF STRONG-LENSING, WEAK-LENSING SHEAR, AND MAGNIFICATION DATA FOR 20 GALAXY CLUSTERS*

ABSTRACT We present a comprehensive analysis of strong-lensing, weak-lensing shear and magnification data for a sample of 16 X-ray-regular and 4 high-magnification galaxy clusters at 0.19 ≲ z ≲ 0.69 selected from Cluster Lensing And Supernova survey with Hubble (CLASH). Our analysis combines constraints from 16-band Hubble Space Telescope observations and wide-field multi-color imaging taken primarily with Suprime-Cam on the Subaru Telescope, spanning a wide range of cluster radii (10″–16′). We reconstruct surface mass density profiles of individual clusters from a joint analysis of the full lensing constraints, and determine masses and concentrations for all of the clusters. We find the internal consistency of the ensemble mass calibration to be ≤5% ± 6% in the one-halo regime (200–2000 kpc h −1) compared to the CLASH weak-lensing-only measurements of Umetsu et al. For the X-ray-selected subsample of 16 clusters, we examine the concentration–mass (c–M) relation and its intrinsic scatter using a Bayesian regression approach. Our model yields a mean concentration of c ∣ z = 0.34 = 3.95 ± 0.35 at M 200c ≃ 14 × 1014 M ⊙ and an intrinsic scatter of σ ( ln c 200 c ) = 0.13 ± 0.06 , which is in excellent agreement with Λ cold dark matter predictions when the CLASH selection function based on X-ray morphological regularity and the projection effects are taken into account. We also derive an ensemble-averaged surface mass density profile for the X-ray-selected subsample by stacking their individual profiles. The stacked lensing signal is detected at 33σ significance over the entire radial range ≤4000 kpc h −1, accounting for the effects of intrinsic profile variations and uncorrelated large-scale structure along the line of sight. The stacked mass profile is well described by a family of density profiles predicted for cuspy dark-matter-dominated halos in gravitational equilibrium, namely, the Navarro–Frenk–White (NFW), Einasto, and DARKexp models, whereas the single power-law, cored isothermal and Burkert density profiles are disfavored by the data. We show that cuspy halo models that include the large-scale two-halo term provide improved agreement with the data. For the NFW halo model, we measure a mean concentration of c 200 c = 3.79 − 0.28 + 0.30 at M 200 c = 14.1 − 1.0 + 1.0 × 10 14 M ⊙ , demonstrating consistency between the complementary analysis methods.

Bandwidth-Efficient Packet Scheduling for Live Streaming With Network Coding

Network coding (NC) brings substantial improvements in terms of throughput and delay in collaborative media streaming applications. A key aspect of NC-driven live peer-to-peer streaming is the packet scheduling policy. Indeed, lack of synchronization among peers usually results in significantly redundant packet transmission, which in turn leads to severe bandwidth inefficiencies. In this paper, we address the problem of finding a suitable asynchronous packet scheduling policy that greatly helps to overcome this critical redundant transmission problem. We propose a bandwidth cost minimization technique under a full video packet recovery constraint. In order to add scalability and improved performance, we also further derive a distributed packet scheduling algorithm. Both implementation and analytical considerations of the proposed approaches are described in this paper. Experimental results confirm that the proposed algorithms deliver higher bandwidth efficiency with reduced redundancy and communication overhead rate and, consequently, better quality-of-service in terms of improved video quality and delivery ratio.

An explicit martingale version of the one-dimensional Brenier’s Theorem with full marginals constraint

We provide an extension of the martingale version of the Fréchet–Hoeffding coupling to the infinitely-many marginals constraints setting. In the two-marginal context, this extension was obtained by Beiglböck and Juillet (2016), and further developed by Henry-Labordère and Touzi (in press), see also Beiglböck and Henry-Labordère (Preprint).Our main result applies to a special class of reward functions and requires some restrictions on the marginal distributions. We show that the optimal martingale transference plan is induced by a pure downward jump local Lévy model. In particular, this provides a new martingale peacock process (PCOC “Processus Croissant pour l’Ordre Convexe,” see Hirsch et al. (2011), and a new remarkable example of discontinuous fake Brownian motions. Further, as in Henry-Labordère and Touzi (in press), we also provide a duality result together with the corresponding dual optimizer in explicit form.As an application to financial mathematics, our results give the model-independent optimal lower and upper bounds for variance swaps.

GPU Robot Motion Planning Using Semi-Infinite Nonlinear Programming

We propose a many-core GPU implementation of robotic motion planning formulated as a semi-infinite optimization program. Our approach computes the constraints and their gradients in parallel, and feeds the result to a nonlinear optimization solver running on the CPU. To ensure the continuous satisfaction of our constraints, we use polynomial approximations over time intervals. Because each constraint and its gradient can be evaluated independently for each time interval, we end up with a highly parallelizable problem that can take advantage of many-core architectures. Classic robotic computations (geometry, kinematics, and dynamics) can also benefit from parallel processors, and we carefully study their implementation in our context. This results in having a full constraint evaluator running on the GPU. We present several optimization examples with a humanoid robot. They reveal substantial improvements in terms of computation performance compared to a parallel CPU version.

Theoretic Studies of Full Constraints on a Star Tracker's Influential Error Sources for In-orbit Calibration

To collect star transits data qualified for in-orbit calibration, this study derives the full error constraints to limit star tracker's influential error sources and computes their error boundaries from a theoretical perspective. The full constraints, including not only the minimum variance estimation of position but also the error bound prediction of scale and intensity of Gaussian-shaped starspots, are studied based on the Cramér–Rao Lower Bound (CRLB) theorem. By imposing these constraints on motion, drift in focal length, and other factors, their boundaries could be determined before launch. Therefore, the in-orbit correction accuracy is expected to be close to CRLB through suitable implementation of these constraints. The correctness of the theoretical position error of motion is demonstrated by the data-fitting procedure against test results of star tracker on dynamic performance. The simulation result shows that the drift in focal length can generate an error with the same magnitude as detector noise and thus might be the dominant error source when star tracker is working under stationary circumstance. Using the accuracy performance of some typical star trackers, this study shows that the CRLB constraint may be very effective to estimate the overall position error of a starspot or one axis, valuable data that can be used for online calibration. The overall position uncertainty analysis shows that a weighted method can be employed for calibration, a process where star data can be given a weight in inverse proportion to the CRLB value.

Experimental Determination of Deformation Induced Lattice Rotation by EBSD Technique for Slip System Analysis

A method was proposed to experimentally determine the deformation induced lattice rotation by electron backscatter diffraction (EBSD) technique, based on which the activated slip systems could be predicted. The method is to create a project file including the EBSD data of the sample before and after deformation, which allows the lattice rotation to be calculated and visualized using the commercial EBSD software. This method was applied to a polycrystalline Ni subjected to quasi-static compression. The lattice rotation of one grain was calculated and visualized and the activated slip systems were predicted. The comparison with the slip systems predicted by full-constraints (FC) Taylor model highlights the advantage of the present method.

Study on the Transportation Problem of Petrol Secondary Distribution with Considering Shortage Cost

Petrol is a kind of strategic natural resources. Provide legitimate transportation plans for the petrol secondary distribution are the key links to guarantee the petrol provision. If the total supply is insufficient, some petrol stations can’t avoid shortage because their demands could not be met. So the shortage cost will appear. This paper studies the problem of how to arrange the transportation plan in order to minimize the total cost when the total volume of supply is insufficient. Given the storage volume, the sales rate and the unit shortage cost of every petrol station, considering the full loading constraints of the compartment vehicle, a mixed integer programming model for minimizing the total cost of petrol secondary distribution is established. A Lingo program is compiled for solving the model. Finally, simulation on an example has been done and a reasonable transportation plan is obtained. The model and algorithm in this paper can provide a theoretical basis for dispatching department to make transportation plan.

Matrix-free aerostructural optimization of aircraft wings

In structural optimization subject to failure constraints, computing the gradients of a large number of functions with respect to a large number of design variables may not be computationally practical. Often, the number of constraints in these optimization problems is reduced using constraint aggregation at the expense of a higher mass of the optimal structural design. This work presents results of structural and coupled aerodynamic and structural design optimization of aircraft wings using a novel matrix-free augmented Lagrangian optimizer. By using a matrix-free optimizer, the computation of the full constraint Jacobian at each iteration is replaced by the computation of a small number of Jacobian-vector products. The low cost of the Jacobian-vector products allows optimization problems with thousands of failure constraints to be solved directly, mitigating the effects of constraint aggregation. The results indicate that the matrix-free optimizer reduces the computational work of solving the optimization problem by an order of magnitude compared to a traditional sequential quadratic programming optimizer. Furthermore, the use of a matrix-free optimizer makes the solution of large multidisciplinary design problems, in which gradient information must be obtained through iterative methods, computationally tractable.

SDPNAL $$+$$ + : a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints

In this paper, we present a majorized semismooth Newton-CG augmented Lagrangian method, called SDPNAL $$+$$ , for semidefinite programming (SDP) with partial or full nonnegative constraints on the matrix variable. SDPNAL $$+$$ is a much enhanced version of SDPNAL introduced by Zhao et al. (SIAM J Optim 20:1737–1765, 2010) for solving generic SDPs. SDPNAL works very efficiently for nondegenerate SDPs but may encounter numerical difficulty for degenerate ones. Here we tackle this numerical difficulty by employing a majorized semismooth Newton-CG augmented Lagrangian method coupled with a convergent 3-block alternating direction method of multipliers introduced recently by Sun et al. (SIAM J Optim, to appear). Numerical results for various large scale SDPs with or without nonnegative constraints show that the proposed method is not only fast but also robust in obtaining accurate solutions. It outperforms, by a significant margin, two other competitive publicly available first order methods based codes: (1) an alternating direction method of multipliers based solver called SDPAD by Wen et al. (Math Program Comput 2:203–230, 2010) and (2) a two-easy-block-decomposition hybrid proximal extragradient method called 2EBD-HPE by Monteiro et al. (Math Program Comput 1–48, 2014). In contrast to these two codes, we are able to solve all the 95 difficult SDP problems arising from the relaxations of quadratic assignment problems tested in SDPNAL to an accuracy of $$10^{-6}$$ efficiently, while SDPAD and 2EBD-HPE successfully solve 30 and 16 problems, respectively. In addition, SDPNAL $$+$$ appears to be the only viable method currently available to solve large scale SDPs arising from rank-1 tensor approximation problems constructed by Nie and Wang (SIAM J Matrix Anal Appl 35:1155–1179, 2014). The largest rank-1 tensor approximation problem we solved (in about 14.5 h) is nonsym(21,4), in which its resulting SDP problem has matrix dimension $$n = 9261$$ and the number of equality constraints $$m =12{,}326{,}390$$ .

A simplified constitutive model for predicting shape memory polymers deformation behavior

Shape memory polymers (SMPs) can keep a temporary shape after pre-deformation at a higher temperature and subsequent cooling. When they are reheated, their original shapes can be recovered. Such special characteristics of SMPs make them widely used in aerospace structures, biomedical devices, functional textiles and other devices. Increasing usefulness of SMPs motivates us to further understand their thermomechanical properties and deformation behavior, of which the development of appropriate constitutive models for SMPs is imperative. There is much work in literatures that address constitutive models of the thermo-mechanical coupling in SMPs. However, due to their complex forms, it is difficult to apply these constitutive models in the real world. In this paper, a three-element model with simple form is proposed to investigate the thermo-mechanical small strain (within 10%) behavior of polyurethane under uniaxial tension. Two different cases of heated recovery are considered: (1) unconstrained free strain recovery and (2) stress recovery under full constraint at a strain level fixed during low temperature unloading. To validate the model, simulated and predicted results are compared with Tobushi's experimental results and good agreement can be observed.

Coupled FEM and Alamel-type Polycrystal Plasticity Modelling Applied to Extrusion of Aluminium Alloys

The evolution of deformation texture during an axisymmetric extrusion of an Al-Mg-Si aluminium alloy is simulated by coupled finite element method (FEM) and polycrystal plasticity modelling. The FEM-simulations provide spatial and temporal history of strain, strain-rate and temperature, i.e. the deformation history, along selected particle paths. The deformation history is subsequently transferred to polycrystal plasticity models for the simulation of the deformation texture evolution. In particular, Alamel-type models which are advanced Taylor-type polycrystal plasticity models have been employed. The predicted textures are compared to experimental results and to full-constraint (FC) Taylor texture predictions. It is shown that the Alamel-type models perform better than the FC-Taylor model and compare well with the experimental results.

Conserved quantities of harmonic asymptotic initial data sets

In the first half of this article, we survey the new quasi-local and total angular momentum and center of mass defined in [9] and summarize the important properties of these definitions. To compute these conserved quantities involves solving a nonlinear PDE system (the optimal isometric embedding equation), which is rather difficult in general. We found a large family of initial data sets on which such a calculation can be carried out effectively. These are initial data sets of harmonic asymptotics, first proposed by Corvino and Schoen to solve the full vacuum constraint equation. In the second half of this article, the new total angular momentum and center of mass for these initial data sets are computed explicitly.