Continuous Relaxation Research Articles

Distribution Grid Modeling Using Smart Meter Data

The knowledge of distribution grid models, including topologies and line impedances, is essential for grid monitoring, control and protection. However, such information is often unavailable, incomplete or outdated. The increasing deployment of smart meters (SMs) provides a unique opportunity to tackle this issue. This paper proposes a two-stage framework for distribution grid modeling using SM data. In the first stage, the network topology is identified by reconstructing a weighted Laplacian matrix of distribution networks. In the second stage, a least absolute deviations (LAD) regression model is developed for estimating line impedance of a single branch based on the nonlinear (inverse) power flow model, wherein a conductor library is leveraged to narrow down the solution space. The LAD regression model is originally a mixed-integer nonlinear program whose continuous relaxation is still non-convex. Thus, we specially address its convex relaxation and discuss the exactness. The modified regression model is then embedded within a bottom-up sweep algorithm to achieve the identification across the network in a branch-wise manner. Numerical results on the IEEE 13-bus, 37-bus and 69-bus test feeders validate the effectiveness of the proposed methods.

Deep parameter-free attention hashing for image retrieval

Deep hashing method is widely applied in the field of image retrieval because of its advantages of low storage consumption and fast retrieval speed. There is a defect of insufficiency feature extraction when existing deep hashing method uses the convolutional neural network (CNN) to extract images semantic features. Some studies propose to add channel-based or spatial-based attention modules. However, embedding these modules into the network can increase the complexity of model and lead to over fitting in the training process. In this study, a novel deep parameter-free attention hashing (DPFAH) is proposed to solve these problems, that designs a parameter-free attention (PFA) module in ResNet18 network. PFA is a lightweight module that defines an energy function to measure the importance of each neuron and infers 3-D attention weights for feature map in a layer. A fast closed-form solution for this energy function proves that the PFA module does not add any parameters to the network. Otherwise, this paper designs a novel hashing framework that includes the hash codes learning branch and the classification branch to explore more label information. The like-binary codes are constrained by a regulation term to reduce the quantization error in the continuous relaxation. Experiments on CIFAR-10, NUS-WIDE and Imagenet-100 show that DPFAH method achieves better performance.

Dielectric spectroscopy of nanofluids in deionized water: Method of removing electrode polarization effect

HypothesisThe electrode polarization observed in the measured complex dielectric frequency responses of the nanosuspensions could be isolated by using time-domain analysis. ExperimentsComplex impedance and dielectric frequency responses of various ferroelectric and magnetic nanofluids were ultrasonically dispersed in deionized water and measured within 20 Hz to 6 GHz range for the first time. A general Kramer-Krönig continuous relaxation model was fitted to the dielectric spectra in the least-squares sense using the Tikhonov’s regularization. The independent ζ-potential measurements of the BTO-C2 and Fe3O4 nanosuspensions were performed. FindingsThree distinct peaks were observed in the time-domain responses. Zero padding of the two slowest peaks, followed by the inversion of the corrected time domain responses, resulted in the flattening of the lower frequency portion of the dielectric constant. The effective medium theory model coupled with the pattern search optimization routine, were used to match these flattened responses. The surface charge on the nanoparticles was estimated from the measured ζ-potential using the Gouy-Chapman-Stern-Grahame model. The resulting values were comparable with the ones obtained from the effective medium theory fitting procedure, which proves effectiveness of the proposed approach at removing the electrode polarization effects. The proposed method has the advantage over the existing ones, because it is carried out in time domain and requires no prior knowledge about the underlying relaxation time amplitude distributions or specific equivalent circuits.

Stochastic Planning and Scheduling with Logic-Based Benders Decomposition

We apply logic-based Benders decomposition (LBBD) to two-stage stochastic planning and scheduling problems in which the second stage is a scheduling task. We solve the master problem with mixed integer/linear programming and the subproblem with constraint programming. As Benders cuts, we use simple no-good cuts as well as analytic logic-based cuts we develop for this application. We find that LBBD is computationally superior to the integer L-shaped method. In particular, a branch-and-check variant of LBBD can be faster by several orders of magnitude, allowing significantly larger instances to be solved. This is due primarily to computational overhead incurred by the integer L-shaped method while generating classic Benders cuts from a continuous relaxation of an integer programming subproblem. To our knowledge, this is the first application of LBBD to two-stage stochastic optimization with a scheduling second-stage problem and the first comparison of LBBD with the integer L-shaped method. The results suggest that LBBD could be a promising approach to other stochastic and robust optimization problems with integer or combinatorial recourse. Summary of Contribution: We study an important class of optimization problems, namely, two-stage stochastic programs with integer recourse, which are known to be extremely difficult to solve in general. We focus on an application in which the second-stage problem is a scheduling problem, a first in the literature to the best of our knowledge. Our study exemplifies how one can exploit the combinatorial structure of the scheduling problem to derive novel analytic Benders cuts and use them within a branch-and-check algorithm. The proposed algorithm solves instances that are intractable for commercial solvers and state-of-the-art decomposition-based methods, such as the integer L-shaped method. We believe that our study will inspire further research in the use of hybrid logic-based optimization methods for solving stochastic combinatorial optimization problems.

Neural network for a class of sparse optimization with [formula omitted]-regularization

Sparse optimization involving the L0-norm function as the regularization in objective function has a wide application in many fields. In this paper, we propose a projected neural network modeled by a differential equation to solve a class of these optimization problems, in which the objective function is the sum of a nonsmooth convex loss function and the regularization defined by the L0-norm function. This optimization problem is not only nonconvex, but also discontinuous. To simplify the structure of the proposed network and let it own better convergence properties, we use the smoothing method, where the new constructed smoothing function for the regularization term plays a key role. We prove that the solution to the proposed network is globally existent and unique, and any accumulation point of it is a critical point of the continuous relaxation model. Except for a special case, which can be easily justified, any critical point is a local minimizer of the considered sparse optimization problem. It is an interesting thing that all critical points own a promising lower bound property, which is satisfied by all global minimizers of the considered problem, but is not by all local minimizers. Finally, we use some numerical experiments to illustrate the efficiency and good performance of the proposed method for solving this class of sparse optimization problems, which include the most widely used models in feature selection of classification learning.

Oxidative ageing of elastomers: experiment and modelling

During an extensive test programme at the Bundesanstalt für Materialforschung und prüfung, material property changes of EPDM O-rings were investigated at different ageing times and two ageing temperatures of 125∘C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$125\\,^{\\circ }\\,\\hbox {C}$$\\end{document} and 150∘C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$150\\,^{\\circ }\\, \\hbox {C}$$\\end{document}. To exclude possible diffusion-limited oxidation (DLO) effects that can distort the data, IRHD microhardness measurements were taken over the cross section of compressed O-rings. Continuous stress relaxation measurements were taken on samples free of DLO effects. The additional effect of physical processes to irreversible chemical ones during a long-term thermal exposure is quantified by the analysis of compression set measurements under various test conditions. By combining the different experimental methods, characteristic times relative to the degradation processes were determined. On the basis of experimental data, a microphysically motivated model that takes into account reversible and irreversible processes was developed. The parameter identification strategy of the material model is based on our experimental investigations on homogeneously aged elastomer O-rings. The simulated results are in good agreement with the experiments.

Design of Teaching Platform for ABS Wheel Speed Sensor

In order to ensure driving safety, ABS brake systems are currently installed on cars. When the ABS is working, it needs to detect the wheel speed signal through the wheel speed sensor to realize continuous braking and relaxation to prevent the wheels from locking up. In daily teaching, it is difficult for students to observe the working process of the wheel speed sensor, and then understand the working condition of ABS in the braking process. So according to the working principle of electromagnetic induction wheel speed sensor, a simple experimental bench was designed and manufactured. This bench can clearly display the changes of the voltage generated by the sensors at different speeds during the rotation of the wheel, and then simulate the changes in the signal when the ABS is working.

Nanoindentation creep and stress relaxation tests of polycarbonate: Analysis of viscoelastic properties by different rheological models

Abstract Feedback-controlled nanoindentation with a Berkovich diamond tip has been used to perform creep and stress relaxation tests on polycarbonate at room temperature for a wide range of loads (10 – 30000 μN) and indentation depths (30 – 3000 nm). The creep compliance J(t) and relaxation modulus G(t) have been calculated from experimental data as a function of time in the range t = 0.1 – 100 (1000) s. The data are analysed by different rheological models which are compared: (1) the Burgers model, (2) the generalised Maxwell/generalised Kelvin model, and two empirical approaches: (3) a logarithmic model, and (4) a power law model. The Burgers model gives a poor description of the material behaviour since it assumes a steady-state flow of material which is not observed in the experimental time range. The generalised models yield a set of discrete relaxation- and retardation time constants. It is shown that these time constants do not correlate with specific molecular moving processes in the polymer, but are only one of several possible parameterisations of the creep and relaxation curves. Numerical differentiation of G(t) and J(t) shows that polycarbonate has continuous relaxation- and retardation time spectra, respectively, and the dynamic viscosity η(t) of the material increases linearly with time. The behaviour of polycarbonate is best represented by the empirical power law model, which allows optimum fit of creep/relaxation curves, relaxation and retardation time spectra and time-dependent viscosity.

Fast-Acquiring High-Quality Prony Series Parameters of Asphalt Concrete through Viscoelastic Continuous Spectral Models.

Prony series representations have been extensively applied to characterizing the time-domain linear viscoelastic (LVE) material functions for asphalt concrete. However, existing methods that can generate high-quality Prony series parameters (i.e., discrete spectra) mostly involve complicated programming algorithms, which poses a challenge for quick access of Prony series parameters. Also, very limited research has been devoted to establishing methods for simultaneously determining both retardation and relaxation spectra. To resolve these issues, this study presented a practical approach to fast acquiring high-quality Prony series parameters for both relaxation modulus and creep compliance of asphalt concrete by using the complex modulus test data. The approach adopts the analytical representations of the continuous relaxation and retardation spectra from the Havriliak-Negami (HN) and 2S2P1D complex modulus models to directly determine the discrete spectra, and the elastic constants, Ee and Dg, for both LVE modulus and compliance functions are further calculated by fitting the corresponding generalized Maxwell model representations to smoothed data from the storage modulus representations of the HN and 2S2P1D complex modulus models. In this way, all the procedures in the proposed method can be easily implemented in Microsoft Excel. The results showed that the HN and 2S2P1D models yielded slightly different continuous spectral patterns at shorter relaxation times and longer retardation times. However, at the region covered by the test data, the continuous spectra of the two complex modulus models were very close to each other. Thus, the two models can generate comparable Prony series parameters within the time or frequency range covered by the test data. Considering that the quality of the resulting Prony series parameters are closely related to the master curve models used for presmoothing, the HN and 2S2P1D models were compared with the conventional Sigmoidal model. Additionally, the Black diagram was recommended for examining the quality of the complex modulus test data before constructing the master curves.

A Scalable Algorithm for Sparse Portfolio Selection

The sparse portfolio selection problem is one of the most famous and frequently studied problems in the optimization and financial economics literatures. In a universe of risky assets, the goal is to construct a portfolio with maximal expected return and minimum variance, subject to an upper bound on the number of positions, linear inequalities, and minimum investment constraints. Existing certifiably optimal approaches to this problem have not been shown to converge within a practical amount of time at real-world problem sizes with more than 400 securities. In this paper, we propose a more scalable approach. By imposing a ridge regularization term, we reformulate the problem as a convex binary optimization problem, which is solvable via an efficient outer-approximation procedure. We propose various techniques for improving the performance of the procedure, including a heuristic that supplies high-quality warm-starts, and a second heuristic for generating additional cuts that strengthens the root relaxation. We also study the problem’s continuous relaxation, establish that it is second-order cone representable, and supply a sufficient condition for its tightness. In numerical experiments, we establish that a conjunction of the imposition of ridge regularization and the use of the outer-approximation procedure gives rise to dramatic speedups for sparse portfolio selection problems. Summary of Contribution: This paper proposes a new decomposition scheme for tackling the problem of sparse portfolio selection: the problem of selecting a limited number of securities in a portfolio. This is a challenging problem to solve in high dimensions, as it belongs to the class of mixed-integer, nonseparable nonlinear optimization problems. We propose a new Benders-type cutting plane method and demonstrate its efficacy on a wide set of both synthetic and real-world problems, including problems with thousands of securities. Our approach also provides insights for other mixed-integer optimization problems with logical constraints.

A smoothing proximal gradient algorithm for matrix rank minimization problem

In this paper, we study the low-rank matrix minimization problem, where the loss function is convex but nonsmooth and the penalty term is defined by the cardinality function. We first introduce an exact continuous relaxation, that is, both problems have the same minimizers and the same optimal value. In particular, we introduce a class of lifted stationary points of the relaxed problem and show that any local minimizer of the relaxed problem must be a lifted stationary point. In addition, we derive lower bound property for the nonzero singular values of the lifted stationary point and hence also of the local minimizers of the relaxed problem. Then the smoothing proximal gradient (SPG) algorithm is proposed to find a lifted stationary point of the continuous relaxation model. Moreover, it is shown that any accumulating point of the sequence generated by SPG algorithm is a lifted stationary point. At last, numerical examples show the efficiency of the SPG algorithm.

Multi-Manifold Deep Discriminative Cross-Modal Hashing for Medical Image Retrieval.

Benefitting from the low storage cost and high retrieval efficiency, hash learning has become a widely used retrieval technology to approximate nearest neighbors. Within it, the cross-modal medical hashing has attracted an increasing attention in facilitating efficiently clinical decision. However, there are still two main challenges in weak multi-manifold structure perseveration across multiple modalities and weak discriminability of hash code. Specifically, existing cross-modal hashing methods focus on pairwise relations within two modalities, and ignore underlying multi-manifold structures across over 2 modalities. Then, there is little consideration about discriminability, i.e., any pair of hash codes should be different. In this paper, we propose a novel hashing method named multi-manifold deep discriminative cross-modal hashing (MDDCH) for large-scale medical image retrieval. The key point is multi-modal manifold similarity which integrates multiple sub-manifolds defined on heterogeneous data to preserve correlation among instances, and it can be measured by three-step connection on corresponding hetero-manifold. Then, we propose discriminative item to make each hash code encoded by hash functions be different, which improves discriminative performance of hash code. Besides, we introduce Gaussian-binary Restricted Boltzmann Machine to directly output hash codes without using any continuous relaxation. Experiments on three benchmark datasets (AIBL, Brain and SPLP) show that our proposed MDDCH achieves comparative performance to recent state-of-the-art hashing methods. Additionally, diagnostic evaluation from professional physicians shows that all the retrieved medical images describe the same object and illness as the queried image.

Discrete and Parameter-Free Multiple Kernel k-Means.

The multiple kernel k -means (MKKM) and its variants utilize complementary information from different sources, achieving better performance than kernel k -means (KKM). However, the optimization procedures of most previous works comprise two stages, learning the continuous relaxation matrix and obtaining the discrete one by extra discretization procedures. Such a two-stage strategy gives rise to a mismatched problem and severe information loss. Even worse, most existing MKKM methods overlook the correlation among prespecified kernels, which leads to the fusion of mutually redundant kernels and bad effects on the diversity of information sources, finally resulting in unsatisfying results. To address these issues, we elaborate a novel Discrete and Parameter-free Multiple Kernel k -means (DPMKKM) model solved by an alternative optimization method, which can directly obtain the cluster assignment results without subsequent discretization procedure. Moreover, DPMKKM can measure the correlation among kernels by implicitly introducing a regularization term, which is able to enhance kernel fusion by reducing redundancy and improving diversity. Noteworthily, the time complexity of optimization algorithm is successfully reduced, through masterly utilizing of coordinate descent technique, which contributes to higher algorithm efficiency and broader applications. What's more, our proposed model is parameter-free avoiding intractable hyperparameter tuning, which makes it feasible in practical applications. Lastly, extensive experiments conducted on a number of real-world datasets illustrated the effectiveness and superiority of the proposed DPMKKM model.

Coupled effects of temperature and compressive strain on aging of silicone rubber foam

The coupled effects of temperature and compressive strain on aging behaviors and mechanisms of silicone rubber foam were investigated by conducting the accelerated aging tests. The silicone rubber foams subjected to various levels of temperature and compressive strain were characterized by Attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy, micro hardness, volume fraction, compression set, continuous stress relaxation, mechanical properties, and thermogravimetric analysis (TGA) etc. The ATR-FTIR results indicate that the complex oxidation reactions (crosslinking, chain scission, and oxidation of side chains) occurred simultaneously with the formation of oxidation products. The high temperature facilitated the increase in crosslinking density and enhanced the thermal stability of the foams, implying that the oxidation crosslinking predominated over chain scission leading to the formation of a denser network structure. The physical and mechanical properties of the foams underwent significant changes due to the oxidation reactions and the irreversible collapse of the porous microstructure. The elevated temperature and the compressive stress both have a direct effect on the degradation of the foam. The elevated temperature played a more important role in changes of the physical-mechanical properties and microstructure.

Monte Carlo Concrete DropPath for epistemic uncertainty estimation in pollen images classification

The paper presents the results of a new method for training the NASNet neural network called Monte Carlo Concrete DropPath for epistemic uncertainty estimation to classify pollen images. The developed method is compared with existing methods for epistemic uncertainty estimation. The method turns an arbitrary multipath neural network into a Bayesian one by sampling from the predictive distribution. The Monte Carlo method samples different masks of DropPath to estimate uncertainty. Moreover, the probability of DropPath is optimized using continuous relaxation. The proposed method was tested for the classification task on the state-of-the-art NASNet architecture. The method demonstrated advantages on the task of classifying pollen images. The classification accuracy increased for 13 pollen species of allergen plants by 0.73 % on average compared to the baseline NASNet, reaching 98.34 % by F1 measure. Furthermore, the method increased calibration and reduced the epistemic uncertainty of the model by two times compared to the NASNets ensemble. It is shown that continuous relaxation of the DropPath probability parameter increases the accuracy of problem solving and reduces the epistemic uncertainty of the model. These results contribute to the automation of aeropalinological monitoring to reduce the time of informing patients who suffer from pollinosis and hence to prevent allergy symptoms. The developed method can be applied to train a neural network for other computer vision tasks on any image dataset.

Delay-Limited Computation Offloading for MEC-Assisted Mobile Blockchain Networks

The proof-of-work (PoW) mining process requires a large amount of intensive computing, which leads to some plights such as heavy equipment and fixed access nodes in traditional blockchain networks. A novel mobile blockchain network with the help of a mobile edge computing (MEC) server is presented, where all mobile users participate in the PoW mining process. The traditional Bitcoin network adjusts the target difficulty value to ensure a stable block time. However, for MEC-assisted mobile blockchain networks, the adjusted difficulty value needs to be broadcast to all mobile users, which results in expensive communication costs. To maintain a stable block time of mobile blockchain networks, we formulate the delay-limited computation offloading strategy of the PoW-based mining task as a non-cooperative game that maximizes an individual revenue in the MEC-assisted mobile blockchain network. Specifically, the non-cooperative game problem can be divided into multiple sub-game optimization problems to obtain final solutions for all users. We analyze the sub-game optimization problem and prove the existence of Nash equilibrium (NE) of the non-cooperative game. Moreover, we design an alternating iterative algorithm based on the continuous relaxation and greedy rounding (CRGR) to achieve the NE of this game. Given the sub-optimal delay-limited computation offloading results, we also derive the optimal transmit power for an individual user within the maximum mining delay range. From the analytical results, we can see that the proposed CRGR-based alternating iterative algorithm can efficiently attain the sub-optimal delay-limited computation offloading strategies of all mobile users in the polynomial time. The individual transmit power increases accordingly with the delay-limited computation offloading strategies of all users. Numerical results demonstrate that the proposed CRGR-based alternating iterative algorithm has fast convergence and good stability.

CMDNet: Learning a Probabilistic Relaxation of Discrete Variables for Soft Detection With Low Complexity

Following the great success of Machine Learning (ML), especially Deep Neural Networks (DNNs), in many research domains in 2010s, several ML-based approaches were proposed for detection in large inverse linear problems, e.g., massive MIMO systems. The main motivation behind is that the complexity of Maximum A-Posteriori (MAP) detection grows exponentially with system dimensions. Instead of using DNNs, essentially being a black-box, we take a slightly different approach and introduce a probabilistic Continuous relaxation of disCrete variables to MAP detection. Enabling close approximation and continuous optimization, we derive an iterative detection algorithm: Concrete MAP Detection (CMD). Furthermore, extending CMD by the idea of deep unfolding into CMDNet, we allow for (online) optimization of a small number of parameters to different working points while limiting complexity. In contrast to recent DNN-based approaches, we select the optimization criterion and output of CMDNet based on information theory and are thus able to learn approximate probabilities of the individual optimal detector. This is crucial for soft decoding in today's communication systems. Numerical simulation results in MIMO systems reveal CMDNet to feature a promising accuracy complexity trade-off compared to State of the Art. Notably, we demonstrate CMDNet's soft outputs to be reliable for decoders.

Column generation and rounding heuristics for minimizing the total weighted completion time on a single batching machine

This paper deals with the single-machine, parallel batching, total weighted completion time scheduling problem. A new graph-based formulation of the problem is proposed, where such graph has an exponential number of nodes and arcs. The problem is modeled as an integer linear program on this graph, combining features of a minimum cost flow problem and features of a set-partition problem as well. The continuous relaxation of this integer problem is solved via column generation, providing a very tight lower bound. Two different flavors of column generation are tested, leading to two models with identical performances in terms of bound tightness but in practice very different in terms of running time. A simple and effective rounding strategy applied to the faster model allows to generate heuristic solutions with values within a few percentage points from the optimum. Two different variants of the heuristic rounding procedure are tested; one allows to certify the optimality gap, while the other trades the ability to certify the gap with a greater computational speed.

Deep Learning Triplet Ordinal Relation Preserving Binary Code for Remote Sensing Image Retrieval Task

As satellite observation technology rapidly develops, the number of remote sensing (RS) images dramatically increases, and this leads RS image retrieval tasks to be more challenging in terms of speed and accuracy. Recently, an increasing number of researchers have turned their attention to this issue, as well as hashing algorithms, which map real-valued data onto a low-dimensional Hamming space and have been widely utilized to respond quickly to large-scale RS image search tasks. However, most existing hashing algorithms only emphasize preserving point-wise or pair-wise similarity, which may lead to an inferior approximate nearest neighbor (ANN) search result. To fix this problem, we propose a novel triplet ordinal cross entropy hashing (TOCEH). In TOCEH, to enhance the ability of preserving the ranking orders in different spaces, we establish a tensor graph representing the Euclidean triplet ordinal relationship among RS images and minimize the cross entropy between the probability distribution of the established Euclidean similarity graph and that of the Hamming triplet ordinal relation with the given binary code. During the training process, to avoid the non-deterministic polynomial (NP) hard problem, we utilize a continuous function instead of the discrete encoding process. Furthermore, we design a quantization objective function based on the principle of preserving triplet ordinal relation to minimize the loss caused by the continuous relaxation procedure. The comparative RS image retrieval experiments are conducted on three publicly available datasets, including UC Merced Land Use Dataset (UCMD), SAT-4 and SAT-6. The experimental results show that the proposed TOCEH algorithm outperforms many existing hashing algorithms in RS image retrieval tasks.

A triaxial linear viscoelastic characterization framework for asphalt concrete based on the 2S2P1D model

Asphalt concrete materials are known to exhibit pressure dependence in response to mechanical loading. However, for conventional dense-graded asphalt mixtures, only weak pressure sensitivity was noted in the relaxation spectrum, time-temperature shift factors, and low-temperature moduli. Given these facts, a triaxial linear viscoelastic characterization framework was developed, which consisted of a convenient experimental protocol for the confined dynamic modulus test and a modeling approach based on the 2S2P1D model. In this framework, the same relaxation spectrum and time-temperature equivalence were applied across all different confining conditions, while the pressure dependence was fully assigned to the equilibrium modulus. The resultant prediction errors in dynamic modulus were in general below or comparable to typical test variability. Numerical implementation of the modeling method in the time domain was accomplished via Prony discretization of the continuous relaxation spectrum, and was demonstrated via application to triaxial relaxation and creep data. The model's satisfactory performance suggested that the confining condition had an insignificant impact on the molecular processes occurring in the asphalt phase during relaxation, owing to the low aggregate mobility and thus minimal asphalt flow as restrained by the dense structure. Limitations of the proposed modeling scheme as well as methods available from the literature were revealed lastly upon asphalt concrete materials with unconventional gap and open gradations.