Dynamic Problem Research Articles

Quantum kernels for classifying dynamical singularities in a multiqubit system

Dynamical quantum phase transition is a critical phenomenon involving out-of-equilibrium states and broken symmetries without classical analogy. However, when finite-sized systems are analyzed, dynamical singularities of the rate function can appear, leading to a challenging physical characterization when parameters are changed. Here, we report a quantum support vector machine algorithm that uses quantum Kernels to classify dynamical singularities of the rate function for a multiqubit system. We illustrate our approach using N long-range interacting qubits subjected to an arbitrary magnetic field, which induces a quench dynamics. Inspired by physical arguments, we introduce two different quantum Kernels, one inspired by the ground state manifold and the other based on a single state tomography. Our accuracy and adaptability results show that this quantum dynamical critical problem can be efficiently solved using physically inspiring quantum Kernels. Moreover, we extend our results for the case of time-dependent fields, quantum master equation, and when we increase the number of qubits.

Peasant Displacement and Food Sustainability: The Colombian Case

Social migration affects the development of rural territories in multiple ways, as it poses a threat to food security and hinders the achievement of sustainable development objectives. The purpose of this research is to represent peasant migration and measure its impact on food security, since it creates conditions that alter people’s access to healthy food. Our research question is: What variables can be used to measure the impact of peasant migration on food security? A three-stage model is implemented, which includes (i) the acquisition of knowledge, (ii) the representation of knowledge, and (iii) decision-making. These stages are the basis of the methodology developed by the ARCOSES research group (Méndez A. System Dynamics and Social Problems. Bogotá: Universidad Distrital Francisco José de Caldas, 2012). The model developed to represent peasant migration and its impact on food security has five components. The model representation was applied in 58 typical rural municipalities, observing a potential loss of 30,580,000 tons of food, which amounts to 5% of the national production. Likewise, it was observed that 70% of migrating farmers are part of the economically active population. Colombian governorships should strive towards a greater and more comprehensive development of rural municipalities in order to avoid massive displacement to urban regions, which affects the availability of rural labor, causes poor agricultural production levels and compromises food sustainability. To ensure peasants’ full access to food and their well-being, an assertive intervention should be carried out by the Colombian State.

Numerical investigation of mesoscale multiphase mass transport mechanism in fibrous porous media

At present, the proton exchange membrane fuel cell (PEMFC) is one of the most promising new energy solutions. The structure and material properties of the gas diffusion layer (GDL) are important factors that restrict the efficient water management and structural stability of PEMFCs. The complex mesoscopic fibrous porous structure of the GDL results in complex multiphase flow dynamics problems that have highly nonlinear characteristics. It is difficult to describe the details of mesoscopic multiphase coupled transport dynamics and numerically solve problems in which there is a two-phase flow with a high-density ratio. To solve these problems, a mesoscopic multiphase coupled transport model based on a lattice Boltzmann method and volume-of-fluid (LBM-VOF) model is proposed. Moreover, we also discuss the mechanism of the interaction between the fibrous porous structure and internal multiphase flow. The results obtained illustrate that the proposed method can obtain dynamic details of the flow field for fibrous porous media. The surface wettability of fibres strongly influences both the distribution and stability of liquid water clusters within porous materials. Concurrently, the fibre diameter assumes a pivotal role in governing lateral water diffusion and exclusion efficiency. This work lays a foundation for efficient water and thermal management of PEMFCs.

A dynamic multi-objective optimization evolutionary algorithm with adaptive boosting

Dynamic multi-objective optimization problems (DMOPs) are prevalent in the real world, where the challenge in solving DMOPs is how to track the time-varying Pareto-optimal front (PF) and Pareto-optimal set (PS) quickly and accurately. However, balancing convergence and diversity is challenging as a single strategy can only address a particular type of DMOP. To solve this issue, a dynamic multi-objective optimization evolutionary algorithm with adaptive boosting (AB-DMOEA) is proposed in this paper. In the AB-DMOEA, an adaptive boosting response mechanism will increase the weights of high-performing strategies, including those based on prediction, memory, and diversity, which have been improved and integrated into the mechanism to tackle various problems. Additionally, the dominated solutions reinforcement strategy optimizes the population to ensure the effective operation of the above mechanism. In static optimization, the static optimization boosting mechanism selects the appropriate static multi-objective optimizer for the current problem. AB-DMOEA is compared with the other seven state-of-the-art DMOEAs on 35 benchmark DMOPs. The comprehensive experimental results demonstrate that the overall performance of the AB-DMOEA is superior or comparable to that of the compared algorithms. The proposed AB-DMOEA is also successfully applied to the smart greenhouses problem.

Lifetime Prediction of Permanent Magnet Synchronous Motor in Selective Compliance Assembly Robot Arm Considering Insulation Thermal Aging.

The direct-drive selective compliance assembly robot arm (SCARA) is widely used in high-end manufacturing fields, as it omits the mechanical transmission structures and has the advantages of high positioning accuracy and fast movement speed. However, due to the intensifying dynamic coupling problem of structures in the direct-drive SCARA, the permanent magnet synchronous motors (PMSMs) located at the joints will take on nonstationary loads, which causes excessive internal temperature and reduces the lifetime of PMSMs. To address these issues, the lifetime prediction of PMSMs is studied. The kinematic and dynamic models of the SCARA are established to calculate the torque curve required by the PMSM in specific typical motion tasks. Additionally, considering thermal stress as the main factor affecting lifetime, accelerated degradation tests are conducted on insulation material. Then, the reliability function of the PMSM is formulated based on the accelerated degradation model. Based on the parameters and working conditions of the PMSM, the temperature field distribution is obtained through simulation. The maximum temperature is used as the reference temperature to conduct reliability evaluation and lifetime prediction of the PMSM. The research results show that for a typical point-to-point task, the PMSM can run for 102,623 h while achieving the reliability requirement of 0.99.

A dynamic multi-objective evolutionary algorithm based on Mahalanobis distance and intra-cluster individual correlation rectification

Responding quickly and accurately to environmental changes is a challenge in addressing dynamic multi-objective optimization problems (DMOPs). Although many dynamic multi-objective evolutionary algorithms (DMOEAs) have demonstrated impressive performance, there is still room for improvement in accurately predicting population behavior. To address this limitation, this paper proposes a prediction strategy based on Mahalanobis distance and intra-cluster individual correlation rectification (MCIR) to deal with DMOPs. First, a manifold clustering method is used to partition the Pareto set of the population into subpopulations, in which individuals with similar movement trends are grouped into clusters. Second, the Mahalanobis distance is introduced to systematically measure the relationships between clusters in adjacent environments. Time series models are established for each cluster center to predict their positions in the neighboring environment. On this basis, the movement characteristics of individuals within clusters are further rectified by calculating the correlation between intra-cluster individuals and the cluster center, facilitating more accurate tracking of the changing Pareto set/Pareto front. Finally, Gaussian noise is introduced to ensure the diversity of new individuals. The effectiveness of the MCIR algorithm is demonstrated by comparing it with four DMOEAs using 18 test instances. Experimental results confirm that MCIR holds great promise in addressing DMOPs.

Dynamic Robust Optimization Method Based on Two-Stage Evaluation and Its Application in Optimal Scheduling of Integrated Energy System

As an emerging energy allocation method, shared energy storage devices play an important role in modern power systems. At the same time, with the continuous improvement in renewable energy penetration, modern power systems are facing more uncertainties from the source side. Therefore, a robust optimization algorithm that considers both shared energy storage devices and source-side uncertainty is needed. Responding to the above issues, this paper first establishes an optimal model of a regional integrated energy system with shared energy storage. Secondly, the uncertainty problem is transformed into a dynamic optimization problem with time-varying parameters, and a modified robust optimization over time algorithm combined with scenario analysis is proposed to solve such optimization problems. Finally, an optimal scheduling objective function with the lowest operating cost of the system as the optimization objective is established. In the experimental part, this paper first establishes a dynamic benchmark test function to verify the validity of proposed method. Secondly, the multi-mode actual verification of the proposed algorithm is carried out through a regional integrated energy system. The simulation results show that the modified robust optimization over time (ROOT) algorithm could find solutions with better robustness in the same dynamic environment based on the two-stage evaluation strategy. Compared with the existing algorithms, the average fitness and survival time of the robust solution obtained by the modified ROOT algorithm are increased by 94.41% and 179.78%. At the same time, the operating cost of the system is reduced by 11.65% by using the combined optimization scheduling method proposed in this paper.

DpEA: A dual-population evolutionary algorithm for dynamic constrained multiobjective optimization

Dynamic Constrained Multiobjective Optimization Problems (DCMOPs) are very difficult to solve because both of the objectives and constraints may change over time. The existing approaches for solving DCMOPs mainly develop dynamic response techniques and constraint handling techniques. But they do not focus on the search capability of the static optimizer in each environment, which ignores the intrinsic requirement of quickly locating Pareto-optimal Front (PF) in each environment when solving DCMOPs. To this end, this paper proposes a dual-population evolutionary algorithm for solving DCMOPs, called as DpEA, which maintains a population without considering constraints (called UP) for exploration and a population with considering constraints (called CP) for exploitation in each environment. In each iteration of a new environment, UP firstly adopts a stratified mutation strategy (SMS) and a dominated solution repairment strategy (DSR) to enhance the exploration ability of finding promising regions where the PF may reside. SMS uses solutions from different nondominated fronts to generate offspring, while DSR repairs the single-optimal variables of the dominated solutions by sampling from the distribution of those variables of nondominated solutions. Secondly, this paper uses an adaptive offspring ratio adjustment strategy to control the offspring number generated by UP and CP according to the normalized Hausdorff distance between nondominated solution sets from the two latest generations of UP. This strategy is helpful to balance the intensity between exploration and exploitation and thereby ensures efficient search. Experimental results on CEC 2023 DCF test suite show that DpEA has a superior performance over six state-of-the-art algorithms.

Large-scale dynamic surgical scheduling under uncertainty by hierarchical reinforcement learning

Dynamic surgical scheduling within a workday is a complicated decision-making process. The critical challenge is that the actual duration of surgery and the arrival process of emergency patients are uncertain and unknown in advance. In this work, we propose a two-level dynamic scheduling framework based on hierarchical reinforcement learning to solve dynamic surgical scheduling problems considering both elective and emergency patients. Specifically, with the realisation of uncertainty, the upper-level agent (UA) dynamically decides whether to trigger rescheduling to optimise the workday total cost. The lower-level agent (LA) aims at obtaining subscheduling solutions when rescheduling is triggered. The subproblem at the LA can be formulated as a mixed integer programming model, which can be generalised to unrelated parallel machine scheduling with machine eligibility restrictions and sequence- and machine-dependent setup times. Such problems can be solved in small-scale cases and suffers the combinatorial explosion in large scale cases. To address this issue, we propose a heuristic method that is built upon deep reinforcement learning to obtain high-quality solutions. We conduct extensive simulation experiments with real data to test the effective of our framework. The results for different scenarios show that our proposed framework outperforms existing methods in terms of overall performance and has strong generalisation ability.

Second order hemivariational inequality driven by evolution differential inclusion to a dynamic thermoviscoelastic contact problem

In this paper we study an abstract system which consists of a hyperbolic hemivariational inequality coupled with a differential evolution inclusion involving a history-dependent operator in Banach spaces. A hybrid iterative system corresponding to the hemivariational inequality is introduced. Combining the Rothe method, a feedback iterative technique, and a surjectivity result for pseudomonotone operators, we establish existence and a priori estimate for solutions to an approximate problem. Next, through a limiting procedure for solutions of the hybrid iterative system, we show the existence of a mild solution to the original problem. Finally, we apply the main results to a dynamic contact problem in thermoviscoelasticity.

Dynamic analysis with point-masses of perforated pallet rack structural members by means of the Generalized Beam Theory

This paper presents two different formulations for introducing point-masses into a dynamic problem using the Generalized Beam Theory (GBT) method. The first one implies placing a point-mass at a beam-node (with or without eccentricities) while the other implies placing a point-mass at a cross-section node. In order to evaluate the accuracy of such formulations, different modal analyses of members have been performed using GBT beam elements, shell elements and classical beam elements. The values of natural modal frequencies obtained through different models have been successfully compared. The results of various harmonic analyses are also presented. Some of the studied structural members include perforations. Finally, the influence of GBT modes and perforations when using point-masses is discussed.

Non-degenerate necessary conditions for non-convex differential inclusions

This paper concerns dynamic optimization problems with pathwise state constraints, in which the dynamics are formulated as a differential inclusion. First order necessary conditions of optimality are available for these problems. Foremost among these conditions is the Euler Lagrange inclusion (combined with a transversality and Weierstrass conditions), which improves on earlier conditions such as Clarke's Hamiltonian inclusion. The most recent version of the Euler Lagrange inclusion (which we call the standard Euler Lagrange condition) has been validated under unrestrictive conditions, which allow the velocity sets of the differential inclusion to be non-convex. If the initial state is fixed and located in the boundary of the state constraint set then the Euler Lagrange inclusion conveys no information about minimizers. This is the degeneracy phenomenon for state constrained dynamic optimization. The non-degenerate necessary conditions literature provides additional conditions, to supplement the standard necessary conditions. These typically identify some properties of the boundary values of the maximized Hamiltonian which ensure non-triviality of the necessary conditions, under a simple controllability hypothesis. Non-degenerate conditions, incorporating the Euler Lagrange inclusion are currently available only under the hypothesis that the velocity sets are convex. Using new perturbation techniques, we derive a non-degenerate Euler Lagrange condition that is valid for non-convex velocity sets. These conditions bring into line non-degenerate optimality conditions for differential inclusion problems with those for problems involving controlled differential equations which have previously been validated for non-convex velocity sets.

3‐D impulse‐based level‐set method for granular flow modeling

AbstractWe explore the viability of modeling dynamic problems with a new formulation of an impulse‐based Level‐Set DEM (LS‐DEM). The new formulation is stable, fast, and energy conservative. However, it can be numerically stiff when the assembly has substantial mass differences between particles. We also demonstrate the feasibility of modeling deformable structures in a rigid body framework and propose several enhancements to improve the convergence of collision resolution, including a hybrid time integration scheme to separately handle at rest contacts and dynamic collisions. Finally, we extend the impulse‐based LS‐DEM to include arbitrarily shaped topographic surfaces and exploit its algorithmic advantages to demonstrate the feasibility of modeling realistic behavior of granular flows. The new formulation significantly improves the performance of dynamic simulations by allowing larger time steps, which is advantageous for observing the full development of physical phenomena such as rock avalanches, which we present as an illustrative example.

Molecular dynamics simulation of argon isochoric transition to supercritical state

AbstractThe effect of the initial atoms distribution on the molecular dynamics (MD) simulation of a model atomic fluid (argon) is investigated for the case of the isochoric phase transition to the supercritical state. In particular, the case of uniformly distributed atoms in the simulation domain is compared with the case of separated liquid and vapor atoms. The sensitivity of simulations to asymmetric nanoscale perturbations in the boundary is also studied. Despite its high computational cost, the MD approach has the potential to successfully address long‐standing problems in computational fluid dynamics (CFD), especially those associated with mathematical singularities, such as contact angles, vortices, phase transitions and so forth. Unlike conventional CFD simulations, where the initial condition is the pressure or velocity distribution in the simulation domain, MD simulations also require the initial position of each molecule. Thus, it is important to understand whether a judicious choice of the initial distribution of molecules can reduce the overall computation time of the simulation. The evolution of the model fluid system during the phase transition was simulated using a Lennard‐Jones interatomic potential, corrected with the Lorentz–Berthelot mixing rule for the interactions with the solid walls. The system was allowed to relax until equilibrium, and then a Heaviside temperature step was applied to the wall to bring the system to supercritical conditions. Results show the initial choice of the atoms distribution can significantly affect the computational time, while the effect of asymmetric perturbations on the boundary is negligible.

A Metaheuristic Framework with Experience Reuse for Dynamic Multi-Objective Big Data Optimization

Dynamic multi-objective big data optimization problems (DMBDOPs) are challenging because of the difficulty of dealing with large-scale decision variables and continuous problem changes. In contrast to classical multi-objective optimization problems, DMBDOPs are still not intensively explored by researchers in the optimization field. At the same time, there is lacking a software framework to provide algorithmic examples to solve DMBDOPs and categorize benchmarks for relevant studies. This paper presents a metaheuristic software framework for DMBDOPs to remedy these issues. The proposed framework has a lightweight architecture and a decoupled design between modules, ensuring that the framework is easy to use and has enough flexibility to be extended and modified. Specifically, the framework now integrates four basic dynamic metaheuristic algorithms, eight test suites of different types of optimization problems, as well as some performance indicators and data visualization tools. In addition, we have proposed an experience reuse method, speeding up the algorithm’s convergence. Moreover, we have implemented parallel computing with Apache Spark to enhance computing efficiency. In the experiments, algorithms integrated into the framework are tested on the test suites for DMBDOPs on an Apache Hadoop cluster with three nodes. The experience reuse method is compared to two restart strategies for dynamic metaheuristics.

Generic load regulation strategy for enhancing energy efficiency of chiller plants

In many chiller plants, high coefficient of performance (COP) is only achieved at a few favorable part load ratios (PLRs), while the COP is low at many other non-favorable PLRs. To address this issue, this study proposes a generic load regulation strategy that aims to maintain chiller plants operating at high COP, particularly under non-favorable PLRs. This is achieved by incorporating thermal energy storage (TES) units and timely optimizing the charging and discharging power of the integrated TES units. The optimal charging and discharging power is determined by solving a dynamic optimization problem, taking into account the performance constraints of the TES units and the chiller plants. To provide an overview of the energy-saving potential of the proposed strategy, a comprehensive analysis was conducted, considering factors such as building load profiles, COP/PLR curves of chillers, and attributes of the TES units. The analysis revealed that the proposed load regulation strategy has the potential to achieve energy savings ranging from 5.7% to 10.8% for chiller plants with poor COPs under unfavorable PLRs, particularly in buildings with significant load variations.

Price regulation, network externality, and product innovation strategies: A dynamic analysis

AbstractFor many high‐tech and Internet‐related products, consumers' utility depends partly on the scale of user groups, which is called network externality. This phenomenon plays a crucial role in shaping firms' innovation strategies, especially in markets with price regulation. This paper aims to investigate a monopolist's dynamic product innovation problem in a price‐regulated market exhibiting network externality. We identify the sufficient conditions guaranteeing the existence of optimal steady‐state equilibrium. Our analysis mainly shows the following: (i) the product quality and network size move in opposite directions along the path to the steady‐state equilibrium; (ii) the equilibrium result of product innovation increases with the regulated price but decreases with the intensity of network externality; (iii) the social‐welfare maximizing path of product innovation can be replicated by a dynamic price regulation regime, involving a premium on quality and a premium or a penalty on network size. Numerical experiments are performed to characterize the dynamic patterns of product innovation. We find that firms with high brand power prefer adopting mild product innovation strategy while for firms with low brand power, almost constant high‐quality strategy is better.

A non-linear stress–strain relationship for soil and rock

While many employ a hyperbolic stress–strain relationship for soils, it is known that such a relationship is accurate over the small-strain range as encountered in earthquake and soil dynamics problems. For large strains, a relationship with different input parameters is needed, as is required for finite-element analyses of large-deformation behaviour. These separate characterisations do not carry over into the other application. Here, a proposed power relationship is presented that was developed to characterise the triaxial test stress–strain behaviour of cohesionless material from lubricated or ‘frictionless’ cap and base tests (144 tests) covering a range in the natural variation in particle size, particle shape and surface roughness, over low to high confining pressure. This relationship covers the strain range from 10−6 to soil failure. To date, it has been successfully used in laterally loaded pile response characterisation (the strain wedge model) and shallow-foundation load–settlement–bearing capacity response. Most recently, it has been extended to assess the behaviour of rock-like material (caliche). The relationship and its comparison with the hyperbolic relationship for large strain and the shear modulus reduction curve for seismic behaviour are presented.

Dynamic Task Allocation for Heterogeneous Multi-UAVs in Uncertain Environments Based on 4DI-GWO Algorithm

As the missions and environments of unmanned aerial vehicles (UAVs) become increasingly complex in both space and time, it is essential to investigate the dynamic task assignment problem of heterogeneous multi-UAVs aiming at ground targets in an uncertain environment. Considering that most of these existing tasking methods are limited to static allocation in a deterministic environment, this paper firstly constructs the fuzzy multiconstraint programming model for heterogeneous multi-UAV dynamic task assignment based on binary interval theory, taking into account the effects of uncertain factors like target location information, mission execution time, and the survival probability of UAVs. Then, the dynamic task allocation strategy is designed, consisting of two components: dynamic time slice setting and the four-dimensional information grey wolf optimization (4DI-GWO) algorithm. The dynamic time slices create the dynamic adjustment of solving frequency and effect, and the 4DI-GWO algorithm is improved by designing the four-dimensional information strategy that expands population diversity and enhances global search capability and other strategies. The numerical analysis shows that the proposed strategy can effectively solve the dynamic task assignment problem of heterogeneous multi-UAVs under an uncertain environment, and the optimization of fitness values demonstrates improvements of 5~30% in comparison with other optimization algorithms.

Given a wingspan, which windplane design maximizes power?

Windplanes (i.e. Fly-Gen airborne wind energy systems) harvest wind power via the turbines placed on the tethered wing, which flies crosswind trajectories. In this paper, the optimal design of windplanes is investigated with simplified models, enabling an intuitive understanding of their physical characteristics. The windplane is then idealized as a point mass flying circular fully crosswind trajectories. If the gravity is neglected, the dynamic problem is axial symmetric and the solution is steady. The generated power can be expressed in non-dimensional form by normalizing it with the wind power passing by a disk with radius the wingspan. Since the reference area is taken to be a function of just the wingspan, looking for the design which maximizes this power coefficient addresses the question ”Given a wingspan, which design maximizes power?”. This is different from the literature, where the design problem is formulated per wing area and not per wingspan. The optimal designs have a finite aspect ratio and operate at the maximum lift-to-drag ratio of the airfoil. Airfoils maximizing the lift-to-drag ratio are then optimal for windplanes. If gravity is included in the model, gravitational potential energy is being exchanged over one revolution. Since this exchange comes with an associated efficiency, the plane mass and the related trajectory radius are designed to reduce the potential energy fluctuating over the loop. However, for decreasing turning radii, the available wind power decreases because the windplane sweeps a lower area. For these two conflicting reasons, the optimal mass is finite.