Hard Constraints Research Articles

Optimal control of a dengue model with cross-immunity

Mathematical modelling of a dengue epidemic with two serotypes including a temporary cross-immunity yields a nonlinear system consisting of ordinary differential equations (ODEs). We investigate an optimal control problem, where the integral of the infected humans is minimised within a time interval. The controls represent human actions to decrease the number of mosquitos in the model. An integral constraint is added, which takes a limitation on the sum of the human actions into account. On the one hand, we derive and apply a direct approach to solve the optimal control problem. Therein, a discretisation of the controls is constructed using spline interpolation in time. Consequently, a finite-dimensional constrained minimisation problem can be solved. On the other hand, we employ an indirect approach, where necessary conditions for an optimal solution are considered. This technique yields a multipoint boundary value problem of a larger system of ODEs including adjoint equations. We present results of numerical computations, where the two methods are compared.

An optimization approach to establish dynamical equivalence for soft and rigid impact models

This paper studies a computational approach aimed at establishing equivalent dynamical responses within oscillatory impacting systems subject to soft and rigid constraints. The proposed method incorporates an adaptive differential evolution algorithm with the Metropolis criterion to determine the stiffness and damping parameters of the soft constraint for a prescribed coefficient of restitution governing the rigid constraint. The proposed algorithm aims to establish an equivalent dynamical response of the two models based on constraints regarding energy dissipation and contact time duration. Upon examining the dynamical responses of the two impact cases, they exhibit nearly identical outcomes in the two-parameter bifurcation diagrams when subjected to a large restitution coefficient. However, discrepancies arise between the results of the two models when the restitution coefficient is low. Detailed numerical tests, conducted using the proposed method, demonstrate enhanced effectiveness compared to previous techniques, such as the prediction formulas for the different related soft impact model outlined by Okolewski and Blazejczyk-Okolewska [Chaos 31(8), 083110 (2021)]. This method not only finds application in experimentally identifying the physical properties of an impact surface but also provides convenience in employing soft models within impacting systems, which could then avoid potential inaccuracies in handling discontinuities by some integrator during velocity jumps before and after impacts.

A Precise Temperature Control Method for Lithium-ion Battery Pack based on the Nonlinear Model Predictive Control Algorithm

Abstract To utilize the maximum performance of the battery while ensuring its thermal safety, a battery thermal management system is used to control the battery maximum temperature within a safe range. This paper centres on the establishment of a temperature prediction model and the development of the nonlinear-based model predictive control (MPC) strategy. First, to address the need of predicting battery temperature, this paper develops a distributed parameter thermal resistance model to predict battery temperature quickly and accurately. Secondly, the open-loop formulation of the nonlinear-based MPC is derived based on the established state space equations. Then the soft and hard constraints of the model are established based on the actual current conditions, pump conditions, temperature difference and temperature rise indexes, so as to establish the objective function of the MPC algorithm. Finally, the established temperature nonlinear MPC algorithm is embedded on the board and the hardware platform of battery liquid cooling system is established. The experiment test result shows that the maximum error of temperature control is less than 0.1°C, and the effectiveness of the temperature control strategy of lithium-ion battery is verified through experiments.

Unified Spatial Clustering of Territory Risk to Uncover Impact of COVID-19 Pandemic on Major Coverages of Auto Insurance

This research delves into the fusion of spatial clustering and predictive modeling within auto insurance data analytics. The primary focus of this research is on addressing challenges stemming from the dynamic nature of spatial patterns in multiple accident year claim data, by using spatially constrained clustering. The spatially constrained clustering is implemented under hierarchical clustering with a soft contiguity constraint. It is highly desirable for insurance companies and insurance regulators to be able to make meaningful comparisons of loss patterns obtained from multiple reporting years that summarize multiple accident year loss metrics. By integrating spatial clustering techniques, the study not only improves the credibility of predictive models but also introduces a strategic dimension reduction method that concurrently enhances the interpretability of predictive models used. The evolving nature of spatial patterns over time poses a significant barrier to a better understanding of complex insurance systems as these patterns transform due to various factors. While spatial clustering effectively identifies regions with similar loss data characteristics, maintaining up-to-date clusters is an ongoing challenge. This research underscores the importance of studying spatial patterns of auto insurance claim data across major insurance coverage types, including Accident Benefits (AB), Collision (CL), and Third-Party Liability (TPL). The research offers regulators valuable insights into distinct risk profiles associated with different coverage categories and territories. By leveraging spatial loss data from pre-pandemic and pandemic periods, this study also aims to uncover the impact of the COVID-19 pandemic on auto insurance claims of major coverage types. From this perspective, we observe a statistically significant increase in insurance premiums for CL coverage after the pandemic. The proposed unified spatial clustering method incorporates a relabeling strategy to standardize comparisons across different accident years, contributing to a more robust understanding of the pandemic effects on auto insurance claims. This innovative approach has the potential to significantly influence data visualization and pattern recognition, thereby improving the reliability and interpretability of clustering methods.

Convex Approach to Real-Time Multiphase Trajectory Optimization for Urban Air Mobility

Electric vertical takeoff and landing technology has emerged as a promising solution to alleviate ground transportation congestion. However, the limited capacity of onboard batteries enforces hard time constraints for vehicle operations in a complex urban environment. Therefore, a constrained, real-time trajectory optimization method is necessary to enable safe and energy-efficient vehicle flight. Unfortunately, most existing trajectory optimization methods suffer from low computational efficiency, unpredictable convergence processes, and strong dependence on a good initial trajectory. In this paper, we employ a successive convex programming approach to solve the multiphase minimum-energy-cost electric vertical takeoff and landing vehicle trajectory optimization problem for urban air mobility applications. The main contribution is the development and validation of two novel convexification methods that find approximate optimal solutions to the multiphase nonlinear trajectory optimization problem in real time by solving a sequence of convex subproblems. Specifically, the first method transforms the original nonlinear problem into a sequence of second-order cone programming problems through a convenient change of variables and lossless convexification, while the second approach achieves a similar goal without the need for control convexification. The resulting convex subproblems can be solved reliably in real time by advanced interior point methods. The proposed methods are demonstrated through numerical simulations of two different urban air mobility scenarios and compared with the solution obtained from GPOPS-II, a state-of-the-art general-purpose optimal control solver. Our proposed sequential convex programming methods can obtain near-optimal solutions with faster computational speed than GPOPS-II.

Multi-Agent System Based Cooperative Control for Speed Convergence of Virtually Coupled Train Formation.

This paper investigates the problem of spacing control between adjacent trains in train formation and proposes a distributed train-formation speed-convergence cooperative-control algorithm based on barrier Lyapunov function. Considering practical limitations such as communication distance and bandwidth constraints during operation, not all trains can directly communicate with the leader and obtain the expected trajectory it sends, making it difficult to maintain formation consistency as per the predetermined ideal state. Furthermore, to address the challenge of unknown external disturbances encountered by trains during operation, this paper designs a distributed observer deployed on each train in the formation. This observer can estimate and dynamically compensate for unknown reference trajectories and disturbances solely based on the states of adjacent trains. Additionally, to ensure that the spacing between adjacent trains remains within a predefined range, a safety hard constraint, this paper encodes the spacing hard constraint using barrier Lyapunov function. By integrating nonlinear adaptive control theory to handle model parameter uncertainties, a barrier Lyapunov function-based adaptive control method is proposed, which enables all trains to track the reference trajectory while ensuring that the spacing between them remains within the preset interval, therefore guaranteeing the asymptotic stability of the closed-loop system. Finally, a practical example using data from the Guangzhou Metro Line 22, specifically the route from Shiguang Road Station to Chentougang Station over three stations and two sections, is utilized to validate the effectiveness and robustness of the proposed algorithm.

Physics-constrained machine learning for electrodynamics without gauge ambiguity based on Fourier transformed Maxwell’s equations

We utilize a Fourier transformation-based representation of Maxwell’s equations to develop physics-constrained neural networks for electrodynamics without gauge ambiguity, which we label the Fourier–Helmholtz–Maxwell neural operator method. In this approach, both of Gauss’s laws and Faraday’s law are built in as hard constraints, as well as the longitudinal component of Ampère–Maxwell in Fourier space, assuming the continuity equation. An encoder–decoder network acts as a solution operator for the transverse components of the Fourier transformed vector potential, A^⊥(k,t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{{\ extbf {A}}}_\\perp ({\ extbf {k}}, t)$$\\end{document}, whose two degrees of freedom are used to predict the electromagnetic fields. This method was tested on two electron beam simulations. Among the models investigated, it was found that a U-Net architecture exhibited the best performance as it trained quicker, was more accurate and generalized better than the other architectures examined. We demonstrate that our approach is useful for solving Maxwell’s equations for the electromagnetic fields generated by intense relativistic charged particle beams and that it generalizes well to unseen test data, while being orders of magnitude quicker than conventional simulations. We show that the model can be re-trained to make highly accurate predictions in as few as 20 epochs on a previously unseen data set.

A mixed finite element method for the forward problem of electrical impedance tomography with the shunt model

We propose a mixed finite element method for the forward problem of electrical impedance tomography with the shunt model. The method is based on a constrained minimization formulation in terms of the current density, where parts of the Lagrange multiplier are interpreted as the voltages on the electrodes. We justify the well-posedness of this continuous formulation, estimate the regularity of its solution, and use Raviart–Thomas elements for its discretization. The resulting mixed method is then proved to be stable, and converge especially with respect to the voltages on the electrodes. Simulation on a 2D model also gives consistent results.

Just-in-time scheduling of unrelated parallel machines with family setups and soft time window constraints

ABSTRACT This study addresses an unrelated parallel machine scheduling problem with family setups and soft time windows, which includes considerations for machine eligibility. The objective is to minimize the total weighted tardiness and earliness, and to maximize the number of Just-in-Time jobs. Four different metaheuristic algorithms are compared to determine which type – single-point (simulated annealing), population-based evolutionary (artificial immune system, genetic algorithm), or swarm intelligence algorithms (ant colony optimization) – is more effective in solving this problem. Two strategies, namely penalty and repair, are proposed to handle precedence constraints. Experimental results demonstrate that ant colony optimization with local search which employs the repair strategy, as a swarm intelligence-based algorithm outperforms its rivals in terms of objective function values and robustness. The performance of this algorithm has shown an improvement in objective function values ranging from 2.12% to 8.52% on average, with a relative percentage deviation of 10.35.

Reducing the lateral dose penumbra in IMPT by incorporating transmission pencil beams

ObjectiveIn intensity-modulated proton therapy (IMPT), Bragg peaks result in steep distal dose fall-offs, while the lateral IMPT dose fall-off is often less steep than in photon therapy. High-energy pristine transmission (‘shoot through’) pencil beams have no Bragg peak in the patient, but show a sharp lateral penumbra at the target level. We investigated whether combining Bragg peaks with Transmission pencil beams (‘IMPT&TPB’) could improve head-and-neck plans by exploiting the steep lateral dose fall-off of transmission pencil beams. ApproachOur system for automated multi-criteria IMPT plan optimisation was extended for combined optimisation of BPs and TPBs. The system generates for each patient a Pareto-optimal plan using a generic ‘wish-list’ with prioritised planning objectives and hard constraints. For eight nasopharynx cancer patients (NPC) and eight oropharynx cancer (OPC) patients, the IMPT&TPB plan was compared to the competing conventional IMPT plan with only Bragg peaks, which was generated with the same optimiser, but without transmission pencil beams. Main resultsClinical OAR and target constraints were met in all plans. By allowing transmission pencil beams in the optimisation, on average 14 of the 25 investigated OAR plan parameters significantly improved for NPC, and 9 of the 17 for OPC, while only one OPC parameter showed small but significant deterioration. Non-significant differences were found in the remaining parameters. In NPC, cochlea Dmean reduced by up to 17.5 Gy and optic nerve D2% by up to 11.1 Gy. ConclusionCompared to IMPT, IMPT&TPB resulted in comparable target coverage with overall superior OAR sparing, the latter originating from steeper dose fall-offs close to OARs.

Continuous-time nonlinear model predictive control based on Pontryagin Minimum Principle and penalty functions

Pontryagin's Minimum Principle (PMP) is a powerful tool for solving Nonlinear Model Predictive Control problems (NMPC), enabling the handling of time-varying input constraints and cost functions. However, applying PMP encounters challenges when state constraints must be satisfied. This arises because the optimal trajectory often requires a blend of unconstrained and constrained arcs with unknown junction points. To address this issue, relaxation methods are frequently explored, where state constraints are replaced with penalty functions. The contributions of this paper are as follows. First, a method of penalty functions allowing for coping with soft state constraints is examined. We prove the recursive feasibility of this method and demonstrate its efficiency in a numerical example. Second, the finite-time practical stability for the optimal reference tracking NMPC problem is addressed. By appropriately choosing the terminal cost, one can guarantee the convergence of the state vector to a predefined neighbourhood of the target state.

A goal-conditioned policy search method with multi-timescale value function tuning

PurposeCurrent reinforcement learning (RL) algorithms are facing issues such as low learning efficiency and poor generalization performance, which significantly limit their practical application in real robots. This paper aims to adopt a hybrid model-based and model-free policy search method with multi-timescale value function tuning, aiming to allow robots to learn complex motion planning skills in multi-goal and multi-constraint environments with a few interactions.Design/methodology/approachA goal-conditioned model-based and model-free search method with multi-timescale value function tuning is proposed in this paper. First, the authors construct a multi-goal, multi-constrained policy optimization approach that fuses model-based policy optimization with goal-conditioned, model-free learning. Soft constraints on states and controls are applied to ensure fast and stable policy iteration. Second, an uncertainty-aware multi-timescale value function learning method is proposed, which constructs a multi-timescale value function network and adaptively chooses the value function planning timescales according to the value prediction uncertainty. It implicitly reduces the value representation complexity and improves the generalization performance of the policy.FindingsThe algorithm enables physical robots to learn generalized skills in real-world environments through a handful of trials. The simulation and experimental results show that the algorithm outperforms other relevant model-based and model-free RL algorithms.Originality/valueThis paper combines goal-conditioned RL and the model predictive path integral method into a unified model-based policy search framework, which improves the learning efficiency and policy optimality of motor skill learning in multi-goal and multi-constrained environments. An uncertainty-aware multi-timescale value function learning and selection method is proposed to overcome long horizon problems, improve optimal policy resolution and therefore enhance the generalization ability of goal-conditioned RL.

A bankszabályozás lehetőségei és korlátai az endogén pénzelmélet keretében

The article questions whether the current system of bank regulation can guarantee that banks are subject to a hard budget constraint. We use the framework of post-­Keynesian endogenous money theory. Banks deposit loans in companies’ bank accounts, and no external source is needed for the transaction, so banks can in principle create an unlimited amount of money if there is a demand for credit. However, banks’ ability to create money is limited by a number of factors. Using János Kornai’s concept of a soft budget constraint we analyze the factors that cause inherently soft budget constraints for banks. We point out that neither monetary policy, nor the profit goals of banks, nor the banks’ internal risk management practices would guarantee that banks face a hard budget constraint. This must be imposed on them by an external factor, the banking regulation. However, the current system of banking regulation is not well suited to do this, so the soft budget constraint is inherent to banking. This contributes to the fact that banking crises are natural part of the financial system.

Optimizing Inventory and Pricing for Substitute Products with Soft Supply Constraints

This paper presents a profit optimization model for substitute products in a competitive, time-sensitive market with scarcity and shifting user preferences. The model maximizes profit, considering production costs and inventory maintenance. It uses a discrete choice model to represent demand, sensitivity to price, availability, and changing preferences. A two-phase PSO-type metaheuristic solution tackles the nonlinear, recursive model, efficiently managing inventories and evolving consumer preferences. The model integrates production decisions, inventories, and sales prices, considering scarcity conditions and user preferences. It uses a multinomial logit for the consumers’ demand function with soft exogenous constraints, which influence utility and change consumption preferences and choices. This research offers a tool for companies to manage stock, production, and pricing in a context where goods are substitutes, providing a new perspective on business strategy.

A holistic approach to multi-depot electric bus scheduling for energy saving considering limitations in charging facilities

Under “double carbon” policies, the shift towards bus electrification is unavoidable but is hindered by operational challenges due to electric buses’ limited range. These challenges are intensified by heterogenous bus fleets, inadequate charging facilities, and depot limitations. This paper introduces a pragmatic approach to address the multi-depot electric bus scheduling problem, comprehensively addressing all aforementioned complexities. A tailored adaptive large neighborhood search (ALNS) is designed to solve the problem, wherein several ingenious accelerating techniques are integrated to generate a high-quality solution within an acceptance time frame, including: 1) relaxation of hard constraints to expedite iterations; 2) specialized operators designed to enhance the diversity of neighborhood spaces; 3) the meticulous setting of operator scores to prioritize operators with higher efficiency. A small-scale case study is conducted to compare the tailored ALNS with the commercial solver. The results substantiate the superior performance of the proposed algorithm and the significant role of these accelerating techniques. Furthermore, the algorithm presents its practical applicability in large-scale scenarios. The findings reveal that the proposed approach reduces the fleet size by 35 vehicles and concurrently achieves a significant 13.61 % reduction in electricity consumption, which provides a holistic solution to real-world operational challenges and offers recommendations for operators.

Incorporating background knowledge in symbolic regression using a computer algebra system

Symbolic regression (SR) can generate interpretable, concise expressions that fit a given dataset, allowing for more human understanding of the structure than black-box approaches. The addition of background knowledge (in the form of symbolic mathematical constraints) allows for the generation of expressions that are meaningful with respect to theory while also being consistent with data. We specifically examine the addition of constraints to traditional genetic algorithm (GA) based SR (PySR) as well as a Markov-chain Monte Carlo (MCMC) based Bayesian SR architecture (Bayesian Machine Scientist), and apply these to rediscovering adsorption equations from experimental, historical datasets. We find that, while hard constraints prevent GA and MCMC SR from searching, soft constraints can lead to improved performance both in terms of search effectiveness and model meaningfulness, with computational costs increasing by about an order of magnitude. If the constraints do not correlate well with the dataset or expected models, they can hinder the search of expressions. We find incorporating these constraints in Bayesian SR (as the Bayesian prior) is better than by modifying the fitness function in the GA.

Chemical reaction inspired approach for routing problems with hard time constraints

ABSTRACT One of the most common issues in logistics and transportation planning is the vehicle routing problem. The objective is to find minimum cost-vehicle routes for serving a set of dispersed customers with deterministic demands while satisfying some constraints. In this paper, we focus on two main constraints, which are vehicle capacity and time windows for customers. We propose to tackle this NP-hard problem with a bio-inspired approach based on a hybridization of Chemical Reaction Optimization and local search method. The solving process of our approach mimics the chemical reactions between molecules to attain their stability with lowest energy. For more diversification of the search space, we involved in the initialization stage a local search method based on greedy adaptive procedure. The performances of our hybrid approach are assessed on the base of various benchmark instances. Simulation results show the good performances and the efficiency of the proposed approach.

Motion Coordination of Multiple Autonomous Mobile Robots under Hard and Soft Constraints

This paper presents a distributed approach to the motion control problem for a platoon of unicycle robots moving through an unknown environment filled with static obstacles under multiple hard and soft operational constraints. Each robot has an onboard camera to determine its relative position in relation to its predecessor and proximity sensors to detect and avoid nearby obstascles. Moreover, no robot apart from the leader can independently localize itself within the given workspace. To overcome this limitation, we propose a novel distributed control protocol for each robot of the fleet, utilizing the Adaptive Performance Control (APC) methodology. By utilizing the APC approach to address input constraints via the on-line modification of the error specifications, we ensure that each follower effectively tracks its predecessor without encountering collisions with obstacles, while simultaneously maintaining visual contact with its preceding robot, thus ensuring the inter-robot visual connectivity. Finally, extensive simulation results are presented to demonstrate the effectiveness of the presented control system along with a real-time experiment conducted on an actual robotic system to validate the feasibility of the proposed approach in real-world scenarios.

Soft budget constraints and technological innovations: evidence from China

Soft budget constraints and technological innovations: evidence from China

Theory guided Lagrange programming neural network for subsurface flow problems

A deep learning model can perform efficient uncertainty quantification (UQ) for reservoir flow with uncertain model parameters, but usually requires large amounts of training data to ensure accuracy. However, the cost of obtaining large amounts of data is prohibitive, and the performance will deteriorate if sufficient training data is lacking. Alternatively, more interpretable neural networks with embedded physical laws have recently been used to solve partial differential equations as well as to solve UQ problems. This approach has received a lot of attention due to its low data volume requirements and its adherence to the laws of physics during the training process. In this paper, we propose a theory-guided framework based on a bilevel programming model with hard constraints to embed physical meaning in the model. Theory guided Lagrange programming neural network (TGLPNN) combines the method of Lagrange programming neural network approach where physical laws such as stochastic partial differential equations and boundary conditions are incorporated into the training process of a convolutional neural network. At the same time, the upper-level variables are iteratively optimized. The method based on Lagrange programming neural network inherently embeds physical laws in the network. Practical applications have shown that TGLPNN can provide higher prediction accuracy compared to state-of-the-art physics-driven methods and improved efficiency compared to numerical methods.