Optimal Theory Research Articles

An Improved Longitudinal Driving Car-Following System Considering the Safe Time Domain Strategy.

Car-following models are crucial in adaptive cruise control systems, making them essential for developing intelligent transportation systems. This study investigates the characteristics of high-speed traffic flow by analyzing the relationship between headway distance and dynamic desired distance. Building upon the optimal velocity model theory, this paper proposes a novel traffic car-following computing system in the time domain by incorporating an absolutely safe time headway strategy and a relatively safe time headway strategy to adapt to the dynamic changes in high-speed traffic flow. The interpretable physical law of motion is used to compute and analyze the car-following behavior of the vehicle. Three different types of car-following behaviors are modeled, and the calculation relationship is optimized to reduce the number of parameters required in the model's adjustment. Furthermore, we improved the calculation of dynamic expected distance in the Intelligent Driver Model (IDM) to better suit actual road traffic conditions. The improved model was then calibrated through simulations that replicated changes in traffic flow. The calibration results demonstrate significant advantages of our new model in improving average traffic flow speed and vehicle speed stability. Compared to the classic car-following model IDM, our proposed model increases road capacity by 8.9%. These findings highlight its potential for widespread application within future intelligent transportation systems. This study optimizes the theoretical framework of car-following models and provides robust technical support for enhancing efficiency within high-speed transportation systems.

Integration of Density Functional Theory and Machine Learning for Electrolyte Optimization in High-Voltage Dual-Ion Battery Design.

Designing dual-ion batteries (DIBs) by using various electrolytes through experiments or computationally is highly time-consuming and needs high-cost sophisticated resources. Here, we have utilized the ultrafast screening capability of machine learning (ML) to search for suitable salt-electrolytes toward the design of DIBs, choosing voltage as the desirable descriptor. Considering 50 different salts and their suitable staging mechanisms, the XGBoost Regressor ML model has been found to perform with remarkable accuracy. This is further validated by density functional theory, cross-validation, and experimental findings. An interpretable ML technique has been employed for local and global feature analysis to interpret the ML predicted results, underscoring the importance of choosing input features. This ML assisted DIB design approach has the potential to explore unknown salt-electrolytes that have yet to be tested in DIBs. Finally, we introduce the predicted voltages for all of the salt-electrolyte combinations as well as their probable staging mechanism. We signify the absence of a general trend in the predicted voltages, as various combinations of cations and anions are found to deliver unique voltages. Our study can guide researchers toward tuning constituent salts as well as staging mechanisms for the design of efficient DIBs.

The Economic Effects of Euro Adoption: An Analysis for the Czech Republic Using the Optimal Currency Area Theory

The Economic Effects of Euro Adoption: An Analysis for the Czech Republic Using the Optimal Currency Area Theory

Studying the influence of correction codes on coherent reception of M-PSK signals in the presence of noise and harmonic interference

Objectives. Signals with multiple phase shift keying (M-PSK) exhibiting good spectral and energy characteristics are successfully used in many information transmission systems. These include satellite communication systems, GPS, GLONASS, DVB/DVB-S2, and a set of IEEE 802.11 wireless communication standards. In radio communication channels, the useful signal is affected by various interferences in addition to noise. One of these is harmonic interference. As a result, high intensity harmonic interference practically destroys the reception of M-PSK signals. One of the important requirements for the quality of data transmission is the system error tolerance. There are different ways of improving the quality of information transmission. One of these is the use of corrective encoding technology. The aim of the paper is to assess the noise immunity of a coherent demodulator of M-PSK signals using Hamming codes (7,4) and (15,11), and convolutional encoding with Viterbi decoding algorithm (7,5) when receiving M-PSK signals under noise and harmonic interference in the communication channel.Methods. The methods of statistical radio engineering, optimal signal reception theory and computer simulation modeling were used.Results. Experimental dependencies of the bit error rate on the signal-to-noise ratio and on the intensity of harmonic interference of coherent reception of M-PSK signals in a channel with noise and harmonic interference were obtained using computer simulation modeling. This was done without using correction codes and with Hamming code (7.4) and (15.11) and convolutional encoding with Viterbi decoding algorithm (7,5).Conclusions. It is shown that the application of the correction codes effectively corrects errors in the presence of noise and harmonic interference with lower intensity. The correction is ineffective in the presence of high intensity interference. These results can provide important guidance in designing the reliable and energy efficient system.

Optimising height-growth predicts trait responses to water availability and other environmental drivers.

Future changes in climate, together with rising atmospheric , may reorganise the functional composition of ecosystems. Without long-term historical data, predicting how traits will respond to environmental conditions-in particular, water availability-remains a challenge. While eco-evolutionary optimality theory (EEO) can provide insight into how plants adapt to their environment, EEO approaches to date have been formulated on the assumption that plants maximise carbon gain, which omits the important role of tissue construction and size in determining growth rates and fitness. Here, we show how an expanded optimisation framework, focussed on individual growth rate, enables us to explain shifts in four key traits: leaf mass per area, sapwood area to leaf area ratio (Huber value), wood density and sapwood-specific conductivity in response to soil moisture, atmospheric aridity, and light availability. In particular, we predict that as conditions become increasingly dry, height-growth optimising traits shift from resource-acquisitive strategies to resource-conservative strategies, consistent with empirical responses across current environmental gradients of rainfall. These findings can explain both the shift in traits and turnover of species along existing environmental gradients and changing future conditionsand highlight the importance of both carbon assimilation and tissue construction in shaping the functional composition of vegetation across climates.

Research and application of the flatness target curve discrete dynamic programming based on two-dimensional decision making

The flatness target curve (FTC) is a fundamental process model in cold rolling flatness control, which directly affects the quality control effect of the strip. The accurate and efficient setting of the flatness target curve is the key to ensuring continuous rolling and is a common problem faced by various production companies. This paper establishes a discrete dynamic planning (DDP) setting method for FTC with two-dimensional decision-making. To quantitatively analyze the roles of the coefficients in the FTC, the preprocessing process is established using standardized processing methods and statistical analysis methods. The flatness target curve discrete dynamic programming (FTC-DDP) is based on Bellman optimization theory with a dual structure of local and system decision-making. The decision-making functions are established based on the effect of each coefficient on FTC geometric characteristics. The concepts of “curvature factor” and “wedge factor” are innovatively proposed to obtain the decision-making value functions. The regression analysis establishes the solution equations of even number coefficients, odd number coefficients, and gain coefficients, respectively. Roll bending and tilting roll analyze the FTC’s ability to correct flatness defects. Meanwhile, utilizing a 1450 mm five-stand six-roll cold rolling mill, it is verified that FTC-DDP can quickly and accurately set the FTC, which provides an effective solution for obtaining high-precision and high-quality cold-rolled strips. Application results show that FTC-DDP can reduce the difficulty of setting up FTC by more than 70 %, reduce the setup time to milliseconds, and improve the setup accuracy by more than 50 %.

State Observer-Based Iterative Learning Control Design for Discrete Systems Using the Heavy Ball Method

The paper considers a state observer-based iterative learning control design problem for discrete linear systems. To accelerate the convergence of the learning error, a combination of the heavy ball method from optimization theory and the vector Lyapunov function method for a class of two-dimensional systems known as repetitive processes is used to develop a new design. A supporting numerical example is given, including a comparison with an existing design.

Daily activities of older adults before and during the COVID pandemic.

This study examines how older adults' (65 years old plus) daily activities shifted in the years around the coronavirus disease (COVID) pandemic. Using data from American Time Use Survey, this study compares activities across the pre-pandemic (2019 to March 2020), early-pandemic (May to December 2020), and pandemic-normal (2021) periods. In the first year of the pandemic, there was less time spent on average on leisure outside the home, traveling, and with nonhousehold members, and more time alone and at home, compared with before the pandemic. Moving beyond averages, sequence and cluster analyses find 5 similar typologies of days across the three periods, characterized by days predominated by (a) housework, (b) leisure at home, (c) TV, (d) a combination of leisure at home and outside with TV, and (e) paid work. Duration of time across various daily activities differed, however, even for the same clusters. For example, in days predominated by indoor leisure, adults spent 405min in this activity before the pandemic, 432min during the early-pandemic period, and 549min during the pandemic-normal period. We also observed changes in the proportion of older adults in each cluster. Across the pre-pandemic and early-pandemic periods, the proportion of days predominated by leisure at home increased (9.9%-17.9%) whereas the proportion belonging to days predominated by housework decreased (45.7%-17.6%). COVID-19 shifted the daily life of older adults, and our findings are consistent with selection, optimization, and compensation theory, documenting that older adult adapted across the first 2 years of the pandemic.

Design of 1.1T/300mm Bitter-type magnet for gyro-traveling-wave tube with power consumption optimization theory.

To improve the portability of magnets in gyrotron devices, we designed a compact Bitter-type magnet with power consumption optimization theory. This magnet operates at room temperature in a small volume. The theory revises existing electromagnetic theory for non-uniform structural Bitter-type magnets and achieves the lowest energy consumption through iterative optimization. To extend the magnetic field homogeneity region, the ferromagnetic material armature is applied to the Bitter-type system without additional power consumption. Unlike previous manual designs, the proposed Bitter-type magnets can obtain optimal parameters with a significant reduction in computing time. Through the introduction of correction factors, we improve accuracy through multiple verifications of simulations and experiments. On this basis, a room-temperature Bitter-type magnet system for Ka-band fundamental mode gyrotron amplifiers is designed. Its maximum magnetic field strength is 1.1T, and the length of the homogeneity region is 300mm. Through optimization, its energy consumption is only 27.5 kW.

Stability criteria and calculus rules via conic contingent coderivatives in Banach spaces

This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between Banach spaces important in optimization theory and its applications. Our tools of generalized differentiation revolve around the newly introduced concept of ε-regular normal cone to sets and associated coderivative notions for set-valued mappings. Based on these constructions, we establish several characterizations of the central stability notion known as the relative Lipschitz-like property of set-valued mappings in infinite dimensions. Applying a new version of the constrained extremal principle of variational analysis, we develop comprehensive sum and chain rules for our major constructions of conic contingent coderivatives for multifunctions between appropriate classes of Banach spaces.

Improved multi-objective differential evolution algorithm and its application in the capacity configuration of urban rail photovoltaic hybrid energy storage systems

With the rapid expansion of urban rail transit, energy demand is continuously increasing. Integrating photovoltaic (PV) systems into hybrid energy storage systems (HESS) to form a rail transit PV hybrid energy storage system (RTPHESS) is an effective energy-saving and emission reduction measure. However, the integration changes the energy composition of the rail power supply system, making traditional HESS capacity configuration schemes inadequate to meet the stability requirement. In light of this, an RTPHESS model was established aiming at suppressing traction network voltage fluctuations and minimizing the total life-cycle cost of HESS. The model introduces traction network voltage fluctuation rate and HESS total life-cycle cost as evaluation objectives. Based on this, an improved multi-objective differential evolution algorithm (IMODE) was proposed to optimize HESS capacity. Optimal point set theory was used for population initialization to enhance the uniformity and diversity of the initial population, thereby improving global optimization capabilities. During the mutation phase, a hybrid Gaussian-Cauchy mutation strategy was introduced to improve both global and local search capabilities. The proposed algorithm's effectiveness was evaluated using IGD, SP, MS, and ER metrics on eight benchmark test functions with different characteristics, and compared with SaMODE_LS, MODE, MOPSO, MOALO, and MOMGA. Finally, IMODE was applied to the capacity configuration of RTPHESS. The results demonstrate that IMODE outperforms traditional algorithms in terms of accuracy and stability, reducing traction network voltage fluctuations by approximately 4.1 % and lowering the total life-cycle cost to 3,201,100 yuan.

Strong Optimal Classification Trees

Decision trees are among the most interpretable and popular machine learning models that are used routinely in applications ranging from revenue management to medicine. Traditional heuristic methods, although fast, lack modeling flexibility for incorporating constraints such as fairness and do not guarantee optimality. Recent efforts aim to overcome these limitations using mixed-integer optimization (MIO) for better modeling flexibility and optimality, but speed remains an issue. In “Strong Optimal Classification Trees,” Aghaei, Gómez, and Vayanos use integer optimization and polyhedral theory to create an MIO-based formulation with a strong LO relaxation resulting in a 29% speed-up in training time compared with state-of-the-art MIO-based formulations, as well as up to an 8% improvement in out-of-sample accuracy.

Optimal Transport with Constraints: From Mirror Descent to Classical Mechanics.

Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is limited by the lack of principled and flexible ways to incorporate realistic constraints. We propose a principled physics-based approach to impose constraints flexibly in optimal transport problems. Constraints are included in mirror descent dynamics using the D'Alembert-Lagrange principle from classical mechanics. This results in a sparse, local and linear approximation of the feasible set leading in many cases to closed-form updates.

Ambitious, misaligned, or uncertain? The occupational and educational aspirations of immigrant-origin youth in Germany

ABSTRACT Immigrant-origin students often hold higher educational aspirations than native-origin peers, accounting for socioeconomic status and school grades. The consequences of this ‘Immigrant Aspiration Paradox’ (IAP) on their socioeconomic attainment are debated. Although individuals’ occupational aspirations and how they compare with their educational aspirations (i.e. their alignment) also affect status attainment, they are understudied in the IAP literature. We contribute to the debate on the benefits of the IAP by investigating immigrant-native gaps in the level, (mis)alignment, and (un)certainty of teenage occupational and educational aspirations and their consequences on educational attainment in Germany. First, we describe immigrant-native gaps in teenage aspirations. Then, we investigate whether these differences mediate immigrant-native gaps in upper secondary attainment and tertiary enrollment. In line with the immigrant optimism theory, Asian-origin and Turkish-origin students are more likely to hold aligned high aspirations. On average, immigrant-origin students are less likely to have aligned low aspirations compared to native-origin students, and equally likely to hold misaligned or uncertain aspirations. We find that students from most immigrant-origin groups have a higher upper secondary attainment and tertiary enrollment than native-origin students, net of controls. Large portions of these advantages are mediated by the aspirations of immigrant-origin students, which we interpret as evidence of the benefits of the IAP.

Online Retailers based on Different Consumer Types Discount Pricing Strategy Research

In recent years online, retailers have continuously conducted discount sales to stimulate consumers' shopping desire. In this paper, we consider the different responses of three types of consumers: short-sighted, strategic, and discount-seeking consumers to the sales discount period, construct a Steinberg model for e-commerce platforms and online retailers with discount sales periods, and analyze the optimal pricing strategies of different consumer types for e-commerce platforms and merchants. Starting from consumer utility and combining optimization and game theory, it seeks to provide a reference for merchants and e-commerce platforms to make decisions.

Efficient Study Design and Analysis of Longitudinal Dose-Response Data Using Fractional Polynomials.

Correctly characterising the dose-response relationship and taking the correct dose forward for further study is a critical part of the drug development process. We use optimal design theory to compare different designs and show that using longitudinal data from all available timepoints in a continuous-time dose-response model can substantially increase the efficiency of estimation of the dose-response compared to a single timepoint model. We give theoretical results to calculate the efficiency gains for a large class of these models. For example, a linearly growing Emax dose-response in a population with a between/within-patient variance ratio ranging from 0.1 to 1 measured at six visits can be estimated with between 1.43 and 2.22 times relative efficiency gain, or equivalently, with 30% to a 55% reduced sample size, compared to a single model of the final timepoint. Fractional polynomials are a flexible way to incorporate data from repeated measurements, increasing precision without imposing strong constraints. Longitudinal dose-response models using two fractional polynomial terms are robust to mis-specification of the true longitudinal process while maintaining, often large, efficiency gains. These models have applications for characterising the dose-response at interim or final analyses.

Velocity model-based adapted meshes using optimal transport

In geophysical numerical models using the finite-element method or its variant, the spectral-element method, to solve seismic wave equations, a mesh is employed to discretize the domain. Generating or adapting a mesh to complex geological properties is a challenging task. To tackle this challenge, we develop an r-adaptivity method to generate or adapt a two-dimensional mesh to a seismic velocity field. Our scheme relies on the optimal transport theory to perform vertices relocation, which generates good-shaped meshes and prevents tangled elements. The mesh adaptation can delineate different regions of interest, like sharp interfaces, salt bodies, and discontinuities. The algorithm has a few user-defined parameters that control the mesh density. With typical seismic velocity examples (e.g., Camembert, SEAM Phase, Marmousi-2), mesh adaptation capability is illustrated within meshes with triangular and quadrilateral elements, commonly employed in seismic codes. Besides its potential use in mesh generation, the method developed can be embedded in seismic inversion workflows like multiscale full waveform inversion to adapt the mesh to the field being inverted without incurring the I/O cost of re-meshing and load rebalancing in parallel computations. The method can be extended to three-dimensional meshes.

The Unified Description of Abstract Convexity Structures

The convexity of space is essential in nonlinear analysis, variational inequalities and optimization theory because it guarantees the existence and uniqueness of solutions to a certain extent. Because of its wide variety of applications, mathematicians have extensively promoted and researched convexity. This paper reviews some representative convexity structures and discusses their relations from their definitions, unifying them in the abstract convex structure. Moreover, applications of main convexity structures including KKM theory and fixed point theory will be reviewed.

Theory and tests for coordination among hydraulic and photosynthetic traits in co-occurring woody species.

Co-occurring plants show wide variation in their hydraulic and photosynthetic traits. Here, we extended 'least-cost' optimality theory to derive predictions for how variation in key hydraulic traits potentially affects the cost of acquiring and using water in photosynthesis and how this, in turn, should drive variation in photosynthetic traits. We tested these ideas across 18 woody species at a temperate woodland in eastern Australia, focusing on hydraulic traits representing different aspects of plant water balance, that is storage (sapwood capacitance, CS), demand vs supply (branch leaf : sapwood area ratio, AL : AS and leaf : sapwood mass ratio and ML : MS), access to soil water (proxied by predawn leaf water potential, ΨPD) and physical strength (sapwood density, WD). Species with higher AL : AS had higher ratio of leaf-internal to ambient CO2 concentration during photosynthesis (ci : ca), a trait central to the least-cost theory framework. CS and the daily operating range of tissue water potential (∆Ψ) had an interactive effect on ci : ca. CS, WD and ΨPD were significantly correlated with each other. These results, along with those from multivariate analyses, underscored the pivotal role leaf : sapwood allocation (AL : AS), and water storage (CS) play in coordination between plant hydraulic and photosynthetic systems. This study uniquely explored the role of hydraulic traits in predicting species-specific photosynthetic variation based on optimality theory and highlights important mechanistic links within the plant carbon-water balance.

Trilateral Evolutionary Game Strategy for the Design Optimization of Engineering General Contracting Projects in the Chinese Context

The engineering general contracting mode is an advanced engineering transaction mode, and design optimization is one of the important driving forces for vigorously promoting the general contracting mode. The application proportion of the general contracting mode in infrastructure projects is not high, the number of successful projects is not large, and the implementation effect is not ideal. One of the main reasons is that the design optimization theory and practice of international standard general contracting projects cannot adapt to the general contracting projects in the Chinese context, making local general contracting projects face huge challenges such as low enthusiasm for design optimization from all parties and unsatisfactory design optimization effects. Therefore, under the premise of bounded rationality, when the owner adopts control methods of different intensities, an evolutionary game study on the selection of design optimization strategies between the design and construction parties is carried out, and stability control strategies are proposed through case experiments and simulations. The research results indicate the following: firstly, the design optimization of general contracting projects in the Chinese context is feasible, but it depends on the distribution ratio of benefits obtained from the design optimization. Compared with general civil construction general contracting projects, the design optimization allocation ratio of industrial construction general contracting projects is more significant; secondly, the mixed control method of strong control and weak control is the optimal choice for the owner of the general contracting project; and thirdly, there are multiple evolutionary stable points, and mechanism design or incentive measures should be used to guide owners to choose weak control strategies, while design and construction parties should choose their design optimization strategies. The research results provide a reference for owners to determine the proportion and scheme of design optimization allocation, and for construction parties to determine design optimization strategies.