Mathematical Constraints Research Articles

Multi-objective optimization design of parallel manipulators using a neural network and principal component analysis

Abstract. In this work, a multi-objective optimization design method is proposed based on principal component analysis (PCA) and a neural network to obtain a mechanism's optimal comprehensive performance. First, multi-objective optimization mathematical modeling, including design parameters, objective functions, and constraint functions, is established. Second, the sample data are obtained through the design of the experiment (DOE) and are then standardized to eliminate the adverse effects of a non-uniform dimension of objective functions. Third, the first k principal components are established for p performance indices (k<p) using the variance-based PCA method, and then the factor analysis method is employed to define its physical meaning. Fourth, the overall comprehensive performance evaluation index is established by objectively determining weight factors. Finally, the computational cost of the modeling is improved by combining the neural network and a particle swarm optimization (PSO) algorithm. Dimensional synthesis of a Sprint (3RPS) parallel manipulator (PM) is taken as a case study to implement the proposed method, and the optimization results are verified by a comprehensive performance comparison of robots before and after optimization.

Electroosmotic flow of cobalt-ferrite nanoparticles in water and ethylene glycol through a ciliary annulus: A biomedical application.

Unique magnetic characteristics of cobalt-ferrite nanoparticles make them suitable for biological imaging and therapeutic applications. Understanding their activity in nanofluids via the ciliary annulus could lead to better contrast agents for magnetic resonance imaging and improved cancer therapy and other medical therapies. This article provides a comprehensive analysis of the theoretical conclusions regarding the transport of a nanofluid by electroosmosis across a ciliary annulus. The nanofluid consists of cobalt-ferrite nanoparticles (CoFe2O4), water (H2O), and ethylene glycol (C2H6O2). As part of the investigation into constructing a physical model, mathematical analysis is performed based on the conservation of mass, momentum, and energy. Dimension-free analysis and mathematical constraints are utilized to learn more about the system. By generating differential equations and including suitable boundary conditions, one can obtain exact solutions, which can then be visually inspected. Recent studies have demonstrated an inverse relationship between flow velocity and cilia length, zeta potential, and Helmholtz-Smoluchowski velocity. The streamlines show that the growth of the trapping boluses is affected by several factors, including the nanoparticles' volume fraction, the cilia's length, the amplitude ratio, the eccentricity, and the zeta potential. These results not only shed light on how nanofluids move, but they also have potential applications in microfluidics, heat transfer, and biomedical engineering.

The explanatory nature of constraints: Law-based, mathematical, and causal

This paper provides an analysis of explanatory constraints and their role in scientific explanation. This analysis clarifies main characteristics of explanatory constraints, ways in which they differ from “standard” explanatory factors, and the unique roles they play in scientific explanation. While current philosophical work appreciates two main types of explanatory constraints, this paper suggests a new taxonomy: law-based constraints, mathematical constraints, and causal constraints. This classification helps capture unique features of constraint types, the different roles they play in explanation, and it includes causal constraints, which are often overlooked in this literature.

Robust optimal scheduling of integrated energy systems considering multiple uncertainties

AbstractMultiple uncertainties such as renewable energy output, energy purchase prices and integrated demand responses have brought about severe challenges to the safe and economic operation of integrated energy system (IES). To meet this challenge, this study takes the combined cooling heating and power as an example of IES and proposes an optimization model considering multiple uncertainties. First, the structure of IES is given, and these mathematical models and constraints are listed according to the energy supply characteristics. Second, considering uncertain factors such as the wind and solar output, comprehensive demand response and energy purchase price, the different characterization methods are selected to model the uncertainty sources by identifying the characteristics of multiple uncertainty sources. Then, combining the stochastic scenario method and robust optimization method, a day‐ahead optimal scheduling model of IES with multiple uncertainties is established, and the whale optimization algorithm is improved to obtain the optimal solution of the model. Finally, the actual data of an IES is selected to verify the rationality and effectiveness of the model. Meanwhile, the influence of uncertain factors on scheduling is introduced to verify the perfect coordination of economy and robustness of the model at runtime.

Discretized Cell Modeling for Optimal Layout of Multiple Tower Cranes

Multiple tower crane layout planning (MTCLP) refers to the selection of the types, quantities, and positions of tower cranes and material storage positions. In a construction project, choosing tower cranes with a larger covering radius and lifting capacity can reduce the transportation time of materials. However, it can also simultaneously raise the rental cost and the risk of crane crashes. Determining an optimal multiple tower crane layout plan to achieve high construction efficiency with low cost is still a challenge. Mathematically, MTCLP is a complex combinatorial problem controlled by a number of variables, such as site configuration, building layout, material storage positions, and workload. To precisely describe irregular shaped sites and buildings, this research partitioned the site into unit cells and proposed a cell-based optimization model. For the optimal crane layout plan, the problem was formulated as a mixed integer linear problem (MILP). The model’s mathematical constraints comprised coverage of the given positions, the crane’s safety distance, sufficient crane capacity, and the utilization ratio. The objectives were to increase the crane coverage ratio while reducing the cost and the working areas overlapped by more than two cranes. Two case studies are presented to demonstrate the effectiveness of the model. The first construction project consisted of seven buildings with irregular shapes. By strictly forbidding the areas to be overlapped by more than three tower cranes, the model successfully obtained the optimal crane layout plan using the Gurobi Optimizer. Compared with the contractor’s layout plan, the optimal plan reduced the rental cost by 10.7% and the area overlapped by more than three tower cranes by 4.56%. In the second project, alternative plans were identified by the Gurobi Optimizer and ε-constraint method to enhance confidence in selecting the ultimate crane layout plan. The optimization procedure involved (1) optimizing the layout plan with minimum crane cost and maximum coverage ratio, (2) identifying all possible layouts as the Pareto fronts when the coverage ratio could not be raised without increasing the crane cost, and (3) minimizing the areas of crane overlap covered by more than three tower cranes. The effectiveness of the proposed model is also proved by comparing the differences in layout plans caused by “regular” and “urgent” lifting demands.

Offshore wind energy prospects for power-to-direct air capture and power-to-gas

Direct air capture of carbon dioxide (CO2) is technically a feasible solution for reducing atmospheric CO2 concentrations at scale, building on decades of global research. However, powering such systems even partially with CO2-intensive fossil fuels results in more CO2 emissions. This paper presents a novel energy management strategy (EMS) to further explore modular offshore wind energy off Canada's West Coast via power-to-direct air capture and power-to-gas systems. The system architecture includes a 15 MW wind turbine paired with a hydrogen energy storage system, i.e. hydrogen production and storage, and direct air capture (DAC) units. Hydrogen production from wind generation is stored and used to offer two key benefits: to deliver the thermal loads of the DAC system, and to meet hydrogen demand for external consumers. The proposed EMS offers an extra degree of freedom to operate the designed system by setting the priority either to maximize the amount of CO2 capture or to maximize the amount of H2 production for external consumers. In particular, the study incorporates dynamic mathematical modeling and constraints formulation for the aforementioned scenarios; DAC priority for CO2 capture and H2 for external hydrogen demand satisfaction. The effectiveness of the proposed EMS is shown through extensive simulations with different seasonal conditions.

Melting thermal transportation in bioconvection Casson nanofluid flow over a nonlinear surface with motile microorganism: Application in bioprocessing thermal engineering

Bioconvection in fluids can be significantly influenced by melting thermal transport, especially when it comes to heat transfer and energy transmission. In a fluid, microbes or biological particles may move together due to physical or chemical gradients, such as light, temperature, or chemical concentrations. This process is known as bioconvection. In bioprocessing, mobile microorganisms can be employed to create beneficial substances including biofuels, medicines, and food additives. They can move around freely in the fluid thanks to their motility, which improves the mixing and distribution of other substrates like nutrients. The main outcomes of the current study are to provide the comprehensive numerical analysis of existing situation where the melting transportation impact along with the action of microorganisms on MHD non-Newtonian nano fluid model under velocity, thermal and concentration slip. Also, our derived results are validated with the previously published data against various convergence flow parameters, which are demonstrated through tables. To provide more meaningful data, numerous mathematical and technical constraints are taken into consideration. Using the required conversion technique, the system of PDEs is transmuted into a non-linear ODEs. Using the shooting strategy, evaluate expressions numerically by transforming them with the MATLAB function bvp4c. The literature elaborates on a few observations on the bio-convection process and its additional unique features. The graphs demonstrate the effects of various flows on dimensionless quantities. The current theoretic model might be used to increase heat transmission, engineering practices, and thermal energy.

Design of tilted and decentered anamorphic optical system based on nodal aberration control

This paper proposes a design method for tilted and decentered anamorphic projection optics. In this method, the structure is designed in groups according to the magnification requirements; the anamorphic system section’s primary aberration is analyzed based on vector aberration theory, the tilted and decentered system section’s node behavior is analyzed based on node aberration theory, and spatial ray tracing is used to control the anamorphic optical system’s pupil to be elliptical to realize pupil matching between groups. A mathematical aberration balance and constraint control model is established. The node position is used as an evaluation function such that the node is close to or within the full field, thus controlling the primary aberration for the initial system over the full field. The initial system is constructed with increased optimization potential to satisfy the aberration and structural constraints. The initial structure for the tilted and decentered anamorphic projection optics (βx=1/4,βy=1/8) is constructed with the coma and astigmatism nodes close to or within the full field. The structure is then optimized to achieve a wavefront root-mean-square error for the EUV tilted and decentered anamorphic objective with NA= 0.55 of better than 0.025λ (λ = 13.5 nm).

Deep background-mismodeling-learned reconstruction for high-accuracy fluorescence diffuse optical tomography.

We present a deep background-mismodeling-learned reconstruction framework for high-accuracy fluorescence diffuse optical tomography (FDOT). A learnable regularizer incorporating background mismodeling is formulated in the form of certain mathematical constraints. The regularizer is then learned to obtain the background mismodeling automatically using a physics-informed deep network implicitly. Here, a deep-unrolled FIST-Net for optimizing L1-FDOT is specially designed to obtain fewer learning parameters. Experiments show that the accuracy of FDOT is significantly improved via implicitly learning the background mismodeling, which proves the validity of the deep background-mismodeling-learned reconstruction. The proposed framework can also be used as a general method to improve a class of image modalities based on linear inverse problems with unknown background modeling errors.

Dynamic Modeling and Analysis of Boundary Effects in Vibration Modes of Rectangular Plates with Periodic Boundary Constraints Based on the Variational Principle of Mixed Variables

The modal and vibration-noise response characteristics of plate structures are closely related to their boundary effects, and the analytical modeling and solution of the dynamics of plate structures with complex boundary conditions can reveal mechanisms of the influence of the boundary structure parameters on the modal characteristics. This paper proposes a new method for dynamic modeling of rectangular plates with periodic boundary conditions based on the energy equivalence principle (mixed-variable variational principle) of equating complex boundary “geometric constraints” to “mathematical physical constraints”, taking a rectangular plate structure with periodic boundaries commonly used in engineering as the object. First, the boundary external potential energy of the periodic boundary rectangular plate is obtained by equating the bending moment and deflection to the boundary conditions. Next, we establish the total potential energy model, the amplitude boundary equation, as well as the frequency equation of the periodic boundary rectangular plate in turn. Solving by numerical method, the natural frequency of the theoretical model is obtained. The validity of the theoretical model is then verified by modal test experiments. Finally, the law of the parameters such as the form of boundary constraint, the number of periods, and the clamp support ratio on the natural frequency of the rectangular plate is investigated. The results show that the natural frequency of the rectangular plate is closely related to the boundary form and period distribution of the plate. The modal frequencies of the plate structure can be tuned by the design of the boundary conditions for a certain size of the plate structure. The research in this paper provides a theoretical and technical basis for the vibration noise control of complex boundary plate structures.

Improved Caps for Improved Subdivision Surfaces

The quest for a finite number of bicubic (bi-3) polynomial pieces to smoothly fill multi-sided holes after a fixed number of surface subdivision steps has motivated a number of constructions of finite surface caps. Recent bi-3 and bi-4 subdivision algorithms have improved surface shape compared to classic Catmull–Clark and curvature-bounded ‘tuned’ subdivision. Since the older subdivision algorithms exhibit artifacts that obscure the shortcomings of corresponding caps, it is worth re-visiting their multi-sided fill surfaces. The improved caps address the challenge so that either bi-3 or bi-4 data can be accommodated, as needed. The derivation illustrates the subtle fundamental trade off between formal algebraic mathematical smoothness constraints and good shape in the large.

Graphic Groups, Graph Homomorphisms, and Graphic Group Lattices in Asymmetric Topology Cryptography.

Using asymmetric topology cryptography to encrypt networks on the basis of topology coding is a new topic of cryptography, which consists of two major elements, i.e., topological structures and mathematical constraints. The topological signature of asymmetric topology cryptography is stored in the computer by matrices that can produce number-based strings for application. By means of algebra, we introduce every-zero mixed graphic groups, graphic lattices, and various graph-type homomorphisms and graphic lattices based on mixed graphic groups into cloud computing technology. The whole network encryption will be realized by various graphic groups.

On biological networks capable of robust adaptation in the presence of uncertainties: A linear systems-theoretic approach.

Biological adaptation, the tendency of every living organism to regulate its essential activities in environmental fluctuations, is a well-studied functionality in systems and synthetic biology. In this work, we present a generic methodology inspired by systems theory to discover the design principles for robust adaptation, perfect and imperfect, in two different contexts: (1)in the presence of deterministic external and parametric disturbances and (2)in a stochastic setting. In all the cases, firstly, we translate the necessary qualitative conditions for adaptation to mathematical constraints using the language of systems theory, which we then map back as design requirements for the underlying networks. Thus, contrary to the existing approaches, the proposed methodologies provide an exhaustive set of admissible network structures without resorting to computationally burdensome brute-force techniques. Further, the proposed frameworks do not assume prior knowledge about the particular rate kinetics, thereby validating the conclusions for a large class of biological networks. In the deterministic setting, we show that unlike the incoherent feed-forward network structures (IFFLP), the modules containing negative feedback with buffer action (NFBLB) are robust to parametric fluctuations when a specific part of the network is assumed to remain unaffected. To this end, we propose a sufficient condition for imperfect adaptation and show that adding negative feedback in an IFFLP topology improves the robustness concerning parametric fluctuations. Further, we propose a stricter set of necessary conditions for imperfect adaptation. Turning to the stochastic scenario, we adopt a Wiener-Kolmogorov filter strategy to tune the parameters of a given network structure towards minimum output variance. We show that both NFBLB and IFFLP can be used as a reduced-order W-K filter. Further, we define the notion of nearest neighboring motifs to compare the output variances across different network structures. We argue that the NFBLB achieves adaptation at the cost of a variance higher than its nearest neighboring motifs whereas the IFFLP topology produces locally minimum variance while compared with its nearest neighboring motifs. We present numerical simulations to support the theoretical results. Overall, our results present a generic, systematic, and robust framework for advancing the understanding of complex biological networks.

Letter: Application of optimization algorithms to engineering design problems and discrepancies in mathematical formulas

Engineering design optimization problems have attracted the attention of researchers since they appeared. Those who work on developing optimization algorithms, in particular, apply their developed algorithms to these problems in order to test their new algorithms’ capabilities. The mathematical discrepancy emerges during the implementation of equations and constraints related to these engineering problems. This is due to an error occurring in writing or transmitting these equations from one paper to another. Maintaining these discrepancies will have a negative impact on the assessment and model performance verification of the newly developed algorithms, as well as the decision-making process. To address this issue, this study investigates the mathematical discrepancies occurred by researchers in four well-known engineering design optimization problems (Welded Beam Design WBD, Speed Reducer Design SRD, Cantilever Beam Design CBD, and Multiple Disk Clutch Brake Design MDCBD). We have investigated some of the recently published papers in the literature, identifying discrepancies in their mathematical formulas, and fixing them appropriately by referring and comparing them to the original problem. Furthermore, all mathematical discrepancies , references, parameters, cost functions, constraints, and constraint errors are highlighted, arranged and organized in tables. As a result, this work can help readers and researchers avoid being confused and wasting time when working on these engineering design optimization problems.

Three-dimensional analysis of motile-microorganism and heat transportation of viscoelastic nanofluid with nth order chemical reaction subject to variable thermal conductivity

The most important condition of modern industrial activities is excellent refrigeration performance for conventional buildings. The Buongiorno relation assessment identifies nanofluid's thermal and mass efficiency, which inspires us to specify different properties of random motion and thermophoretic diffusion. Non-Newtonian nanofluids are used in a variety of fields, including thermal exchangers, solar liquid boiler, and heat control in vehicles. Nanoparticles can significantly enhance a fluid's thermal conductivity and heat transfer properties. This makes nanofluids attractive in cooling systems for electronic devices, such as computer chips and LED lights, and in various industrial applications where efficient heat transfer is important. The proposed thermos-electric system depends on nanomaterial heat flow, fractional volume of nanomaterial, density, and motile microorganisms. Because of their numerous applications, ferromagnetic nanoparticles have become extremely popular in biotechnology. Numerous mathematical and technical constraints are considered to generate more useful data. Using the shooting scheme, evaluating numerically by MATLAB function bvp4c to transform expressions. Some observations about the bio-convection procedure its different exclusive characteristics are elaborated in the literature. The graphs show how multiple flows influence non-dimensional quantities. The present theoretical model could be applied to engineering methods, heat transfer improvements, and thermal energy.

Real-Time Path Planning of Driverless Mining Trains with Time-Dependent Physical Constraints

While the increased automation levels of production and operation equipment have led to the improved productivity of mining activity in open pit mines, the capacity of the mine transport system has become a bottleneck. The optimisation of the mine transport system is of great practical significance to reduce the production and operation cost and improve the production and organizational efficiency of mines. In this paper, we first formulate a multiobjective optimisation problem for mine railway scheduling by introducing a set of mathematical constraints. As the problem is NP-hard, we then devise a mixed integer programming-based solution to solve this problem and develop an online framework accordingly. We finally conduct test cases to evaluate the performance of the proposed solution. Experimental results demonstrate that the proposed solution is efficient and able to generate a train schedule in a real-time manner.

Reserve provision of combined-cycle unit in joint day-ahead energy and reserve markets

With the continuous development of natural gas-fired combined cycle power generation technology, the combined cycle (CC) unit's installed capacity is gradually increasing in the power system because of its flexible operation characteristics. Participating in the energy and reserve markets and taking advantage of flexible mode transfer characteristics, the CC unit can provide the system with energy and sufficient reserve capacity. This paper proposes a bi-level strategic bidding model to study the CC unit’s bidding behavior in the day-ahead energy and reserve markets. The upper-level model is an optimal bidding model for the configuration-based CC unit aiming to maximize its profit. The lower-level model is the joint market clearing model of the energy and reserve markets managed by the independent system operator (ISO). CC unit and ISO in this model influence each other by the locational marginal electricity prices (LMEP) and the locational marginal reserve prices (LMRP) obtained from the lower-level market-clearing model. The CC unit submits the bids to the ISO and arranges the generation plan according to the market clearing results of the lower-level market-clearing model carried out by the ISO. The proposed bi-level optimization model is transformed into a mathematical equilibrium constraint (MPEC) problem by Karush-Kuhn-Tucker (KKT) conditions and duality theory. In this paper, the improved IEEE-6 bus and IEEE-57 bus systems are used as case studies to verify the effectiveness of the proposed bidding strategy for the CC unit. The results show that the proposed bidding strategy can effectively improve the profits of the CC unit in the electricity market. Compared with the case of the CC unit only participating in the energy market, the profits of the CC unit in the market increased by 8.84% and 12.3%.

Predicting of educational buildings locations by integrating spatial distribution assessment techniques high schools in Mosul as a case study1

The paper assesses the existing spatial distribution locations of Mosul's high schools respecting the local standards using QGIS. It evaluates the school area and capacity to determine the lack in its region; proposing additional school loca- tions to overcome the shortage concerning multiple criteria using City-Engine to represent mathematical and formal constraints through numerical code. Then, it evaluates the schools' proposed locations to explore the solutions' quality in compliance with the local standards.

Piecewise integrable neural network: An interpretable chaos identification framework.

Artificial neural networks (ANNs) are an effective data-driven approach to model chaotic dynamics. Although ANNs are universal approximators that easily incorporate mathematical structure, physical information, and constraints, they are scarcely interpretable. Here, we develop a neural network framework in which the chaotic dynamics is reframed into piecewise models. The discontinuous formulation defines switching laws representative of the bifurcations mechanisms, recovering the system of differential equations and its primitive (or integral), which describe the chaotic regime.

Precautionary Saving and Liquidity Shortage

Most of the canonical macroeconomic models simulate liquidity anomalies by changing the economic fundamentals or adding massive financial shock to firms’ collateral constraints, but a few facts somehow tell a different story. Instead of relying on the exogenous shocks, we introduce uncertainty into an otherwise classical liquidity framework and try to answer what worsens the aggregate liquidity in the absence of exogenous simulations and what a firm dynamics and financing strategy would be. Our analysis shows that (1) uncertainty induces agents to make decisions under the worst-case scenario and hence generates a unique expectation threshold that drags market (or firms) liquidity from sufficiency to insufficiency even without any shock or economic changes. (2) Precautionary saving occurs before the real liquidity shortage as the expectation shifts, causing firms to secure external financing by raising the equity issuing price and hoarding liquid assets, such as fiat money, against liquidity tightening. (3) To achieve liquidity stability and sustainability, an extra mathematical constraint is supplemented for the uniqueness and the existence of equilibrium under uncertainty. Other properties of firms’ intertemporal allocations, such as the bid-ask spread and return of holding of the illiquid asset, are derived. Moreover, some approaches for further empirical research are discussed.