Multidimensional Optimization Algorithm Research Articles

Multi-Dimensional Adaptive Learning Rate Gradient Descent Optimization Algorithm for Network Training in Magneto-Optical Defect Detection

Multi-Dimensional Adaptive Learning Rate Gradient Descent Optimization Algorithm for Network Training in Magneto-Optical Defect Detection

Information interaction and partial growth-based multi-population growable genetic algorithm for multi-dimensional resources utilization optimization of cloud computing

Optimizing multi-dimensional resource utilization is a critical research area in distributed computing, particularly in cloud computing, where various heterogeneous resources are integrated to offer a wide range of services. Addressing this issue necessitates the simultaneous consideration of multiple resource bottlenecks. This paper presents a new solution, called the Multi-Population Growth Genetic Algorithm (MPGGA), which consists of a central management unit responsible for executing information interaction and growth quota reallocation, and multiple population evolution executors to perform crossover and regeneration within each population. The proposed MPGGA combines elite sharing and priority support for the weaker population (ESPW), resulting in better convergence and optimality than other combinations of strategies. This outcome is corroborated by extensive ablation experiments on various strategies. Furthermore, the experimental results for minimizing the maximum utilization of resources in each dimension indicate that MPGGA-ESPW outperforms other popular algorithms, such as GHW-NSGA II (1.363x), GHW-MOEA/D (1.339x), NSGA II (1.948x), and MOEA/D (2.151x) in terms of convergence speed. For energy consumption-related optimization problems, the experimental results demonstrate that the adaptability of a single algorithm in MPGGA family is limited by the algorithm of growth route, while also showing that the MPGGA framework is flexible to allow various algorithms as its growth route to adapt to various scenarios.

A Branch and Bound algorithm for multidimensional Holder optimization: Estimation of the age-dependent viral hepatitis A infection force

In the present framework, we develop a branch and bound multidimensional Holder optimization method. This method is composed of two subroutines. The first one allows converting the multivariate objective function into a single variable one using the alpha-dense space fitting curves. In the second subroutine, we minimize the single variable function resulting from the first subroutine. To achieve this task, we develop a novel iterative optimization method reducing the feasible region in each iteration taking into account the property of Holder of the objective function. We apply this method to solve a parameters identification problem resulting from the modelling of the spread of viral hepatitis A in the central west of Tunisia following the increase in the number of infections. The Tunisian health authorities wanted to know the prevalence and the infection force of the virus in order to identify the situation and take the necessary measures. The modelling leads to a minimization problem of the least square multivariate error between the observed values and the theoretical ones. Besides, we implement the proposed method in some numerical experiments to evaluate its efficiency.

Effective Scheme for Inductive Wireless Power Coil Design Using Scan-and-Zoom Optimization

In inductive power transfer (IPT) systems, the coil design is crucial since the power transfer efficiency (PTE) of IPT depends on the coil characteristics such as geometric shape, diameter, wire thickness, etc. The most commonly used technique for the coil is finite element analysis (FEA). Nevertheless, if there are more than two parameters to be designed, FEA design requires a long simulation time since the coil design problem is separated into a series of single-parameter optimization problems. Another issue of conventional FEA is difficulty in interfacing with circuit simulation. To mitigate this issue, a novel co-simulation framework of MATLAB/ANSYS Maxwell is proposed in this paper. In MATLAB, multi-dimensional optimization algorithms like scan-and-zoom are employed to determine geometric parameters to achieve high PTE and minimize the number of FEA executions while Maxwell serves to extract the circuit parameters from the geometric parameters and enhance the accuracy of calculation. The 100 W prototype IPT system is built to verify the proposed coil design scheme in this paper. The performance comparisons with the conventional methods in terms of design accuracy, simulation time, and application flexibility are performed on a pair of designed single-layer circular coils.

Improved bond graph model for fault diagnosis under uncertain conditions

The effectiveness of model-based diagnosis strongly depends on the model’s authenticity and is impacted by various uncertainties. Measurement uncertainty is governed by the probability method, and parameter uncertainty can be handled by the linear fractional transformation, whereas structure uncertainty and errors are rarely considered. In this paper, an improved bond graph (BG) model is proposed, which adopts subsystems to substitute modelling errors, namely parameter uncertainty and structure uncertainty. A multi-dimensional Fibonacci optimization algorithm is developed to identify the parameters of subsystems to obtain the subsystem-based diagnostic hybrid BG (SDHBG) model. Fault diagnosis is realized by comparing the residuals and thresholds derived from the SDHBG. Experiments are conducted to validate the key concepts of the proposed methods. Subsequently, the results suggest its effectiveness.

Energy-saving method and performance analysis of chiller plants group control based on Kernel Ridge Regression and Genetic Algorithm

The upgrading of traditional chiller plants to the high-efficiency refrigerator room is conducive to effective utilization and conservation of energy. An energy-saving method of chiller plants group control based on Kernel Ridge Regression and Genetic Algorithm are presented. Combined with machine learning and the classic model of the chiller plants, the multiple nonlinear problems between the system parameters of the chiller plants are solved. A more detailed group control model of chiller plants is established, which is suitable for multiple chillers, variable-speed pumps, and variable-frequency fans. Incorporate the start-up time of the chiller, the difference between the actual cooling capacity and the target cooling capacity into the penalty function, and use the Genetic Algorithm for multi-dimensional optimization to find the best efficiency point of the entire refrigeration room and achieve the goal of energy saving. A comparative analysis of the actual operation of the cold room system of a large electronics factory in Guangdong for three months is carried out. Compared with the traditional PID algorithm, the three-month power saving rate of this group control energy saving method is: 31.34%, 14.33%, 19.22%.

High‐resolution 2.5D multifocusing imaging of a crooked seismic profile in a crystalline rock environment: Results from the Larder Lake area, Ontario, Canada

ABSTRACTA high‐resolution seismic reflection transect was acquired over a hard‐rock geological setting along an existing roadway in the Larder Lake area of the Superior Craton of Canada for the Metal Earth project in 2017. This profile, as well as other Metal earth transects, primarily aims to enhance the knowledge and to better understand the subsurface geology of the Abitibi Greenstone Belt within the Canadian Shield. The complex geological settings of the study area as well as the tribulations caused by the survey geometry have made the imaging and velocity field estimation more challenging. A recently introduced 2.5D multifocusing stacking method is one potential solution for processing crooked‐line seismic data with a poor signal‐to‐noise ratio. The 2.5D multifocusing approach offers more realistic modelling of the zero‐offset wavefield by explicitly accounting for the midpoint dispersion and cross‐dip effects. The main practical problem of the 2.5D multifocusing implementation is the simultaneous determination of the optimal wavefield parameters for each image point and time location. We address this optimization problem using a multidimensional constrained differential evolution global optimization algorithm, as this improves the efficiency and accuracy of the estimation. We have also designed an efficient processing sequence for multifocusing seismic imaging. The performance of the 2.5D multifocusing procedure has been examined on a synthetic model, generated using the same real acquisition geometry. Numerical tests demonstrate that the 2.5D multifocusing technique can produce a more focused stack with the primary reflections appearing at their poststack correct locations, and the procedure can also provide reliable estimates of interface dips. Due to the importance and difficulty of imaging the data, several conventional and advanced processing strategies have been attempted on the transect, specifically: 2D phase‐shift time migration of a dip moveout corrected stack; 2D prestack Kirchhoff time migration; swath 3D poststack migration; and our 2.5D multifocusing imaging algorithm. We found that applying the 2.5D multifocusing stacking algorithm followed by a poststack time migration approach improved the resolution of the image significantly compared to all the conventional and advanced methods and identified new reflections. The 2.5D multifocusing method also focused the steeply dipping reflections more coherently, which resolved ambiguities in geological architecture by understanding the location and continuity of structures. The method also accurately extracts 3D structural information and results in an improved signal‐to‐noise ratio.

Integration of energy and seismic-structural design variables through the optimization of a multi-story residential light-frame timber building with different seismic lateral connectors and building stories

The structural and energy performance of the light-frame buildings is intrinsically linked, but the design process of both domains is not. Light-frame timber buildings are subjected to overheating due to the lack of thermal mass. A solution to eliminate or mitigate overheating is adding thermal mass, but the main drawback is increasing the seismic forces the building needs to withstand. Furthermore, the length of exterior shearwalls, fenestration openings, and studs spacing affect both the energy and structural performances. This paper aims to analyze and integrate energy and seismic-structural design variables for a light-frame residential timber building with different lateral seismic connectors and building stories. An Energy and Structural Timber Building Optimization (ESTIBO) methodology is proposed to integrate energy and seismic-structural design variables by optimizing the building energy performance. ESTIBO is based on GenOpt optimization software using a hybrid multidimensional optimization algorithm, while the energy simulations are performed on EnergyPlus using the Rhino's Grasshopper plugin. A structural model is implemented in Matlab under a modal response analysis of the building structure. The main results show that integrating critical design variables achieves different optimal values considering feasible structural solutions with reduced heating and cooling loads. It was found the four main variables that primarily reflect the link between energy and seismic-structural performances are stud spacing, wall insulation thickness, wall insulation type (high or low specific heat capacity), and floor concrete layer thickness. This paper contributes to improving the understanding of light-frame timber buildings' performance regarding the interaction of energy and structural-seismic design variables. Moreover, ESTIBO demonstrated to be able to provide optimal energy and seismic-structural solutions. Thus, it can support the early design stage of light-frame timber buildings.

A novel convergent filled function algorithm for multi-dimensional global optimization

As we all know, the filled function method as an effective algorithm to solve global optimization problems can overcome the defect that the non-linear algorithm is trapped in the local minimizer and cannot jump to attach the global minimizer, which has attracted the attention of researchers. However, when solving multi-dimensional global optimization problems, the filled function often lacks good properties such as mandatory, convexity and continuity, which makes the conventional filled function algorithm to always encounter the difficulty that its convergence cannot be guaranteed. In view of this, a novel convergent filled function algorithm for multi-dimensional global optimization is proposed. In this algorithm, by the way of the coordinates rotate, the multi-dimensional global optimization problem is transformed into several one-dimensional sub-problems, and then the new filled function with good properties is constructed to solve the one-dimensional sub-problem, which leads to attachment of the convergence in algorithm. Finally, compared with the existing algorithms on test optimization problems in NETLIB library, the effectiveness of the algorithm is verified by numerical experiments.

Thermo-electrochemical modeling of oxygen ion-conducting solid oxide fuel cells with internal steam reforming in the water-energy nexus

The precise estimation of chemical equilibrium state is highly crucial when simulating electrochemical and thermodynamic aspects of oxygen ion-conducting solid oxide fuel cells (SOFC). One way to determine the equilibrium state of an internal reforming solid oxide fuel cell system is to compute the total Gibbs free energy of the system (G) and then, adjust the molar amounts of each substance, subject to element balances, so as to minimize G. Multi-dimensional optimization algorithms can be used for this purpose. In this paper, a powerful analytical solution method called Lagrange's method of undetermined multipliers is used for estimating the chemical equilibrium state. The effects of each current density, reaction temperature and pressure of the stack, and fuel and carbon dioxide utilization ratios on the voltage losses and output voltage and power of the stack, efficiency, and molar portions of the exhaust chemical species in anode and cathode, are investigated. The solid oxide fuel cell stack simulations by Lagrange's method at a definite state shows an efficiency of 54.6% and output power of 158.3 kW.

Global optimisation approach for designing high-efficiency piezoelectric beam-based energy harvesting devices

The paper proposes a novel methodology for developing high-power energy harvesting gravity-based devices using an array of piezoelectric beams for wind energy applications. The methodology incorporates a global multidimensional constrained optimisation algorithm, which accounts for the physical size of the device, the physical, geometrical and electrical properties of the piezoelectric beams, and the power management circuit to increase the device’s efficiency. As the beams are plucked sequentially, they vibrate out-of-phase, which consequently leads to charge cancellation issues. The paper proposes and incorporates an electrical circuit design to avoid such problems, being able to further increase the efficiency of the device by 35% when compared against the output from the standard energy harvesting (SEH) circuit with independent rectifiers. The proposed optimisation methodology is applied to the devices utilising flexible polyvinylidene fluoride beams. The developed dynamic numerical model of the beams’ vibration is validated using the experimental results and the results of a Finite Element Analysis. To study the electro-mechanical coupling of the beams, an electric circuit and the power management circuit are created and modelled in Matlab/Simulink software. The optimised device delivers 6 to 17 times higher energy output compared to the unoptimised device. The performance of this device was also compared to that of the device with much stiffer LiNbO3 beams (Clementi et al., 2021, [1]) to demonstrate the direct applicability of such devices to power sensors and transmitter units for structural monitoring of wind turbine blades. It has been demonstrated that the LiNbO3-beam device yields an energy output with one order of magnitude higher. The applied optimisation methodology enabled a 0.057 × 0.017 × 2 m3 dimension device to produce a power output in the range from 0.5 to 1 W depending on the blades’ speed, resulting in 1.06 mW/cm3 power density of the device.

Multi-dimensional constrained energy optimization of a piezoelectric harvester for E-gadgets

SummaryThis paper addresses the design optimization process of an energy harvesting device for scavenging energy from an e-gadget, utilizing its ”rocking” motion. The plucking mechanism inspired by the frequency up-conversion technique provides initial displacement exciting piezoelectric beams and increases the total number of excitations multiple times. The harvester is designed in conjunction with the multidimensional surrogate optimization algorithm to maximize the device’s performance considering the geometrical features of the concept and the constrained operating environment. The established numerical model is validated first using a set of experimental data. The obtained numerical results demonstrate that the developed 10.2″ size device produces 55 mJ in half-period when inclined at 45°, which is equivalent to generating 0.3 W. Considering that an iPad of the same size consumes around 3 W, the proposed energy harvester is capable of extending its battery life by 10%.

A novel strategy for the crossarm length optimization of PSSCs based on multi-dimensional global optimization algorithms

Prestressed stayed steel columns (PSSCs) offer a lightweight alternative for the design of slender compression columns. The stability of compression columns can be significantly enhanced by introducing crossarms. Previous research on this subject has primarily focused on load-carrying capacity estimation or analyses of the influencing factors of PSSCs. Thus, investigations of the design optimization of PSSCs remain scant. This work proposes a novel strategy for crossarm length optimization of PSSCs based on multi-dimensional global optimization algorithms. A multi-population genetic algorithm is introduced in the optimization process. The proposed optimization algorithm was demonstrated to be efficient and accurate in terms of determining the optimal crossarm length of PSSCs.

Deployable Convex Generalized Cylindrical Surfaces Using Torsional Joints

Abstract The ability to deploy a planar surface to a desired convex profile with a simple actuation can enhance foldable or morphing airfoils, deployable antennae and reflectors, and other applications where a specific profile geometry is desired from a planar sheet. A model using a system of rigid links joined by torsional springs of tailorable stiffness is employed to create an approximate curved surface when two opposing tip loads are applied. A system of equations describing the shape of the surface during deployment is developed. The physical implementation of the model uses compliant torsion bars as the torsion springs. A multidimensional optimization algorithm is presented to place joints to minimize the error from the rigid-link approximation and account for additional manufacturing and stress considerations in the torsion bars. A proof is presented to show that equal torsion spring spacing along the horizontal axis of deployed parabolic profiles will result in minimizing the area between the model’s rigid-link approximation and smooth curve. The model is demonstrated through the physical construction of a deployable airfoil surface and a metallic deployable parabolic reflector.

Improving Energy Efficiency of Main Oil Pipeline Systems by Method of Multidimensional Network Optimization of Oil Flows

The aim of this paper is to explore the organization of oil’s traffic from various oilfields through a system of main pipelines adapted to control the rheological properties of the pumped product due to rational oil blending of various oilfields at the nodal points of the pipeline system – at oil pumping stations with storage facilities. The current trend of increasing high-viscosity and high-pour-point oil production and the urgent need of their main pipeline transport are the main problem of our research. Its solution will provide an oil-transfer system from various oilfields that will minimize the total energy consumption for oil pumping. To determine the blending parameters at the nodal points we suggest to use the standard multidimensional optimization algorithm: the simplex method as the main calculation module. The objective function is presented in the form of total energy consumption for oil pumping, depending on the concentration of oil blending at the nodal points of the main oil pipeline system. We propose a method for calculating the objective function for any branched main oil pipeline system using algorithms for constructing a blending tree and determining its properties using the tree traversal algorithm. The issues of determining the limits of possible blending based on mass balance and quality reserve preservation of oils that delivered to consumers were also considered in our paper work. As an example, we solved this problem for an element of a main oil pipeline system with four oil blending nodes in the case of an oil viscosity increase of one of the suppliers. Carrying out multidimensional optimization of energy consumption for this system made it possible to increase its energy efficiency by more than 2%.

Gibbs energy minimization using Lagrange method of undetermined multipliers for electrochemical and thermodynamic modeling of a MCFC with internal steam reforming

Precise determination of the chemical equilibrium state is important for electrochemical and thermodynamic modeling of a molten carbonate fuel cell (MCFC). One method for determining the equilibrium state of a MCFC with internal reforming is to compute the total Gibbs free energy of the system (G) and minimize it by adjusting the molar amounts of each substance. Multi-dimensional optimization algorithms can be used for this purpose. The Lagrange method of undetermined multipliers as a powerful analytical solution is used in the present work to estimate chemical equilibrium state. Under this condition, the effects on voltage losses, output voltage, stack power, efficiency and molar portions of the exhaust chemical species at the anode and cathode are investigated, separately of such parameters as current density, reaction temperature, stack pressure as well as fuel and carbon dioxide utilization ratios. A simulation of a MCFC stack performance by the Lagrange method at a specified state, results in an efficiency of 50.3% and output power of 554.3 kW.

A MULTI-DIMENSIONAL CONFIGURATION ALGORITHM FOR MODULAR PRODUCT ARCHITECTURES

AbstractWith an increasing demand for product individualisation leading to increased product architecture complexity and -costs, modular kits are one common measure to cope with this issue. The management of such a modular kit as well as the methodical determination of a specific product variant is key to the manufacturer's success. As multiple influence factors need to be taken into account when configuring product variants, we propose a multi-dimensional geometric optimisation algorithm, allowing for prioritising varying customer demands and thereby determining the ideally balanced product variant.

Multi-objective optimization to balance thermal comfort and energy use in a mining camp located in the Andes Mountains at high altitude

The mining industry is the largest electricity consumer in Chile. Sustainability reports of Chilean mining companies show that electricity consumption of mining camps is 350–500 kWh/m2 per year. Despite cold climate conditions, mining camps show overheating, and 40% of the miners find them uncomfortable. Mining camps’ energy access is difficult because they are located in remote zones. This paper aims to optimize the building envelope and HVAC system to minimize the total energy consumption and eliminate the overheating risk of a real mining camp located at 4400 m.a.s.l. The mining camp is 30,000 m2, built of timber prefabricated lightweight modules and hosts 1700 workers. The electricity consumption of the baseline case is 330 kWh/m2year and shows overheating. Multi-objective optimization is implemented to minimizing the electricity consumption while avoiding overheating. A hybrid multidimensional optimization algorithm implemented in GenOpt, a building energy simulation program (EnergyPlus) and several scripts developed in Pyhthon for optimizing discrete variables and calculating the overheating risk of each thermal zone are coupled. Two different cases are optimized depending on the heating systems: electric heaters (Case I), which is the current situation; and heat pumps with chilled beams with free cooling option (Case II). This paper shows that an efficient HVAC system (Case II) is crucial for achieving thermal comfort and minimizing electricity consumption, which reaches 112.9 kWh/m2year, representing a significant reduction of 66% compared to the baseline case. The optimization process provides not only the optimum set of energy-efficient strategies but also a set of feasible solutions close to the optimum that allows flexibility to choose other strategies based on economic, transportation and on-site construction constraints.

Global best-guided oppositional algorithm for solving multidimensional optimization problems

This paper presents an alternative optimization algorithm to the literature optimizers by introducing global best-guided oppositional-based learning method. The procedure at hand uses the active and recent manipulation schemes of oppositional learning procedure by applying some modifications to them. The first part of the algorithm deals with searching the optimum solution around the current best solution by means of the ensemble learning-based strategy through which unfeasible and semi-optimum solutions have been straightforwardly eliminated. The second part of the algorithm benefits the useful merits of the quasi-oppositional learning strategy to not only improve the solution diversity but also enhance the convergence speed of the whole algorithm. A set of 22 optimization benchmark functions have been solved and corresponding results have been compared with the outcomes of the well-known literature optimization algorithms. Then, a bunch of parameter estimation problem consisting of hard-to-solve real world applications has been analyzed by the proposed method. Following that, eight widely applied constrained benchmark problems along with well-designed 12 constrained test cases proposed in CEC 2006 session have been solved and evaluated in terms of statistical analysis. Finally, a heat exchanger design problem taken from literature study has been solved through the proposed algorithm and respective solutions have been benchmarked against the prevalent optimization algorithms. Comparison results show that optimization procedure dealt with in this study is capable of achieving the utmost performance in solving multidimensional optimization algorithms.

Minimization of a mismatch time of movement of actuators of a throttle synchronization system*

The selection of optimal (in the sense of a given objective functional) design parameters of pneumatic and hydro-automatic systems is an actual scientific and technical task of computer-aided design. The problem of optimization of throttle hydraulic synchronization systems of actuators of various functional purposes operating under conditions of external dynamic loading is considered taking into consideration the criterion of minimizing the mismatch time of their relative movement in the process of performing the applied task. A generalized non-stationary mathematical model of a synchronization system consisting of several (more than two) power cylinders is proposed. The comparison of the efficiency of two multidimensional optimization algorithms – based on a Hooke-Jeeves method and a binary coded genetic algorithm was provided with the help of the developed software package with the example of a solution of a model problem. Recommendations on the practical application of said optimization methods for achieving the best convergence to the extreme value of a vector of controlled parameters were formulated. The created scientific software can be recommended for use in design organizations in the process of working out the design-layout scheme of the synchronization systems, including in the aerospace industry.