Two-step Optimization Approach Research Articles

A Two-Step Grid–Coordinate Optimization Method for a Wind Farm with a Regular Layout Using a Genetic Algorithm

Currently, most studies on the optimization of wind farm layouts on flat terrain employ a discrete grid-based arrangement method and result in irregular layouts that may damage the visual appeal of wind farms. To meet the practical requirements of wind farms, a two-step optimization method called “grid–coordinate” based on a genetic algorithm is proposed in this paper. The core idea is to initially determine the number of wind turbines and their initial positions using a grid-based approach, followed by a fine-tuning of the wind farm layout by moving the turbines in a row/column manner. This two-step process not only achieves an aesthetically pleasing arrangement but also maximizes power generation. This algorithm is conducted to optimize a 2 km × 2 km wind farm under three classic wind conditions, one improved wind condition, and a real wind condition employing both the Jensen and Gaussian wake models. To validate the effectiveness of the proposed method, the optimization of configurations based on different wake models was conducted, yielding results including the efficiency, total power output, number of wind turbines, and unit cost of electricity generation. These results were compared and analyzed against the classical literature. The findings indicate that the unit cost of electricity generation using the two-step optimization approach with the Gaussian wake model is higher than that of the initial grid optimization method. Additionally, varying the number of wind turbines can lead to instances of high power generation coupled with low efficiency. This phenomenon should be carefully considered in the wind farm layout optimization process.

Optimal Location of Electric Vehicle Charging Station in Reconfigured Radial Distribution Network

Electric vehicles are becoming increasingly popular because they are cleaner-burning and more efficient than combustion-engine automobiles. Due to the diminishing availability of fossil fuels and the carbon emissions produced by cars, electric vehicles (EV) have become a need for mobility in the near future. Electric car charging stations were established as a consequence of the increase in EVs. Electric car charging lowers voltage and increases real power loss in the radial distribution network. In order to mitigate real power loss and provide a stable voltage profile, the charging station has to be placed as efficiently as possible. The current research examines and elucidates the influence of electric vehicle charging stations (EVCS) on the balanced radial distribution network (BRDN) using particle swarm optimization (PSO). There are two steps involved in the planning process. The optimal placement for EVCS [1] in BRDN is identified in the first stage using PSO. The second stage uses reconfiguration to ensure higher EVCS stability. This two-step technique's main goal is to decrease the real power loss due to the placement of charging stations in the radial distribution network (RDN). The correctness of the suggested approach is expounded upon in four different cases. The second, third, and fourth cases use a two-step procedure, which is then compared to the base case. In the base case EVCS is ideally located in BRDN using PSO. The fourth case employs a concurrent two-step optimization approach and demonstrates superior performance compared to other cases. The suggested approach is implemented and evaluated on the IEEE 69 bus BRDN using the MATLAB software.

A novel two-step optimization approach for film water cooling of a photovoltaic module in real ambient conditions

Efficiency of photovoltaic (PV) modules decreases as they get warmer in real working conditions. One way to address this issue is to apply water-film cooling on the front surface of a PV module. In order to circulate water over the surface of a module, a power-consuming pumping system is required. This paper presents a novel two-step optimization algorithm for improving the water-film cooling system to maximize the net energy generation of a photovoltaic (PV) panel. In the first step, the fluctuations of the optimal water flow rate during a specified day are calculated and then ideal water flow rates on daily and monthly basis are determined. Since the value of the optimum specific water flow rate is a nonlinear function of ambient conditions, it was calculated through an iterative algorithm. In the second step, the appropriate activation time interval for a water-cooling system was determined to furthermore maximize power gain and minimize energy consumption. By optimizing both water flow rate and cooling system timing, a significant improvement in net efficiency was achieved, increasing from 13.98%, 13.85%, and 13.87% in June, July, and August to 14.82%, 14.86%, and 14.80% in Shiraz, Iran.

Location-allocation modelling for rational health planning: Applying a two-step optimization approach to evaluate the spatial accessibility improvement of newly added tertiary hospitals in a metropolitan city of China

The inequity of access to healthcare services is still one of the most long-lasting problems confronted by worldwide countries. Under such context where maldistributed healthcare resources have posed huge challenges in achieving cross-regional efficiency and equity of healthcare services, rational allocation of newly added healthcare resources has become rather critical to policy makers. To address this issue, we applied a two-step optimization approach to investigate the spatial allocation of newly added tertiary general healthcare resources in Chengdu, a metropolitan city of China. The case study of Chengdu was utilized as an example to illustrate the feasibility of such spatial optimization approach in practice in terms of supporting regional health planning related decision-making procedures in China, as well as evaluating the performance of healthcare resource allocation related strategies actually implemented. Using current and historical health planning data, we sought to optimize tertiary general hospitals’ locations to maximize population coverage of healthcare services in the first step, and to achieve equitable access to healthcare services among different residential locations via assigning the capacity (beds) to each hospital in the second step. Results suggested that the spatial optimization of newly added healthcare resources would theoretically enhance both efficiency and equity substantially. Specifically, if implemented in practice, such optimized spatial allocation of healthcare resources would theoretically contribute to improved efficiency as reflected by a 5% increase and a 15% increase in population coverage and the weighted median value of spatial accessibility, respectively. In addition, this would contribute to achieve enhanced equity as reflected by a 27% decrease in the weighted standard deviation of spatial access. These findings are anticipated to offer valuable policy implications to inform the spatial allocation decisions of healthcare resources in China as well as other countries confronted with similar challenges, and the two-step optimization approach could be applied to facilitate future rational health plannings.

Effects of Price Range Variation on Optimal Sizing and Energy Management Performance of a Hybrid Fuel Cell Vehicle

The usage of multi-objective cost functions (MOCFs) in sizing and energy management strategy (EMS) of fuel cell hybrid electric vehicles (FCHEVs) has expanded due to the participation of multiple technological and economic disciplines. To better understand the impact of price fluctuation on the component size and EMS of an FCHEV, this article proposed a sensitivity analysis methodology. First, a two-step optimization approach that considers hydrogen consumption, system degradation, and trip cost is used to minimize a MOCF of the Can-Am Spyder electric motorcycle simulator. Then, an effect analysis is carried out for the cost-optimal results under two driving profiles to understand the link between cost variation and system performance. These simulations indicate that each might result in different system sizes and EMS compromise. After that, an online optimization EMS based on sequential quadratic programming is used on a reduced-scale hardware-in-the-loop configuration to evaluate the simulation results with varied weights. Experimental results indicate that when an adequate size is used for each pair of weights, the EMS results in a 6% decrease in the trip cost.

Optimizing Spatial Location and Service Capacity of New Schools Toward Maximum Equity in the Distribution of Educational Resources

Educational facilities are an important part of public service facilities. The scientific planning of educational facilities is conducive to the optimal allocation of educational resources and the equalization of educational services. In view of the insufficient supply and uneven spatial distribution of urban educational service facilities, this study adopted an improved two-step optimization method to maximize the equality of school accessibility by optimizing the spatial location and service capacity of urban primary schools. First, the improved p-median model was constructed, and the Teitz–Bart algorithm was used to solve the model to site new primary schools. Second, a quadratic programming method was used to optimize the service capacity of new primary schools. Finally, the two-step floating catchment area (2SFCA) method was used to analyze and evaluate the accessibility of population centers to schools before and after the site selection and service capacity optimization of new schools. The results show that the improved two-step optimization approach can effectively determine the best locations and service capacity of new schools to improve the spatial accessibility of schools and realize the fair distribution of educational resources.

In Vivo Myelin Water Quantification Using Diffusion–Relaxation Correlation MRI: A Comparison of 1D and 2D Methods

Multidimensional Magnetic Resonance Imaging (MRI) is a versatile tool for microstructure mapping. We use a diffusion weighted inversion recovery spin echo (DW-IR-SE) sequence with spiral readouts at ultra-strong gradients to acquire a rich diffusion–relaxation data set with sensitivity to myelin water. We reconstruct 1D and 2D spectra with a two-step convex optimization approach and investigate a variety of multidimensional MRI methods, including 1D multi-component relaxometry, 1D multi-component diffusometry, 2D relaxation correlation imaging, and 2D diffusion-relaxation correlation spectroscopic imaging (DR-CSI), in terms of their potential to quantify tissue microstructure, including the myelin water fraction (MWF). We observe a distinct spectral peak that we attribute to myelin water in multi-component T1 relaxometry, T1-T2 correlation, T1-D correlation, and T2-D correlation imaging. Due to lower achievable echo times compared to diffusometry, MWF maps from relaxometry have higher quality. Whilst 1D multi-component T1 data allows much faster myelin mapping, 2D approaches could offer unique insights into tissue microstructure and especially myelin diffusion.

Rooster Colony Algorithm: A two-step Multi-Swarm Optimization Approach

Particle Swarm Optimization is a metaheuristic optimization algorithm inspired by the collective behavior of animal swarms where a set of candidate solutions, called particles, are randomly initialized in the search space, and their movements are iteratively updated based on their individual best solutions and the global best solution found by the swarm. This paper proposes a Multi-Swarm rooster colony algorithm (RCA) that considers a set of roosters, each owning a group of hens to compose a team. Each team (rooster and its hens) competes for the resource (food) with the other teams. From the combinatorial optimization point of view, each team analyzes part of the search space by an independent PSO algorithm with the same objective function. The RCA algorithm concurrently executes all PSO algorithms with different inertial weights for exploring different regions and the best solution (Gbest) of each team will compose the initial population for a new further centralized PSO algorithm that will exploit the previous solutions to search for the optimal one. Thus, the proposed RCA is composed of two steps, based on exploration and exploitation strategies to find an optimized solution in the search space. The results show that the proposed algorithm is competitive in solving well-known optimization functions. The objective is to apply this technique to solving real-life scheduling problems.

Investigation of the Laser Powder Bed Fusion Process of Ti-6.5Al-3.5Mo-1.5Zr-0.3Si Alloy

Laser powder bed fusion (LPBF) is an advanced manufacturing technology; however, inappropriate LPBF process parameters may cause printing defects in materials. In the present work, the LPBF process of Ti-6.5Al-3.5Mo-1.5Zr-0.3Si alloy was investigated by a two-step optimization approach. Subsequently, heat transfer and liquid flow behaviors during LPBF were simulated by a well-tested phenomenological model, and the defect formation mechanisms in the as-fabricated alloy were discussed. The optimized process parameters for LPBF were detected as laser power changed from 195 W to 210 W, with scanning speed of 1250 mm/s. The LPBF process was divided into a laser irradiation stage, a spreading flow stage, and a solidification stage. The morphologies and defects of deposited tracks were affected by liquid flow behavior caused by rapid cooling rates. The findings of this research can provide valuable support for printing defect-free metal components.

Towards Optimal Triage and Mitigation of Context-Sensitive Cyber Vulnerabilities

Cyber vulnerabilities are security deficiencies in computer and network systems of organizations, which can be exploited by an adversary to cause significant damage. The technology and security personnel resources currently available in organizations to mitigate the vulnerabilities are highly inadequate. As a result, systems routinely remain unpatched, thus making them vulnerable to security breaches from the adversaries. The potential consequences of an exploited vulnerability depend upon the context as well as the severity of the vulnerability, which may differ among networks and organizations. Furthermore, security personnel tend to have varying levels of expertise and technical proficiencies associated with different computer and network devices. There exists a critical need to develop a resource-constrained approach for effectively identifying and mitigating important context-sensitive cyber vulnerabilities. In this article, we develop an advanced analytics and optimization framework to address this need and compare our approach with rule-based methods employed in real-world cybersecurity operations centers, as well as a vulnerability prioritization method from recent literature. First, we propose a machine learning-based vulnerability priority scoring system (VPSS) to calculate the priority scores for each of the vulnerabilities found in an organization’s network and quantify organizational context-based vulnerability exposure. Next, we propose a decision-support system, which consists of a two-step sequential optimization approach. The first model selects the high priority vulnerability instances from the dense report subject to resource constraints, and the second model then optimally allocates them to the security personnel with matching skill types for mitigation. Experiment results conducted using a real-world vulnerability data set show that our approach 1) outperforms both the rule-based methods and the vulnerability prioritization method from literature in prioritizing context-sensitive vulnerabilities, which are found across highly susceptible organizationally relevant host machines, and 2) maximizes the pairs of vulnerability instance type and the respective security analyst skill type for optimal mitigation.

Heterogeneous Multi-Task Learning With Expert Diversity.

Predicting multiple heterogeneous biological and medical targets is a challenge for traditional deep learning models. In contrast to single-task learning, in which a separate model is trained for each target, multi-task learning (MTL) optimizes a single model to predict multiple related targets simultaneously. To address this challenge, we propose the Multi-gate Mixture-of-Experts with Exclusivity (MMoEEx). Our work aims to tackle the heterogeneous MTL setting, in which the same model optimizes multiple tasks with different characteristics. Such a scenario can overwhelm current MTL approaches due to the challenges in balancing shared and task-specific representations and the need to optimize tasks with competing optimization paths. Our method makes two key contributions: first, we introduce an approach to induce more diversity among experts, thus creating representations more suitable for highly imbalanced and heterogenous MTL learning; second, we adopt a two-step optimization (Finn et al., 2017 and Lee et al., 2020) approach to balancing the tasks at the gradient level. We validate our method on three MTL benchmark datasets, including UCI-Census-income dataset, Medical Information Mart for Intensive Care (MIMIC-III) and PubChem BioAssay (PCBA).

From Pressure Time Series Data to Flame Transfer Functions: A Framework for Perfectly-Premixed Swirling Flames

Abstract We present a two-step optimization (TSO) framework, which uses the pressure data of an unstable combustion process to estimate the Flame Transfer Function (FTF). From the pressure time series, we obtain the instability frequency and the amplitudes of the pressure fluctuations. The first optimization step is based on an acoustic network model of the combustor: the TSO approach uses the pressure data to find a simplified n-tau model, which reproduces the unstable combustion process. This step has already been validated for the Rijke tube, a laminar and a turbulent flame in Ghani et al. (2020). The major contribution of this work adds a second optimization loop to extend the n-tau model to the FTF: the gain and phase obtained by the n-tau model are used to fit a distributed time delay model. Our proposed method is applied to a turbulent, premixed, swirl-stabilized flame operated at two power ratings and two swirler positions. The model results for the FTFs are compared against experimentally measured FTFs for these four configurations and all agree well. To the best of our knowledge, this is the first attempt to estimate the complex-valued FTF solely based on pressure measurements. Compared to classical methods for FTF determination such as experimental tests or numerical simulations, our TSO approach is fast and accurate. The proposed framework is suitable for perfectly-premixed flames stabilized by a swirling flow field, requires two pressure sensors and is easy to implement.

A two-step optimization approach for structures investigation of Pd-Ir bimetallic nanoclusters

The structures of nanoalloys are crucial for understanding their catalytic performance because the stable structures can affect the activity and selectivity of nanocatalysts. Therefore, investigating the stable structures of nanoalloys is important to understand their catalytic activities. In this article, a two-step optimization approach by combining a basin hoping genetic algorithm (BHGA) and DFT calculation is employed to investigate the structural stability of Pd-Ir alloy nanoclusters. Different compositions (Pd and Ir atoms proportion) and different initial configurations of 38-atom Pd-Ir alloys are considered. The combination of BHGA and DFT method can effectively find the stable structures of truncated octahedral (TO) configurations for 38-atom Pd-Ir alloys with high accuracy and low time complexity. Furthermore, the formation energy and bond energy of Pd-Ir clusters are calculated and analyzed, the results show the bond strength follows Pd-Pd > Pd-Ir > Ir-Ir. The most stable configuration is Pd6Ir32 with all the core sites are occupied by Pd, which shows better electrochemical performance.

Two-Step Joint Optimization with Auxiliary Loss Function for Noise-Robust Speech Recognition.

In this paper, a new two-step joint optimization approach based on the asynchronous subregion optimization method is proposed for training a pipeline model composed of two different models. The first-step processing of the proposed joint optimization approach trains the front-end model only, and the second-step processing trains all the parameters of the combined model together. In the asynchronous subregion optimization method, the first-step processing only supports the goal of the front-end model. However, the first-step processing of the proposed approach works with a new loss function to make the front-end model support the goal of the back-end model. The proposed optimization approach was applied, here, to a pipeline composed of a deep complex convolutional recurrent network (DCCRN)-based speech enhancement model and a conformer-transducer-based ASR model as a front-end and a back-end, respectively. Then, the performance of the proposed two-step joint optimization approach was evaluated on the LibriSpeech automatic speech recognition (ASR) corpus in noisy environments by measuring the character error rate (CER) and word error rate (WER). In addition, an ablation study was carried out to examine the effectiveness of the proposed optimization approach on each of the processing blocks in the conformer-transducer ASR model. Consequently, it was shown from the ablation study that the conformer-transducer-based ASR model with the joint network trained only by the proposed optimization approach achieved the lowest average CER and WER. Moreover, the proposed optimization approach reduced the average CER and WER on the Test-Noisy dataset under matched noise conditions by 0.30% and 0.48%, respectively, compared to the approach of separate optimization of speech enhancement and ASR. Compared to the conventional two-step joint optimization approach, the proposed optimization approach provided average CER and WER reductions of 0.22% and 0.31%, respectively. Moreover, it was revealed that the proposed optimization approach achieved a lower average CER and WER, by 0.32% and 0.43%, respectively, than the conventional optimization approach under mismatched noise conditions.

Techno-economic assessment of post-combustion CO2 capture using aqueous piperazine at different flue gas compositions and flowrates via a general optimization methodology

An overall techno-economic assessment of a post-combustion CO2 capture process using aqueous piperazine is presented. A two-step techno-economic optimization approach is developed and implemented. First, two-objective technical optimization problems are solved at different combinations of CO2 capture efficiencies and CO2 concentrations in the flue gas, which aim at minimizing the specific equivalent work while maximizing the volume-based productivity of the capture process. Increasing minimum specific reboiler duties between 2.4 and 2.9 MJthkgCO2captured−1 are obtained for decreasing flue gas CO2 concentrations between 33 and 4 vol%, on a dry basis, with absorber packing heights below 10 m. Then, costs are computed at the technical optimal conditions as a function of the CO2 capture efficiency, flue gas flowrate and CO2 concentration. As a result, maps of minimum cost of CO2 captured, of minimum cost of CO2 avoided, and of minimum cost of CO2 generated by the CO2 point source are obtained, as well as of the associated optimal operating conditions and performance indicators of the capture process, which allow to assess the economic feasibility and performance of the capture process under different cost scenarios and assumptions when applied to different flue gas compositions and flowrates typical of industrial CO2 intensive point sources.

Computing the shape gradient of stellarator coil complexity with respect to the plasma boundary

Coil complexity is a critical consideration in stellarator design. The traditional two-step optimization approach, in which the plasma boundary is optimized for physics properties and the coils are subsequently optimized to be consistent with this boundary, can result in plasma shapes which cannot be produced with sufficiently simple coils. To address this challenge, we propose a method to incorporate considerations of coil complexity in the optimization of the plasma boundary. Coil complexity metrics are computed from the current potential solution obtained with the REGCOIL code (Landreman,Nucl. Fusion, vol. 57, 2017, 046003). While such metrics have previously been included in derivative-free fixed-boundary optimization (Drevlaket al.,Nucl. Fusion, vol. 59, 2018, 016010), we compute the local sensitivity of these metrics with respect to perturbations of the plasma boundary using the shape gradient (Landreman & Paul,Nucl. Fusion, vol. 58, 2018, 076023). We extend REGCOIL to compute derivatives of these metrics with respect to parameters describing the plasma boundary. In keeping with previous research on winding surface optimization (Paulet al.,Nucl. Fusion, vol. 58, 2018, 076015), the shape derivatives are computed with a discrete adjoint method. In contrast with the previous work, derivatives are computed with respect to the plasma surface parameters rather than the winding surface parameters. To further reduce the resolution required to compute the shape gradient, we present a more efficient representation of the plasma surface which uses a single Fourier series to describe the radial distance from a coordinate axis and a spectrally condensed poloidal angle. This representation is advantageous over the standard cylindrical representation used in the VMEC code (Hirshman & Whitson,Phys. Fluids, vol. 26, 1983, pp. 3553–3568), as it provides a uniquely defined poloidal angle, eliminating a null space in the optimization of the plasma surface. In comparison with previous spectral condensation methods (Hirshman & Breslau,Phys. Plasmas, vol. 5, 1998, p. 2664), the modified poloidal angle is obtained algebraically rather than through the solution of a nonlinear optimization problem. The resulting shape gradient highlights features of the plasma boundary that are consistent with simple coils and can be used to couple coil and fixed-boundary optimization.

Fuel cell-supercapacitor topologies benchmark for a three-wheel electric vehicle powertrain

This paper compares three optimal hybrid energy system configurations, namely full-active, semi-active and passive, for the particular purpose of assessing the viability of utilizing the passive architecture in a three-wheel electric vehicle composed of a fuel cell (FC) and a supercapacitor. In this respect, the characteristics of these configurations are investigated through three steps. Firstly, the mathematical model of each component is developed by employing experimental data. Subsequently, the optimal size of each topology is determined by a two-step optimization approach. This approach is based on the optimized sizing of power sources, employing a metaheuristic optimization algorithm, and optimal power flow sharing between the sources with the aim of satisfying the requested power while declining the fuel consumption and enhancing the system’s lifetime. Finally, the best-achieved size of each architecture is compared in terms of trip cost, capital cost, and the system weight. The obtained results show that passive topology can reduce the trip cost by 14.8% and 6.4% compared to full-active and semi-active ones, respectively. However, the active architecture results in less degradation in the FC compared to the other two topologies. Furthermore, a validation phase is done under a real driving profile and the results are further discussed.

Designing stable bimetallic nanoclusters via an iterative two-step optimization approach

Due to the myriad ways in which atoms of two different elements may arrange themselves in a lattice, the design of bimetallic nanoparticles constitutes a complex combinatorial problem necessitating the development of advanced optimization algorithms.

Meta-heuristic algorithm for aircraft pre-tactical conflict resolution with altitude and heading angle change maneuvers

Aircraft conflict resolution is of great importance for the safe and efficient management of air traffic. This study proposes a two-step optimization approach for the aircraft conflict resolution problems within the pre-tactical time window in generic free route airspace. Safe separation between aircraft pairs is maintained using either altitude or heading angle change maneuvers in a pre-defined buffer zone within the boundaries of the airspace. The first step of the model aims to minimize the total number of conflicting aircraft and the total fuel consumption together using altitude change maneuvers. A mixed-integer linear programming model is proposed for the first step but, due to the high computational time, a metaheuristic algorithm (simulated annealing) was developed. If the altitude change does not resolve all conflicts in the first step, the proposed model implements heading angle change maneuvers with minimum extra fuel burn in the second step. A nonlinear programming model is presented for the second step. Numerical results show that the proposed approach can resolve all conflicts in less than 4 min for the highest traffic flow rate.

A statistical learning approach to determine optimal sizing & investment timing of commercial-scale distributed energy resources

The problem of optimal sizing and investment timing for a portfolio of gas-fired and photovoltaic (PV) generation is presented and solved using an optimization- classification technique. It is assumed that the demand, the prices of natural gas, and PV technology are stochastic processes. Our methodology takes advantage of decomposing the problem into two sub-problems. First, the optimal sizing problem is solved using dynamic programming and most likely solutions are identified as clusters. Then, the Investment time problem is formulated as a Real Option for each cluster to determine optimal timing. Although the two-step optimization approach can successfully close the loop between operational dynamics and investment decisions, we are also interested in discovering patterns in a multidimensional space of input parameters that make a certain combination of assets optimal among dozens of discrete choices. On that note, by applying Recursive Partitioning algorithm, decision trees are developed to estimate the structure of solutions rendered from optimization models by a rule-based system. Despite the high level of accuracy, the initial model is biased in favor of highly frequent clusters, and discards the optimal clusters resulted from extreme market behaviors. Value at Risk (VaR) is employed as a risk measure to demonstrate the enhancement risk performance. Finally, in order to investigate the robustness of the results, we conduct extensive sensitivity analysis over different parameter settings. The proposed model can be thought of as a statistically optimal summarizer of optimization models that enables decision makers to have an insight into optimal investment strategies according to characteristics of the building and the long-term energy market outlook.