Conventional Optimization Methods Research Articles

Generating three-dimensional structural topologies via a U-Net convolutional neural network

In this paper, we propose a deep learning based neural network to generate three-dimensional structural topologies in an efficient way. The method consists of three steps. First, conventional three dimensional solid isotropic microstructures with penalization (SIMP) method is utilized to generate datasets consisting of various domain sizes and boundary conditions. Second, a deep learning neural network based on U-Net architecture is constructed and trained by the generated datasets. Third, by feeding new cases with different domain sizes and boundary conditions into the network, near optimal results can be directly obtained without any needs of optimization iterations and finite element analysis. Compared with conventional topology optimization methods as well as recent development of machine learning approaches, our proposed method has two advantages: (1) the design boundary conditions are directly mapped with the 3D optimized structures such that no further dependency on the conventional topology optimization algorithm is required once the model is trained, and (2) topology optimization problems with variable design domain sizes can be supported instead of requiring its size to be fixed as the input of the neural network. Experiments demonstrate that once trained, our deep learning based topology optimization method can realize near optimal three dimensional topology prediction using negligible calculation cost.

Adaptive Particle Swarm Optimization of PID Gain Tuning for Lower-Limb Human Exoskeleton in Virtual Environment

Tuning of a proportional-integral-derivative (PID) controller for a complex multi-joint structure, such as an exoskeleton, using conventional methods is difficult and imprecise. In this paper, an optimal PID tuning method for a 3-dimensional model of a lower-limb human exoskeleton in gait training condition is presented. The dynamic equation of the human-exoskeleton is determined using a Lagrangian approach, and its transfer function is established in a closed-loop control system. PID controller gains, initialized by the Ziegler–Nichols (Z-N) method, are used as the input to an adaptive particle swarm optimization (APSO) algorithm for minimizing the multi-joint trajectory error. The optimized controller is tested in the Gazebo virtual environment and compared with the Z-N and conventional optimization methods. The numerical analysis shows that the PID controller tuned by a combination of Z-N and APSO improves the performance of a lower-limb human exoskeleton in gait training.

Design of optical meta-structures with applications to beam engineering using deep learning

Nanophotonics is a rapidly emerging field in which complex on-chip components are required to manipulate light waves. The design space of on-chip nanophotonic components, such as an optical meta surface which uses sub-wavelength meta-atoms, is often a high dimensional one. As such conventional optimization methods fail to capture the global optimum within the feasible search space. In this manuscript, we explore a Machine Learning (ML)-based method for the inverse design of the meta-optical structure. We present a data-driven approach for modeling a grating meta-structure which performs photonic beam engineering. On-chip planar photonic waveguide-based beam engineering offers the potential to efficiently manipulate photons to create excitation beams (Gaussian, focused and collimated) for lab-on-chip applications of Infrared, Raman and fluorescence spectroscopic analysis. Inverse modeling predicts meta surface design parameters based on a desired electromagnetic field outcome. Starting with the desired diffraction beam profile, we apply an inverse model to evaluate the optimal design parameters of the meta surface. Parameters such as the repetition period (in 2D axis), height and size of scatterers are calculated using a feedforward deep neural network (DNN) and convolutional neural network (CNN) architecture. A qualitative analysis of the trained neural network, working in tandem with the forward model, predicts the diffraction profile with a correlation coefficient as high as 0.996. The developed model allows us to rapidly estimate the desired design parameters, in contrast to conventional (gradient descent based or genetic optimization) time-intensive optimization approaches.

Statistical tolerance allocation design considering form errors based on rigid assembly simulation and deep Q-network

Consideration of form errors involves real machining features in tolerance modeling but increases uncertainties in functional requirement estimation, when tackling the trade-off between the cost and precision performance. In this paper, a statistical tolerance allocation method is presented to solve this problem. First of all, a top-down stepwise designing procedure is designed for complex products, and a combination of Jacobian matrix and Skin Model Shapes is applied in modeling the mechanical joints. Then, rigid assembly simulations of point-based surfaces are further advanced to provide an accurate estimation of the assembly state, through considering physical constraints and termination conditions. A mini-batch gradient descent method and a backtracking strategy are also proposed to promote computational efficiency. Finally, a deep Q-network is implemented in optimal computation after characterizing the systematic state, action domain, and reward function. The general tolerance scheme is then achieved using the trained Q-network. The results of 6 experiments each with 200 samples show the proposed method is capable of assessing tolerance schemes with 35.2% and 47.2% lower manufacturing costs and 16.7% and 28.3% higher precision maintenance on average than conventional particle swarm optimization and Monte Carlo method respectively.

Parent Nested Optimizing Structure for Vibration Reduction in Floating Wind Turbine Structures

A tuned mass damper (TMD) is a system that effectively reduces the vibrations of floating offshore wind turbines (FOWTs). To maximize the performance of TMDs, it is necessary to optimize their design parameters (i.e., stiffness, damping, and installation location). However, this optimization process is challenging because of the existence of multiple local minima. Although various methods have been proposed to determine the global minimum (e.g., exhaustive search, genetic algorithms, and artificial fish swarm algorithms), they are computationally intensive. To address this issue, a novel optimization approach based on a parent nested optimizing structure and approximative search is proposed in this paper. The approximative search determines an initial parameter set (close to the optimal set) with fewer calculations. Then, the global minimum can be rapidly determined using the nested and parent optimizers. The effectiveness of this approach was verified with an FOWT exposed to stochastic winds. The results show that this approach is 30–55 times faster than a conventional global optimization method.

Simultaneous optimization approach for combined control–structural design versus the conventional sequential optimization method

Although controller devices highly improve the seismic performance of civil structures, they usually incur enormous financial costs. A variety of sequential methods for minimizing the cost function have been proposed in the literature. In most of these methods, the control system is optimally designed after the best structural configuration is provided. However, such sequential procedures are unable to yield the best overall design. This paper discusses a combined structural and control optimization approach in which the structural mass and controlled system energy are simultaneously minimized. To this end, a twofold objective function is defined by linearly combining the structural mass and linear quadratic regulator (LQR) performance index. It is shown that the optimal value of this objective function depends on the initial condition, and to circumvent this problem, an alternative objective function is introduced which allows for solving the problem of initial condition dependency. Given the complexity of the problem, a variable neighborhood search (VNS) metaheuristic method is developed. The performance of the developed method is demonstrated through case studies involving the determination of structural responses for shear-type frames. The case studies are presented for evaluating and comparing the effectiveness of the proposed simultaneous technique and the conventional sequential method. The responses of the structures are determined under an array of strong ground motions. The results of the comparative analyses revealed that the simultaneously optimized cases using the proposed methodology had superior dynamic performance compared to the sequentially optimized cases.

Multiobjective Design Optimization of an IPMSM for EVs Based on Fuzzy Method and Sequential Taguchi Method

The Taguchi optimization method is an efficient method for motor design optimization. However, it is hard to handle the multiobjective motor optimization problem with big design space for the parameters. To deal with this problem, in this article, a fuzzy method and sequential Taguchi method to optimize an inter permanent magnet synchronous motor (IPMSM) is employed. The fuzzy inference system is introduced to convert the multiple objectives to a single-objective optimization problem. The sequential Taguchi method is used to optimize the structural parameters at multiple levels to improve the accuracy of optimization. After the optimal selection analysis, the best combination of motor structure factors is obtained. By comparing the optimization result of the proposed method with that of the conventional Taguchi optimization method, the effectiveness and superiority of the proposed method are verified.

A novel method of global optimisation for wavefront shaping based on the differential evolution algorithm

This paper proposes a novel wavefront-shaping-based focusing method, by introducing the differential evolution algorithm (DEA), thereby realising a faster convergence rate and improved enhancement compared to rival algorithms. Via simulations, we show that our proposed DEA-based approach delivers the best focusing performance irrespective of the influence of noise. Experimental results demonstrate that the DEA boosts the enhancement for an equivalent number of measurements compared with conventional optimisation methods. Furthermore, we reveal the influence of certain DEA parameters, leading to the emergence of many modified DEAs that perform impressively. The proposed DEA-based method simplifies the computational complexity and implementation process of wavefront shaping, offering useful insights for the future study of optimisation algorithms for wavefront shaping, as well as potential for practical applications, such as deep tissue focusing.

A Novel Graphics-Based Multi-Epoch Power Adjustment Strategy for WPCNs

In this paper, we focus on a wireless powered communication network where a hybrid access point can wirelessly activate the power of source nodes, and receive their information. Considering the time-switching protocol that implies energy harvesting, and energy usage are separated by time, a novel graphics-based multi-epoch power adjustment (GB-MPA) strategy is proposed to maximize the sum-throughput over a finite time horizon consisting of multiple transmission epochs. The proposed strategy relies on graphical constraint conditions, and allows the elimination of restrictions corresponding to the objective of throughput maximization. Moreover, the proposed GB-MPA strategy can be combined with the time-switching factor optimization by employing an alternating optimization procedure for performance enhancement. Simulation results show the accuracy of the proposed strategy, reduced complexity compared with the conventional convex optimization method, and the existing multi-epoch power adjustment strategy, and the compatibility with the alternating optimization procedure for developing the joint power, and time allocation scheme.

Multi-criteria decision making monarch butterfly optimization for optimal distributed energy resources mix in distribution networks

The optimal integration of distributed energy resources (DERs) is a multiobjective and complex combinatorial optimization problem that conventional optimization methods cannot solve efficiently. This paper reviews the existing DER integration models, optimization and multi-criteria decision-making approaches. Further to that, a recently developed monarch butterfly optimization method is introduced to solve the problem of DER mix in distribution systems. A new multiobjective DER integration problem is formulated to find the optimal sites, sizes and mix (dispatchable and non-dispatchable) for DERs considering multiple key performance objectives. Besides, a hybrid method that combines the monarch butterfly optimization and the technique for order of preference by similarity to ideal solution (TOPSIS) is proposed to solve the formulated large-scale multi-criteria decision-making problem. Whilst the meta-heuristic optimization method generates non-dominated solutions (creating Pareto-front), the TOPSIS approach selects that with the most promising outcome from a large number of alternatives. The effectiveness of this approach is verified by solving single and multiobjective dispatchable DER integration problems over the benchmark 33-bus distribution system and the performance is compared with the existing optimization methods. The proposed model of DER mix and the optimization technique significantly improve the system performance in terms of average annual energy loss reduction by 78.36%, mean node voltage deviation improvement by 9.59% and average branches loadability limits enhancement by 50%, and minimized the power fluctuation induced by 48.39% renewable penetration. The proposed optimization techniques outperform the existing methods with promising exploration and exploitation abilities to solve engineering optimization problems.

An Adaptive Particle Swarm Optimization Algorithm for Unconstrained Optimization

Conventional optimization methods are not efficient enough to solve many of the naturally complicated optimization problems. Thus, inspired by nature, metaheuristic algorithms can be utilized as a new kind of problem solvers in solution to these types of optimization problems. In this paper, an optimization algorithm is proposed which is capable of finding the expected quality of different locations and also tuning its exploration-exploitation dilemma to the location of an individual. A novel particle swarm optimization algorithm is presented which implements the conditioning learning behavior so that the particles are led to perform a natural conditioning behavior on an unconditioned motive. In the problem space, particles are classified into several categories so that if a particle lies within a low diversity category, it would have a tendency to move towards its best personal experience. But, if the particle’s category is with high diversity, it would have the tendency to move towards the global optimum of that category. The idea of the birds’ sensitivity to its flying space is also utilized to increase the particles’ speed in undesired spaces in order to leave those spaces as soon as possible. However, in desirable spaces, the particles’ velocity is reduced to provide a situation in which the particles have more time to explore their environment. In the proposed algorithm, the birds’ instinctive behavior is implemented to construct an initial population randomly or chaotically. Experiments provided to compare the proposed algorithm with the state-of-the-art methods show that our optimization algorithm is one of the most efficient and appropriate ones to solve the static optimization problems.

Analytical model of power system hardening planning for long-term risk reduction

Hardening components is an effective way to decrease the load loss risk caused by component outages in power systems. The system hardening against the long-term risk usually faces the computation burden problem brought up by the risk evaluation. This paper proposes a deterministic hardening planning model to minimize the long-term system risk of load curtailment, which eases the computational cost concern. To accomplish this task, a set of system events with load loss and corresponding load curtailments are obtained by an improved Monte Carlo simulation. An analytical function of system risk index with respect to the unavailability of components is derived and can calculate the risk index rapidly. Then, the deterministic model is constructed by applying the analytical function into the stochastic problem of system hardening planning. The greedy algorithm is developed to solve the model. The proposed model and method improve the computation efficiency by avoiding the repeated time-consuming risk evaluations. Case studies are conducted on the RBTS, RTS79, and a modified RTS96 system. Performances of the proposed model and method are compared with that of the conventional reliability optimization method (CROM). Results demonstrate that the model obtains better solution than the existing study on hardening planning for long-term risk, and has higher computation efficiency than CROM.

Lattice structure design optimization coupling anisotropy and constraints of additive manufacturing

Replacing solid structures with lattice structure is a way enabled by additive manufacturing (AM) to realize part lightweight design. Conventional design optimization method based on homogeneous periodic lattice structure cannot achieve the optimal structure without taking the stress magnitude and orientation into account. A design optimization method of heterogeneous conformal lattice structure coupling constraints and anisotropy of AM based on principal stress lines (PSL) is proposed. (1) The PSL is calculated based on finite element analysis to visualize the path of load transfer. (2) The load-adapted lattice structure is generated guided by the PSL. (3) In order to further optimize lattice structure, the lattice structure optimization model is established by coupling anisotropy and constraints of AM based on the fused deposition modeling (FDM) experiment. Taking a cantilever beam as a case, the maximum force-to-weight ratio and the stiffness-to-weight ratio of the optimized heterogeneous conformal lattice structure are increased by 11.8% and 41.8% respectively compared with homogeneous conformal lattice structure, which verified the feasibility of the proposed method.

A variable neighbourhood search enhanced estimation of distribution algorithm for quadratic assignment problems

Quadratic Assignment Problem (QAP) is one of the most complex combinatorial optimization problems. Many real-world problems such as printed circuit board design, facility location problems, assigning gates to airplanes can be modelled as QAP. Problems of size greater than 35 is not able to solve optimally using conventional optimization methods. This warrants the use of evolutionary optimization methods for obtaining optimal or near optimal solutions for QAPs. This work proposes a hybridization on a univariate Estimation of Distribution Algorithm, namely the Population Based Incremental Learning Algorithm (PBILA), with Variable Neighbourhood Search (VNS) for solving QAPs. The proposed algorithm is employed to solve benchmark instances of QAP and the results are reported. The results of this work reveals that PBILA on its own is not efficient for solving the QAPs. However, when hybridised with VNS, the algorithm performs well providing best known solutions for 95 test instances out of the 101 instances considered. For most of the test instances, the percentage deviation is less than one percentage. The overall average percentage deviation of the obtained solutions from the best-known solutions is 0.037%, which is a significant improvement when compared with state-of-the-art algorithms.

Efficient topology optimization based on DOF reduction and convergence acceleration methods

This paper proposes a highly efficient topology optimization using two accelerated methods, which can reduce the degrees of freedom (DOFs) of the finite element equations and accelerate the iteration convergence of the topology optimization. For the DOF reduction, a method based on the empty elements and the displacement change during the topology iterations is presented to remove the DOFs from the finite element equations. For the convergence acceleration, a gray-scale suppression method is proposed to accelerate the polarization of design variables which accelerates the iteration convergence of the topology optimization. Three numerical examples including 2D and 3D cases are tested, and the results show that the proposed method can significantly improve the efficiency of the topology optimization and obtain the optimization results with the same accuracy. The computational time is only about 7% - 29% compared to the conventional topology optimization method.

Water Cycle Algorithm for Modelling of Fermentation Processes

The water cycle algorithm (WCA), which is a metaheuristic method inspired by the movements of rivers and streams towards the sea in nature, has been adapted and applied here for the first time for solving such a challenging problem as the parameter identification of fermentation process (FP) models. Bacteria and yeast are chosen as representatives of FP models that are subjected to parameter identification due to their impact in different industrial fields. In addition, WCA is considered in comparison with the genetic algorithm (GA), which is another population-based technique that has been proved to be a promising alternative of conventional optimisation methods. The obtained results have been thoroughly analysed in order to outline the advantages and disadvantages of each algorithm when solving such a complicated real-world task. A discussion and a comparative analysis of both metaheuristic algorithms reveal the impact of WCA on model identification problems and show that the newly applied WCA outperforms GA with regard to the model accuracy.

Method for rapid deployment of low-cost sensors for a nationwide project in the Internet of things era: Air quality monitoring in Taiwan

When the air quality problem of PM2.5 first raised public attention and an emerging low-cost sensor technology appeared suitable as a monitoring measure for said problem, Taiwan’s Environmental Protection Administration devised a nationwide project involving large-scale sensor deployment for effective pollution monitoring and management. However, the conventional siting optimization methods were inadequate for deploying thousands of sensors. Therefore, this study develops a rapid deployment method. The current results may serve as a reference for the Taiwan government for use in the aforementioned nationwide project, which is an environmental Internet of things–based plan involving 10,200 sensors to be deployed throughout the country. The four monitoring targets are classified as types of industry, traffic areas, communities, and remoteness, and a three-phase implementation structure is devised in the method. The open-source geographic information system software named QGIS was used to implement the proposed method with relevant spatial data from local open-data resources, which generated new, necessary geographic features and estimated sensor deployment quantity in Taiwan. The deployment result of the 10,200 sensors is 4790 in the type of industry, 708 of the traffic area, 3935 of the communities, and 767 of remoteness. The proposed method could serve as a useful foundation for the sensor deployment of environmental Internet of things. Policymakers may apply this method to budget allocation or integrate this method alongside conventional siting methods for the modification of deployment results based on the local monitoring requirements.

Optimal design of Kaibel dividing wall columns based on improved particle swarm optimization methods

Dividing wall columns (DWCs) are able to reduce operating costs and save capital costs for distillation columns, which verifies that DWC is a useful strategy in terms of distillation process intensification. DWCs are better choices than the corresponding conventional distillation sequences from both economical and environmental point of views. As DWC saves energy considerably and reduces CO2 emissions, it proves to be a breakthrough towards sustainable distilling. The four-product Kaibel DWC can further intensify the distillation process, and save energy cost about 40%. However, due to the complicated structures and strong interactions, the optimal design of the four-product Kaibel DWC is challenging to solve through conventional optimization methods. Therefore, this paper investigates the applicability of probabilistic global optimization algorithms, including standard particle swarm optimization (PSO), chaotic PSO, cellular PSO, and quantum-behaved PSO algorithms. This paper aims to explore the most appropriate improved PSO algorithm for the Kaibel DWC. The standard PSO and chaotic PSO show the premature convergence in the optimization process, while the cellular PSO and quantum-behaved PSO can prevent premature convergence. The chaotic PSO algorithm is more appropriate for the optimization of the continuous function, and it is less suitable for the optimization of the Kaibel DWC. The quantum-behaved PSO algorithm is relatively not appropriate for the optimization of the Kaibel DWC because of the long calculation time for rigorous simulation. The cellular PSO algorithm, based on the concept of cellular neighborhood, is the most appropriate algorithm for the optimization of the Kaibel DWC.

A data-driven evolutionary algorithm for wind farm layout optimization

The wind farm layout model is to optimize the location of wind turbines to maximize the power output of the wind farm. Due to the complexity of the wind farm layout problem, the computation of objective function costs lots of time. To reduce the high computational cost while maintaining the solution performance, a data-driven evolutionary algorithm is proposed. An adaptive differential evolution algorithm (ADE) is proposed as the solver of the wind farm layout model. The adaption mechanism of ADE benefits the automatic adjustment of parameters in the mutation and crossover operators to achieve the optimal solution. The general regression neural network (GRNN) algorithm builds the data-driven surrogate model. The data-driven surrogate model is trained and updated using the data generated by the evolutionary algorithm throughout the evolution process. Through the data-driven surrogate model, the objective function is fast approximated and the bad candidate solutions are identified. The algorithm efficiency is greatly improved by fast filtering the bad candidate solutions. The ADE-GRNN is compared to other three conventional optimization methods based on two different wind scenarios. The results show the super-performance of ADE-GRNN in complex situations in terms of power output and execution time.

Bacteria foraging optimisation algorithm based optimal control for doubly‐fed induction generator wind energy system

In this study, an optimisation method, based on bacteria foraging, is investigated to tune the parameters of the proportional–integral (PI) controllers in a doubly-fed induction generator (DFIG) wind energy system connected to the grid. The generator is connected to the grid directly at the stator and through the back-to-back converter at the rotor. The control system includes PI controllers, at the rotor side, to regulate the rotor currents and PI controller to regulate the dc-link voltage for efficient power transfer. The control parameters, of three PI controllers, are optimised offline using the bacteria foraging optimisation algorithm and a modelled DFIG wind energy system. Various performance criteria, based on the tracking errors, are used to assess the efficiency of the optimisation method. Furthermore, the conventional tuning method and genetic algorithm optimisation method are conducted and compared to the bacteria foraging optimisation method to demonstrate its advantages. The optimised control parameters are evaluated on a DFIG wind energy experimental setup. Experimental and simulation results are provided to validate the effectiveness of each optimisation method.