Deterministic Optimization Methods Research Articles

A Scoping Review on Simulation-Based Design Optimization in Marine Engineering: Trends, Best Practices, and Gaps

AbstractThis scoping review assesses the current use of simulation-based design optimization (SBDO) in marine engineering, focusing on identifying research trends, methodologies, and application areas. Analyzing 277 studies from Scopus and Web of Science, the review finds that SBDO is predominantly applied to optimizing marine vessel hulls, including both surface and underwater types, and extends to key components like bows, sterns, propellers, and fins. It also covers marine structures and renewable energy systems. A notable trend is the preference for deterministic single-objective optimization methods, indicating potential growth areas in multi-objective and stochastic approaches. The review points out the necessity of integrating more comprehensive multidisciplinary optimization methods to address the complex challenges in marine environments. Despite the extensive application of SBDO in marine engineering, there remains a need for enhancing the methodologies’ efficiency and robustness. This review offers a critical overview of SBDO’s role in marine engineering and highlights opportunities for future research to advance the field.

Optimal operation of the dam reservoir in real time based on generalized structure of group method of data handling and optimization technique

The historical data on water intake into the reservoir is collected and used within the framework of a deterministic optimization method to determine the best operating parameters for the dam. The principles that have been used to extract the best values of the flow release from the dam may no longer be accurate in the coming years when the inflow to dams will be changing, and the results will differ greatly from what was predicted. This represents this method’s main drawback. The objective of this study is to provide a framework that can be used to guarantee that the dam is running as efficiently as possible in real time. Because of the way this structure is created, if the dam’s inflows change in the future, the optimization process does not need to be repeated. In this case, deep learning techniques may be used to restore the ideal values of the dam’s outflow in the shortest amount of time. This is achieved by accounting for the environment’s changing conditions. The water evaluation and planning system simulator model and the MOPSO multi-objective algorithm are combined in this study to derive the reservoir’s optimal flow release parameters. The most effective flow discharge will be made feasible as a result. The generalized structure of the group method of data handling (GSGMDH), which is predicated on the results of the MOPSO algorithm, is then used to build a new model. This model determines the downstream needs and ideal release values from the reservoir in real time by accounting for specific reservoir water budget factors, such as inflows and storage changes in the reservoir. Next, a comparison is drawn between this model’s performance and other machine learning techniques, such as ORELM and SAELM, among others. The results indicate that, when compared to the ORELM and SAELM models, the GSGMDH model performs best in the test stage when the RMSE, NRMSE, NASH, and R evaluation indices are taken into account. These indices have values of 1.08, 0.088, 0.969, and 0.972, in that order. It is therefore offered as the best model for figuring out the largest dam rule curve pattern in real time. The structure developed in this study can quickly provide the best operating rules in accordance with the new inflows to the dam by using the GSGMDH model. This is done in a way that makes it possible to manage the system optimally in real time.

Non-deterministic method for semi-automatic calibration of smartphone-based OST HMDs

An Augmented Reality (AR) system must show real and virtual elements as if they coexisted in the same environment. The tridimensional aligment (registration) is particularly challenging on specific hardware configurations such as Head Mounted Displays (HMDs) that use Optical See-Through (OST) technology. In general, the calibration of HMDs uses deterministic optimization methods. However, non-deterministic methods have been proposed in the literature with promising results in distinct research areas. In this work, we developed a non-deterministic optimization method for the semi-automatic calibration of smartphone-based OST HMDs. We tested simulated annealing, evolutionary strategy, and particle swarm algorithms. We also developed a system for calibration and evaluated it through an application that aligned a virtual object in an AR environment. We evaluated our method using the Mean Squared Error (MSE) at each calibration step, considering the difference between the ideal/observed positions of a set of reference points and those estimated from the values determined for the calibration parameters. Our results show an accurate OST HMD calibration for the peripersonal space, with similar MSEs for the three tested algorithms.

A branch-and-bound algorithm with growing datasets for large-scale parameter estimation

The solution of nonconvex parameter estimation problems with deterministic global optimization methods is desirable but challenging, especially if large measurement datasets are considered. We propose to exploit the structure of this class of optimization problems to enable their solution with the spatial branch-and-bound algorithm. In detail, we start with a reduced dataset in the root node and progressively augment it, converging to the full dataset. We show for nonlinear programs (NLPs) that our algorithm converges to the global solution of the original problem considering the full dataset. The implementation of the algorithm extends our open-source solver MAiNGO. A numerical case study with a mixed-integer nonlinear program (MINLP) from chemical engineering and a dynamic optimization problem from biochemistry both using noise-free measurement data emphasizes the potential for savings of computational effort with our proposed approach.

Enhancing virtual flow metering on offshore oil platforms through parallel computing and data reconciliation

Technological advances in recent years have facilitated data accessibility and increased computational resources; consequently, more remarkable numerical performances in data analysis and computational tests have become possible. In this context, parallel computing techniques are considered relevant tools in applications necessitating reduced computational time, such as online and real-time monitoring of industrial processes. For these reasons, the present work develops and implements online and real-time monitoring of offshore oil and gas production, using parallel computing to improve the performance of the data reconciliation methodology implemented, which will estimate the virtual flow metering with more reliability and in real time. To achieve this, three optimization methods (DA, L-BFGS-B, and SLSQP) and two approaches of parallelization schemes were considered: (1) parallelization of the simulations of each production well; (2) parallelization of the numerical gradient, performed by the deterministic optimization method. Parallel implementations allowed the reduction of up to 80% (type 1) and up to 89% (type 2) of the simulation time compared to their serial counterparts. Hence, the parallel execution of type 2 exhibited more promising results, while type 1 demonstrated greater adaptability to optimization methods. Finally, the results indicate that parallel computing techniques facilitate data reconciliation in real-time, enabling online monitoring in a much shorter time and more accurately than achieved with similar sequential procedures. Moreover, the implemented methodology has proven effective for virtual flow metering of each well’s flow rates of oil, water, and gas. In this context, parallelism techniques present the potential for developing the global monitoring of the virtual flow meters for real-time oil, water, and gas flow rates in each well.

Analysis of the Circuit Optimization Process Based on a Generalized Approach and a Genetic Algorithm

Recently - based on generalized optimization - we developed an approach and successfully applied it to the problem of designing electronic circuits using deterministic optimization methods. In this paper, a similar approach is extended to the problem of optimizing electronic circuits using a genetic algorithm (GA) as the main optimization method. The fundamental element of the generalized optimization is an artificially introduced control vector that generates different strategies within the optimization process and determines the number of independent variables of the optimization problem, as well as the length and structure of chromosomes in the GA. In this case, the GA forms a set of populations defined by a fitness function specified in different ways depending on the strategy chosen within the framework of the idea of generalized optimization. The control vector allows generating different strategies, as well as building composite strategies that significantly increase the accuracy of the resulting solution. This, in turn, makes it possible to reduce both the number of generations - required during the operation of the GA - and the processor time by 3–5 orders of magnitude when solving the circuit optimization problem compared to the traditional GA. The performed analysis of the optimization procedure for some electronic circuits shows the effectiveness of this approach. The obtained results prove that the applied modification of the GA makes it possible to overcome premature convergence and increase the minimization accuracy by 3-4 orders of magnitude.

Multi-layered perceptron network for short-term load forecasting

The use of the multi-layer perceptron (MLP) network for short-term load forecasting is performed. Through weather and load data from the Hydro-Quebec database, capabilities, advantages, and limitations of this artificial intelligence method in load forecasting are investigated. Current management tools for energy systems are based on deterministic optimization methods, where supply, demand, and production are assumed to be known. Changes in electricity supply and demand have made their adjustment more complex. It is no longer a question of adjusting centralized production to demand, but rather of adjusting centralized production, decentralized production, and production from decentralized storage facilities. Our approach will be based on a predictive optimization method adapted to energy systems. An artificial neural network is applied to forecast load for Mascouche in Quebec, Canada. It is about a part of the Hydro-Quebec’s grid where the maximum capacity is 140 megawatts.

A study on ship hull form transformation using convolutional autoencoder

Abstract The optimal ship hull form in contemporary design practice primarily consists of three parts: hull form modification, performance prediction, and optimization. Hull form modification is a crucial step to affect optimization efficiency because the baseline hull form is varied to search for performance improvements. The conventional hull form modification methods mainly rely on human decisions and intervention. As a direct expression of the three-dimensional hull form, the lines are not appropriate for machine learning techniques. This is because they do not explicitly express a meaningful performance metric despite their relatively large data dimension. To solve this problem and develop a novel machine-based hull form design technique, an autoencoder, which is a dimensional reduction technique based on an artificial neural network, was created in this study. Specifically, a convolutional autoencoder was designed; firstly, a convolutional neural network (CNN) preprocessor was used to effectively train the offsets, which are the half-width coordinate values on the hull surface, to extract feature maps. Secondly, the stacked encoder compressed the feature maps into an optimal lower dimensional-latent vector. Finally, a transposed convolution layer restored the dimension of the lines. In this study, 21 250 hull forms belonging to three different ship types of containership, LNG carrier, and tanker, were used as training data. To describe the hull form in more detail, each was divided into several zones, which were then input into the CNN preprocessor separately. After the training, a low-dimensional manifold consisting of the components of the latent vector was derived to represent the distinctive hull form features of the three ship types considered. The autoencoder technique was then combined with another novel approach of the surrogate model to form an objective function neural network. Further combination with the deterministic particle swarm optimization method led to a successful hull form optimization example. In summary, the present convolutional autoencoder has demonstrated its significance within the machine learning-based design process for ship hull forms.

Reliability evaluation and optimization design method of piezoelectric actuator vibration suppression system

As an effective means of structural vibration suppression, piezoelectric actuator vibration suppression system(PAVSS) has been gradually applied in structural vibration control. However, the performance degradation or failure of piezoelectric actuator under long service life will lead to the degradation of service reliability of PAVSS, so the scheme obtained by deterministic optimization method is difficult to ensure the service reliability. Aiming at the reliability evaluation and optimal design of PAVSS in service, the failure mechanism considering of the performance degradation or failure of piezoelectric actuator is analyzed, and the reliability evaluation method based on nested sampling and weighted statistics is constructed, which solves the reliability evaluation problem of PAVSS with the characteristics of load-sharing and redundancy. A reliability-based optimization method based on master-slave parallel genetic algorithm is proposed to optimize the position and angle of the actuators. At last, the feasibility and effectiveness of the proposed method are proved by an example, which not only provides a theoretical basis for the high reliability design of PAVSS in service, but also provides a new solution for the engineering problem of structural vibration control.

Comparative analysis of deterministic and reliability-based structural optimization methods

Optimization is the act of obtaining the best possible result under established conditions. Usually, the optimization of a structural design is done considering the structure's dimensions, the materials' properties, and the loads as deterministic values. This way, the optimization process can lead to a more economical design without guaranteeing that this structure is safe. In practice, there are always uncertainties about the final dimensions of the built structure, material properties, and loads. Then, the need arises to use design optimization techniques based on reliability to guarantee a project that is both economical and safe. This objective is achieved by including uncertainties in the optimization process. This article evaluates the parameters that determine the global minimum of the optimization methods DDO (Deterministic Design Optimization) and RBDO (Reliability-Based Design Optimization). This work aims to compare the structural optimization methods of DDO and RBDO through an example. The results are obtained through the codes of the methods implemented in the Python language and show that when comparing the two optimization methods, the presence of uncertainties alters the optimal solution.

A Bayesian Deep Reinforcement Learning-Based Resilient Control for Multi-Energy Micro-Gird

Aiming at a cleaner future power system, many regimes in the world have proposed their ambitious decarboniz-ing plan, with increasing penetration of renewable energy sources (RES) playing an alternative role to conventional energy. As a re-sult, power system tends to have less backup capacity and operate near their designed limit, thus exacerbating system vulnerability against extreme events. Under this reality, resilient control for the multi-energy micro-grid is facing the following challenges, which are: 1) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">the effect from the stochastic uncertainties of</i> RES; 2) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">the need for a model-free and fast-reacting control scheme under extreme events; and</i> 3) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">efficient exploration and robust performance with limited extreme events data</i> . <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">To deal with the aforementioned challenges, this paper pro-poses a novel Bayesian Deep Reinforcement Learning-based resilient control approach for multi-energy micro-grid. In partic-ular, the proposed approach replaces the deterministic network in traditional Reinforcement Learning with a Bayesian probabilistic network in order to obtain an approximation of the value function distribution, which effectively solves the Q-value overestimation issue. Compared with the naive Deep Deterministic Policy Gra-dient (DDPG) method and optimization method, the effectiveness and importance of employing the Bayesian Reinforcement Learn-ing approach are investigated and illustrated across different operating scenarios. Case studies have shown that by using the Monte Carlo posterior mean of the Bayesian value function distribution instead of a deterministic estimation, the proposed Bayesian Deep Deterministic Policy Gradient (BDDPG) method achieves a near-optimum policy in a more stable process, which verifies the robustness and the practicability of the proposed approach.

Evaluating subgradients for convex relaxations of dynamic process models by adapting current tools

Global dynamic optimization problems are often represented as nonlinear optimization problems with embedded parametric ordinary differential equations. Deterministic methods for global optimization typically employ subgradients of convex relaxations to construct crucial lower bounds. Our recent work shows that subgradients in dynamic optimization problems may be obtained by adapting standard forward or adjoint sensitivity approaches; the adjoint approach ought to be computationally favorable except for small problems. However, established adjoint implementations are incompatible with established libraries for subgradient evaluation. At FOCAPO/CPC 2023, we outlined an automated proof-of-concept implementation of adjoint subgradient evaluation in C++, adapting the convexification package MC++, the ODE solver CVODES, and our own differentiation and code generation tools. This article details how these tools were nontrivially adapted, to ultimately implement adjoint ODE sensitivities embedded with either the forward or reverse modes of subgradient automatic differentiation (AD). Numerical examples are presented for illustration.

Robust Topology Optimization of Coated Structures with Surface Layer Thickness Uncertainty Considered

The rapid development of additive manufacturing has made coated structures an innovative configuration with high design flexibility. However, poor forming accuracy and surface roughness during manufacturing will cause uncertainty in surface layer thickness, which results in structure performance deviation and failure to achieve the expected goals. This paper proposes a robust topology optimization method for coated structures considering the surface layer thickness uncertainty to obtain high-quality designs that can resist disturbance by uncertainties. First, an erosion-based approach is used to establish the model of the coated structure surface layer. Second, modeling the surface layer thickness uncertainty applies a random field whose dimensionality of the random fields is reduced by the Expansion Optimal Linear Estimation (EOLE) method. Then, minimizing the weighted sum of the mean and standard deviation of structural compliance is taken as the optimization objective, and robust topology optimization considering uncertainty is established. Finally, estimate the stochastic response by the perturbation technique, then the sensitivity of the objective function with respect to the design variables is derived. Numerical examples show that the structural design obtained with the proposed method has a stronger resistance to uncertainty than the deterministic topology optimization method, proving the method’s effectiveness in this paper.

Structure search method for atomic clusters based on the dividing rectangles algorithm.

The Dividing Rectangles (DIRECT) algorithm is a deterministic optimization method to explore optimal solutions by repeatedly dividing a given hyperrectangle search space into subhyperrectangles. Herein, we propose a structure search method for atomic clusters based on the DIRECT algorithm in combination with a gradient-based local optimizer to enable an efficient structure search in high-dimensional search spaces. We use the Z-matrix representation for defining the hyperrectangle search space, in which the bond lengths, bond angles, and dihedral angles specify a cluster structure. To evaluate its performance, we applied the proposed method to the Lennard-Jones clusters and two kinds of real atomic clusters with many metastable structures, i.e., phosphorus and sulfur clusters, and compared the results with those of conventional methods. The proposed method exhibits a higher efficiency than random search and a comparable efficiency to basin hopping.

Deterministic-based robust design optimization of composite structures under material uncertainty

We propose a new deterministic robust design optimization method for composite laminate structures under worst-case material uncertainty. The method is based on a simultaneous parametrization of topology and material and combines a design problem and a material uncertainty problem into a single min–max optimization problem which provides an efficient approach to handle variation of material properties in stiffness driven design optimization problems. An analysis is performed using a design problem based on a failure criterion formulation to evaluate the ability of the proposed method to generate robust composite designs. The design problem is solved using various loads, boundary conditions and manufacturing constraints. The designs generated with the proposed method have improved objective responses compared to the worst-case response of designs generated with nominal material properties and are less sensitive to the variation of material properties. The analysis indicates that the proposed method can be efficiently applied in a robust structural optimization framework.

Exploring synchronization and lift suppression in fluid flow around vibrating cylinder: a parallel CFD and global optimization investigation

In this study, we employ a parallel Computational Fluid Dynamics (CFD) code integrated with the VTDIRECT95 algorithm, a parallel deterministic global optimization method, to conduct global optimization for an oscillating circular cylinder. We conduct numerical simulations for the flow at a Reynolds number of 500 within the parameter range of 0.1≤Ax≤0.3 and 0.5fst≤fex≤2.5fst where Ax represents the inline oscillating amplitude, fex denotes the forcing oscillation frequency, and fst corresponds to the frequency of a stationary cylinder. To enhance computational efficiency, a combination of VTdirect and a CFD solver is utilized to efficiently identify the synchronization region, thereby reducing computational resources. The results reveal a significant reduction in the lift coefficient within the synchronized region compared to unsynchronized regimes. Furthermore, the study delves into the underlying flow physics behind synchronization and lift suppression. By synchronizing the shedding of vortices, their detrimental effects are nullified, resulting in a reduction in lift. Moreover, the research examines the influence of three-dimensional (3-D) flow by comparing 2-D and 3-D simulations at two different Reynolds numbers. It demonstrates that accounting for 3-D effects yields more accurate predictions of fluid behavior. Synchronization maps and root mean square (rms) lift coefficient plots illustrate the impact of Reynolds number and movement frequency on lift suppression. The findings indicate that achieving synchronization in 3-D flow necessitates stronger amplitudes and higher frequencies. At higher Reynolds numbers, the wake structures become unstable, leading to intricate vortical patterns. Consequently, the synchronization curve shifts towards higher amplitudes and frequencies in 3-D simulations. Understanding these phenomena is vital for reducing lift force in practical applications. This research significantly contributes to knowledge regarding synchronization and lift suppression in fluid flow around vibrating cylinders.

An adjoint-free algorithm for conditional nonlinear optimal perturbations (CNOPs) via sampling

Abstract. In this paper, we propose a sampling algorithm based on state-of-the-art statistical machine learning techniques to obtain conditional nonlinear optimal perturbations (CNOPs), which is different from traditional (deterministic) optimization methods.1 Specifically, the traditional approach is unavailable in practice, which requires numerically computing the gradient (first-order information) such that the computation cost is expensive, since it needs a large number of times to run numerical models. However, the sampling approach directly reduces the gradient to the objective function value (zeroth-order information), which also avoids using the adjoint technique that is unusable for many atmosphere and ocean models and requires large amounts of storage. We show an intuitive analysis for the sampling algorithm from the law of large numbers and further present a Chernoff-type concentration inequality to rigorously characterize the degree to which the sample average probabilistically approximates the exact gradient. The experiments are implemented to obtain the CNOPs for two numerical models, the Burgers equation with small viscosity and the Lorenz-96 model. We demonstrate the CNOPs obtained with their spatial patterns, objective values, computation times, and nonlinear error growth. Compared with the performance of the three approaches, all the characters for quantifying the CNOPs are nearly consistent, while the computation time using the sampling approach with fewer samples is much shorter. In other words, the new sampling algorithm shortens the computation time to the utmost at the cost of losing little accuracy.

Robust optimization design of permanent magnet synchronous motors for a solar airplane based on a lightweight structure

Due to the characteristics of high-altitude solar airplanes, the permanent magnet synchronous motors (PMSMs) require not only high torque density, but also high reliability. The balance of quality, reliability, and performance in a design proposal is particularly important. In this paper, a robust mechanical–electrical integrated optimization method for PMSMs based on 6σ theory is proposed. According to the fatigue characteristics of materials under the propeller working conditions and the uncertainty factors caused by the actual machining dimension tolerance, the electromagnetic dimension, mechanical dimension and reliability of the PMSM are connected. And a robust optimization model for the reliability and performance of the PMSMs is established. The Monte Carlo method and finite element simulation method are used to verify the correctness of the established optimization model. According to the comparison between the deterministic optimization method and the proposed optimization model, this method can significantly improve the output performance and reliability of the PMSMs.

Commuting-pattern-oriented stochastic optimization of electric powertrains for revealing contributions of topology modifications to the powertrain energy efficiency

The performance of an electric vehicle (EV) powertrain is greatly influenced by the design scheme, control strategy, and driving conditions. Owing to uncertainties in driving conditions and the mutual correlation between design scheme and control strategy, identifying the optimal topology and component parameters of EV powertrains for improving the energy efficiency of EVs remains a challenging task. Oriented to the commuting patterns of individuals, this paper proposes a stochastic optimization method for identifying the superior powertrain design that optimizes the expected energy economy of the EV powertrain and reduces the energy economy variability in random driving conditions. This paper also introduces a machine-learning solution to the complex mutual restrictions among design variables, control strategies, and driving conditions, which determines the feasible design space and powertrain performance. Suggested by massive validations, the stochastic optimization method reduces the expectation and deviation of the energy consumption of EV powertrains up to 12.0% and 5.6%, compared with deterministic optimization methods. Additionally, by comparative evaluation among stochastic optimal design results of different topologies, contributions of topology modifications to the energy efficiency of EV powertrains are clarified, and the superior powertrain topology is identified, which improves 17.1% expected energy economy compared with the current popular topology.

Deterministic vs. robust design optimization using DEM-based metamodels

In design optimization of bulk handling equipment (BHE) we generally focus on the mean performance of the equipment. However, granular materials behave stochastic due to irregularities in particle shape and size which leads to stochastic performance of the equipment. To include the stochastic performance we propose robust metamodel-based design optimization (MBDO). The used metamodels are trained with stochastic performance data from randomly repeated discrete element method (DEM) simulations and predict mean and variance of the equipment performance. This method is compared to the conventional deterministic optimization method by means of a case study of a discharging hopper including verification and validation. The robust MBDO shows more distinctive optimal designs compared to the deterministic approach. In addition, the DEM-based metamodel is a relatively accurate method to predict DEM-model simulation results. However, the validation indicates that differences between DEM-model and experimental results highly affect the reliability of the found optima.