Development of an optimization framework for solving engineering design problems.

The integration of optimization methodologies with computational simulations plays a profound role in the product design. Such integration, however, faces multiple challenges arising from computation-intensive simulations, unknown function properties (i.e., black-box functions), complex constraints, and high-dimensionality of problems. To address these challenges, metamodel-based methods which apply metamodels as a cheaper alternative to costly analysis tools prove to be a practical way in design optimization and have gained continuous development. In this thesis, an intrinsically linear function (ILF) assisted and trust region based optimization method (IATRO) is proposed first for solving low-dimensional constrained black-box problems. Then, the economical sampling strategy (ESS), modified trust region strategy and self-adaptive normalization strategy (SANS) are developed to enhance the overall optimization capability. Moreover, as the radial basis function (RBF) interpolation is found to better approximate both objective and constraint functions than ILF, a RBF-assisted optimization framework is established by the combination of the balanced trust region strategy (BTRS), global intelligence selection strategy (GIS) and early termination strategy (ETS). Following that, the fast computation strategy (FCS) and successive refinement strategy (SRS) are proposed for solving large-scale constrained black-box problems and the final optimization framework is called as RATRLO (radial basis function assisted and trust region based large-scale optimization framework). By testing a set of well-known benchmark problems including 22 G-problems, 4 engineering design problems and 1 high-dimensional automotive problem, RATRLO shows remarkable advantages in achieving high-quality results with very few function evaluations and slight parameter tuning. Compared with various state-of-the-art algorithms, RATRLO can be considered one of the best global optimizers for solving constrained optimization problems. Further more, RATRLO provides a valuable insight into the development of algorithms for efficient large-scale optimization

Topology-aware Graph Neural Networks for Learning Feasible and Adaptive ac-OPF Solutions

Solving the optimal power flow (OPF) problem is a fundamental task to ensure the system efficiency and reliability in real-time electricity grid operations. We develop a new topology-informed graph neural network (GNN) approach for predicting the optimal solutions of real-time ac-OPF problem. To incorporate grid topology to the NN model, the proposed GNN-for-OPF framework innovatively exploits the locality property of locational marginal prices and voltage magnitude. Furthermore, we develop a physics-aware (ac-)flow feasibility regularization approach for general OPF learning. The advantages of our proposed designs include reduced model complexity, improved generalizability and feasibility guarantees. By providing the analytical understanding on the graph subspace stability under grid topology contingency, we show the proposed GNN can quickly adapt to varying grid topology by an efficient re-training strategy. Numerical tests on various test systems of different sizes have validated the prediction accuracy, improved flow feasibility, and topology adaptivity capability of our proposed GNN-based learning framework

Design of a Novel UWB Omnidirectional Antenna Using Particle Swarm Optimization

A UWB E-plane omnidirectional microwave antenna is designed and fabricated for IEEE 802.11a communication system and microwave magnetron source system as a radiation monitor. A cooptimization method based on particle swarm optimization (PSO) algorithm and FDTD software is presented. The presented PSO algorithm is useful in many industrial microwave applications, such as microwave magnetron design and other techniques with a high power level. The maximum measured relative bandwidth of 65% is achieved for the proposed antenna after a rapid and efficient optimization. Furthermore, the measured antenna polarization purity reaches about 20 dB at the communication C band. The PSO algorithm is a powerful candidate for microwave passive component design

Efficient hybrid algorithms to solve mixed discrete-continuous optimization problems: A comparative study

Purpose: – In real world cases, it is common to encounter mixed discrete-continuous problems where some or all of the variables may take only discrete values. To solve these non-linear optimization problems, it is very time-consuming in use of finite element methods. The purpose of this paper is to study the efficiency of the proposed hybrid algorithms for the mixed discrete-continuous optimization, and compares it with the performance of Genetic Algorithms (GA). Design/methodology/approach: – In this paper, the enhanced multipoint approximation method (MAM) is utilized to reduce the original nonlinear optimization problem to a sequence of approximations. Then, the Sequential Quadratic Programming (SQP) technique is applied to find the continuous solution. Following that, the implementation of discrete capability into the MAM is developed to solve the mixed discrete-continuous optimization problems. Findings: – The efficiency and rate of convergence of the developed hybrid algorithms outperforming GA are examined by six detailed case studies in the ten-bar planar truss problem and the superiority of the Hooke-Jeeves assisted MAM algorithm over the other two hybrid algorithms and GAs is concluded. Originality/value: – The authors propose three efficient hybrid algorithms: the rounding-off, the coordinate search, and the Hooke-Jeeves search assisted MAMs, to solve nonlinear mixed discrete-continuous optimization problems. Implementations include the development of new procedures for sampling discrete points, the modification of the trust region adaptation strategy, and strategies for solving mix optimization problems. To improve the efficiency and effectiveness of metamodel construction, regressors φ defined in this paper can have the form in common with the empirical formulation of the problems in many engineering subjects

Efficient strategies for constrained black-box optimization by intrinsically linear approximation (CBOILA)

In this paper, a novel trust-region-based surrogate-assisted optimization method, called CBOILA (Constrained Black-box Optimization by Intrinsically Linear Approximation), has been proposed to reduce the number of black-box function evaluations and enhance the efficient performance for solving complex optimization problems. This developed optimization approach utilizes an assembly of intrinsically linear approximations to seek the optimum with incorporation of three strategies: (1) extended-box selection strategy (EBS), (2) global intelligence selection strategy (GIS) and (3) balanced trust-region strategy. EBS aims at reducing the number of function evaluations in current iteration by selecting points close to the given trust region boundary. Whilst, GIS is designed to improve the exploration performance by adaptively choosing points outside the trust region. The balanced trust-region strategy works with four indicators, which will be triggered by the quality of the approximation, the movement direction of the search, the location of the sub-optimum, and the condition of the termination, respectively. By modifying the move limit of each dimension accordingly, CBOILA is capable of attaining a balanced search between exploitation and exploration for the optimal solutions. To demonstrate the potentials of the proposed optimization method, four widely used benchmark problems have been examined and the results have also been compared with solutions by other metamodel-based algorithms in published works. Results show that the proposed method can efficiently and robustly solve constrained black-box optimization problems within an acceptable computational time

A Unified Hard-Constraint Framework for Solving Geometrically Complex PDEs

We present a unified hard-constraint framework for solving geometrically complex PDEs with neural networks, where the most commonly used Dirichlet, Neumann, and Robin boundary conditions (BCs) are considered. Specifically, we first introduce the "extra fields" from the mixed finite element method to reformulate the PDEs so as to equivalently transform the three types of BCs into linear forms. Based on the reformulation, we derive the general solutions of the BCs analytically, which are employed to construct an ansatz that automatically satisfies the BCs. With such a framework, we can train the neural networks without adding extra loss terms and thus efficiently handle geometrically complex PDEs, alleviating the unbalanced competition between the loss terms corresponding to the BCs and PDEs. We theoretically demonstrate that the "extra fields" can stabilize the training process. Experimental results on real-world geometrically complex PDEs showcase the effectiveness of our method compared with state-of-the-art baselines.Comment: 10 pages, 6 figures, NeurIPS 202

Task Aware Dreamer for Task Generalization in Reinforcement Learning

A long-standing goal of reinforcement learning is to acquire agents that can learn on training tasks and generalize well on unseen tasks that may share a similar dynamic but with different reward functions. A general challenge is to quantitatively measure the similarities between these different tasks, which is vital for analyzing the task distribution and further designing algorithms with stronger generalization. To address this, we present a novel metric named Task Distribution Relevance (TDR) via optimal Q functions of different tasks to capture the relevance of the task distribution quantitatively. In the case of tasks with a high TDR, i.e., the tasks differ significantly, we show that the Markovian policies cannot differentiate them, leading to poor performance. Based on this insight, we encode all historical information into policies for distinguishing different tasks and propose Task Aware Dreamer (TAD), which extends world models into our reward-informed world models to capture invariant latent features over different tasks. In TAD, we calculate the corresponding variational lower bound of the data log-likelihood, including a novel term to distinguish different tasks via states, to optimize reward-informed world models. Extensive experiments in both image-based control tasks and state-based control tasks demonstrate that TAD can significantly improve the performance of handling different tasks simultaneously, especially for those with high TDR, and demonstrate a strong generalization ability to unseen tasks