Output Space Entropy Search Framework for Multi-Objective Bayesian Optimization

We consider the problem of black-box multi-objective optimization (MOO) using expensive function evaluations (also referred to as experiments), where the goal is to approximate the true Pareto set of solutions by minimizing the total resource cost of experiments. For example, in hardware design optimization, we need to find the designs that trade-off performance, energy, and area overhead using expensive computational simulations. The key challenge is to select the sequence of experiments to uncover high-quality solutions using minimal resources. In this paper, we propose a general framework for solving MOO problems based on the principle of output space entropy (OSE) search: select the experiment that maximizes the information gained per unit resource cost about the true Pareto front. We appropriately instantiate the principle of OSE search to derive efficient algorithms for the following four MOO problem settings: 1) The most basic single-fidelity setting, where experiments are expensive and accurate; 2) Handling black-box constraints which cannot be evaluated without performing experiments; 3) The discrete multi-fidelity setting, where experiments can vary in the amount of resources consumed and their evaluation accuracy; and 4) The continuous-fidelity setting, where continuous function approximations result in a huge space of experiments. Experiments on diverse synthetic and real-world benchmarks show that our OSE search based algorithms improve over state-of-the-art methods in terms of both computational-efficiency and accuracy of MOO solutions.

Global Optimization Method to Multiple Local Optimals with the Surface Approximation Methodology and Its Application for Industry Problems

Although generally speaking, a great number of functional evaluations may be required until convergence, it can be solved by using neural network effectively. Here, techniques to search the region of interest containing the global optimal design selected by random seeds is investigated. Also techniques for finding more accurate approximation using Holographic Neural Network (HNN) improved by using penalty function for generalized inverse matrix is investigated. Furthermore, the mapping method of extrapolation is proposed to make the technique available to general application in structural optimization. Application examples show that HNN may be expected as potential activate and feasible surface functions in response surface methodology than the polynomials in function approximations. Finally, the real design examples of a vehicle performance such as idling vibration, booming noise, vehicle component crash worthiness and combination problem between vehicle crashworthiness and restraint device performance at the head-on collision are used to show the effectiveness of the proposed method.

Gradient-Enhanced Multifidelity Neural Networks for High-Dimensional Function Approximation

In this work, a novel multifidelity machine learning (ML) algorithm, the gradient-enhanced multifidelity neural networks (GEMFNN) algorithm, is proposed. This is a multifidelity extension of the gradient-enhanced neural networks (GENN) algorithm as it uses both function and gradient information available at multiple levels of fidelity to make function approximations. Its construction is similar to the multifidelity neural networks (MFNN) algorithm. The proposed algorithm is tested on three analytical functions, a one, two, and a 20 variable function. Its performance is compared to the performance of neural networks (NN), GENN, and MFNN, in terms of the number of samples required to reach a global accuracy of 0.99 of the coefficient of determination (R2). The results showed that GEMFNN required 18, 120, and 600 high-fidelity samples for the one, two, and 20 dimensional cases, respectively, to meet the target accuracy. NN performed best on the one variable case, requiring only ten samples, while GENN worked best on the two variable case, requiring 120 samples. GEMFNN worked best for the 20 variable case, while requiring nearly eight times fewer samples than its nearest competitor, GENN. For this case, NN and MFNN did not reach the target global accuracy even after using 10,000 high-fidelity samples. This work demonstrates the benefits of using gradient as well as multifidelity information in NN for high-dimensional problems.

Finite-Time Command-Filtered Approximation-Free Attitude Tracking Control of Rigid Spacecraft

This paper presents a finite-time command-filtered approximation-free attitude tracking control for rigid spacecraft. A novel finite-time prescribed performance function (FTPPF) is first constructed to ensure that the attitude tracking errors converge to the predefined region in finite time. Then, a finite-time error compensation mechanism is constructed and incorporated into the backstepping control design, such that the differentiation of virtual control signals in recursive steps can be avoided to overcome the singularity issue. Compared with most of approximation-based attitude control methods, less computational burden and lower complexity are guaranteed by the proposed approximation-free control scheme due to the avoidance of using any function approximations. Simulations are given to illustrate the efficiency of the proposed method.

Quantum Hermite-Hadamard type inequalities for generalized strongly preinvex functions

<abstract><p>In accordance with the quantum calculus, the quantum Hermite-Hadamard type inequalities shown in recent findings provide improvements to quantum Hermite-Hadamard type inequalities. We acquire a new $ q{_{\kappa_1}} $-integral and $ q{^{\kappa_2}} $-integral identities, then employing these identities, we establish new quantum Hermite-Hadamard $ q{_{\kappa_1}} $-integral and $ q{^{\kappa_2}} $-integral type inequalities through generalized higher-order strongly preinvex and quasi-preinvex functions. The claim of our study has been graphically supported, and some special cases are provided as well. Finally, we present a comprehensive application of the newly obtained key results. Our outcomes from these new generalizations can be applied to evaluate several mathematical problems relating to applications in the real world. These new results are significant for improving integrated symmetrical function approximations or functions of some symmetry degree.</p></abstract>