Helper and Equivalent Objectives:Efficient Approach for Constrained Optimization

Numerous multi-objective evolutionary algorithms have been designed for constrained optimisation over past two decades. The idea behind these algorithms is to transform constrained optimisation problems into multi-objective optimisation problems without any constraint, and then solve them. In this paper, we propose a new multi-objective method for constrained optimisation, which works by converting a constrained optimisation problem into a problem with helper and equivalent objectives. An equivalent objective means that its optimal solution set is the same as that to the constrained problem but a helper objective does not. Then this multi-objective optimisation problem is decomposed into a group of sub-problems using the weighted sum approach. Weights are dynamically adjusted so that each subproblem eventually tends to a problem with an equivalent objective. We theoretically analyse the computation time of the helper and equivalent objective method on a hard problem called ``wide gap''. In a ``wide gap'' problem, an algorithm needs exponential time to cross between two fitness levels (a wide gap). We prove that using helper and equivalent objectives can shorten the time of crossing the ``wide gap''. We conduct a case study for validating our method. An algorithm with helper and equivalent objectives is implemented. Experimental results show that its overall performance is ranked first when compared with other eight state-of-art evolutionary algorithms on IEEE CEC2017 benchmarks in constrained optimisation

Methyl 2-[2-(benzyl­oxycarbonyl­amino)­propan-2-yl]-5-hy­droxy-6-meth­oxy­pyrimidine-4-carboxyl­ate

In the title compound, C18H21N3O6, a pyrimidine derivative, the dihedral angle between the benzene and pyrimidine rings is 52.26 (12)°. The carboxyl­ate unit is twisted with respect to the pyrimidine ring, making a dihedral angle of 12.33 (7)°. In the crystal, mol­ecules are linked by a pair of O—H⋯O hydrogen bonds, forming an inversion dimer. The dimers are stacked into columns along the b axis through weak C—H⋯O inter­actions

WavSpA: Wavelet Space Attention for Boosting Transformers' Long Sequence Learning Ability

Transformer and its variants are fundamental neural architectures in deep learning. Recent works show that learning attention in the Fourier space can improve the long sequence learning capability of Transformers. We argue that wavelet transform shall be a better choice because it captures both position and frequency information with linear time complexity. Therefore, in this paper, we systematically study the synergy between wavelet transform and Transformers. We propose Wavelet Space Attention (WavSpA) that facilitates attention learning in a learnable wavelet coefficient space which replaces the attention in Transformers by (1) applying forward wavelet transform to project the input sequences to multi-resolution bases, (2) conducting attention learning in the wavelet coefficient space, and (3) reconstructing the representation in input space via backward wavelet transform. Extensive experiments on the Long Range Arena demonstrate that learning attention in the wavelet space using either fixed or adaptive wavelets can consistently improve Transformer's performance and also significantly outperform learning in Fourier space. We further show our method can enhance Transformer's reasoning extrapolation capability over distance on the LEGO chain-of-reasoning task

Back-action Induced Non-equilibrium Effect in Electron Charge Counting Statistics

We report our study of the real-time charge counting statistics measured by a quantum point contact (QPC) coupled to a single quantum dot (QD) under different back-action strength. By tuning the QD-QPC coupling or QPC bias, we controlled the QPC back-action which drives the QD electrons out of thermal equilibrium. The random telegraph signal (RTS) statistics showed strong and tunable non-thermal-equilibrium saturation effect, which can be quantitatively characterized as a back-action induced tunneling out rate. We found that the QD-QPC coupling and QPC bias voltage played different roles on the back-action strength and cut-off energy.Comment: 4 pages, 4 figures, 1 tabl

Time series data intelligent clustering algorithm for landslide displacement prediction

The traditional time series data clustering for landslide displacement prediction is based on Euclidean distance measure. The time series data is clustered by distance calculation of two vectors. The correlation between components is not considered. The multiple components with single feature will interfere with the clustering results, and the accuracy of clustering results is greatly reduced. To address this problem, an intelligent clustering algorithm for time series data in landslide displacement prediction based on nonlinear dynamic time bending is proposed in this paper. By reconstructing the phase space of the landslide displacement time series, the phase space transposed matrix is obtained as the time series reconstruction matrix. After embedding dimension processing, the time series of landslide displacement is predicted by SVM data mining model. Dynamic time warping calculation is based on the correlation of time series sequence and the components. The local optimal solution is obtained by recursive search, and the whole curve path is obtained. Clustering calculation of time series data set is carried out by using hierarchical clustering algorithm according to bending path. The intelligent clustering results of time series data in landslide displacement prediction is obtained. Experimental results show that the proposed algorithm has better clustering effect and higher clustering accuracy