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In many applications, the demand arises for algorithms capable of aligning partially overlapping point sets while remaining invariant to the corresponding transformations. This research presents a method designed to meet such requirements through minimization of the objective function of the robust point matching (RPM) algorithm. First, we show that the RPM objective is a cubic polynomial. Then, through variable substitution, we transform the RPM objective to a quadratic function. Leveraging the convex envelope of bilinear monomials, we proceed to relax the resulting objective function, thus obtaining a lower bound problem that can be conveniently decomposed into distinct linear assignment and low-dimensional convex quadratic program components, both amenable to efficient optimization. Furthermore, a branch-and-bound (BnB) algorithm is devised, which solely branches over the transformation parameters, thereby boosting convergence rate. Empirical evaluations demonstrate better robustness of the proposed methodology against non-rigid deformation, positional noise, and outliers, particularly in scenarios where outliers remain distinct from inliers, when compared with prevailing state-of-the-art approaches.

Time series modelling is gaining spectacular popularity in the prediction process of decision making, with applications including real-world management and engineering. However, for short time series, prediction has to face unavoidable limitation for modelling extremely complex systems. It has to apply inadequate and incomplete data from short time to predict unknown observations. With such limited data source, existing techniques, such as statistical modelling or machine learning methods, fail to predict short time series effectively. To address this problem, this paper provides a global framework for short time series modelling predictions, integrating the rolling mechanism, grey model, and meta-heuristic optimization algorithms. In addition, dragonfly algorithm and whale optimization algorithm are investigated and deployed to optimize the framework by enhancing its predicting accuracy with less computational costs. To verify the performance of the proposed framework, three industrial cases are introduced as simulation experiments in this paper. Experimental results confirm that the framework solves corresponding short time series modelling predictions with greater accuracy and speed than the standard GM(1,1) models. The source codes of this framework are available at: https://github.com/zhesencui/HybridRollingGreyFramework.git.

The slime mould algorithm (SMA) is a recently developed meta-heuristic optimization algorithm which is based on the oscillation mode of slime mould in nature. However, the SMA is often trapped in local optima for global continuous optimization problems. To strengthen SMA’s exploration for global optimum, we propose a modified SMA, which takes randomization based on a Levy distribution instead of the traditional uniform one, namely LF-SMA. Our LF-SMA is integrated with Levy-flight guidance to its optimal paths for connecting food with excellent exploratory propensity. Experimental results show that the proposed LF-SMA achieves better performance in 13 benchmark test functions and one investigated engineering case in terms of both computation cost and solution.

Short-term electrical load forecasting is an important part in the management of electrical power because electrical load is an extreme, complex non-linear system. To obtain parameter values that provide better performances with high precision, this paper proposes a new hybrid electrical load forecasting model, which combines ensemble empirical mode decomposition, extreme learning machine, and grasshopper optimization algorithm for short-term load forecasting. The most important difference that distinguishes this electrical load forecasting model from other models is that grasshopper optimization can search suitable parameters (weight values and threshold values) of extreme learning machine, while traditional parameters are selected randomly. It is applied in Australia electrical load prediction to show its superiority and applicability. The simulation studies are carried out using a data set collected from five main states (New South Wales, Queensland, Tasmania, South Australia and Victoria) in Australia from February 1 to February 27, 2018. Compared with all considered basic models, the proposed hybrid model has the best performance in predicting electrical load.