New approach to global minimization of normal multivariate polynomial based on tensor
Zhong Wan Chunhua Yang
Journal of Industrial & Management Optimization 2008, 4(2): 271-285 doi: 10.3934/jimo.2008.4.271
In this paper, we first present a concise representation of multivariate polynomial, based on which we deduce the calculation formulae of its derivatives using tensor. Then, we propose a solution method to determine a global descent direction for the minimization of general normal polynomial. At a local and non-global maximizer or saddle point, we could use this method to get a global descent direction of the objective function. By using the global descent direction, we can transform an $n$-dimensional optimization problem into a one-dimensional one. Based on some efficient algorithms for one dimensional global optimization, we develop an algorithm to compute the global minimizer of normal multivariate polynomial. Numerical examples show that the proposed algorithm is promising.
keywords: polynomial optimization representation of polynomials global minimization. global descent direction tensor
Anode effect prediction based on collaborative two-dimensional forecast model in aluminum electrolysis production
Zuguo Chen Yonggang Li Xiaofang Chen Chunhua Yang Weihua Gui
Journal of Industrial & Management Optimization 2018, 13(5): 1-24 doi: 10.3934/jimo.2018060

In this study, a new prediction algorithm is proposed, based on the collaborative two-dimensional forecast model (CTFM) that combines the traditional method and similarity search technique. The main idea of the algorithm is that the prediction of the change trend of the slope and the accumulated slope of the cell resistance as well as the useful knowledge obtained using the similarity search technique are used as the main criteria to calculate anode effect (AE)-prediction reliability. The accumulated mass deviation value is used as an auxiliary criterion to adjust the AE-prediction reliability. Finally, the current AE-process is marked according to the current AE-prediction reliability. The prediction model based on CTFM is tested on a real situation, in which multiple samples are extracted from the production of a 400 kA aluminum electrolysis cell. We observe that when the time advance of AE-prediction is within 20 ~ 40 min, the accuracy rate of the CTFM algorithm is greater than 95% and the applicability of the method is excellent, showing a high prediction accuracy for different aluminum electrolysis cells.

keywords: Anode effect prediction collaborative two-dimensional forecast model similarity search square-root cubature Kalman filter
Robust real-time optimization for blending operation of alumina production
Lingshuang Kong Changjun Yu Kok Lay Teo Chunhua Yang
Journal of Industrial & Management Optimization 2017, 13(3): 1149-1167 doi: 10.3934/jimo.2016066

The blending operation is a key process in alumina production. The real-time optimization (RTO) of finding an optimal raw material proportioning is crucially important for achieving the desired quality of the product. However, the presence of uncertainty is unavoidable in a real process, leading to much difficulty for making decision in real-time. This paper presents a novel robust real-time optimization (RRTO) method for alumina blending operation, where no prior knowledge of uncertainties is needed to be utilized. The robust solution obtained is applied to the real plant and the two-stage operation is repeated. When compared with the previous intelligent optimization (IRTO) method, the proposed two-stage optimization method can better address the uncertainty nature of the real plant and the computational cost is much lower. From practical industrial experiments, the results obtained show that the proposed optimization method can guarantee that the desired quality of the product quality is achieved in the presence of uncertainty on the plant behavior and the qualities of the raw materials. This outcome suggests that the proposed two-stage optimization method is a practically significant approach for the control of alumina blending operation.

keywords: Robust real-time optimization alumina production exact penalty function method alumina blending process operational control
A unified parameter identification method for nonlinear time-delay systems
Qinqin Chai Ryan Loxton Kok Lay Teo Chunhua Yang
Journal of Industrial & Management Optimization 2013, 9(2): 471-486 doi: 10.3934/jimo.2013.9.471
This paper deals with the problem of identifying unknown time-delays and model parameters in a general nonlinear time-delay system. We propose a unified computational approach that involves solving a dynamic optimization problem, whose cost function measures the discrepancy between predicted and observed system output, to determine optimal values for the unknown quantities. Our main contribution is to show that the partial derivatives of this cost function can be computed by solving a set of auxiliary time-delay systems. On this basis, the parameter identification problem can be solved using existing gradient-based optimization techniques. We conclude the paper with two numerical simulations.
keywords: nonlinear optimization. Time-delay system parameter identification
State transition algorithm
Xiaojun Zhou Chunhua Yang Weihua Gui
Journal of Industrial & Management Optimization 2012, 8(4): 1039-1056 doi: 10.3934/jimo.2012.8.1039
In terms of the concepts of state and state transition, a new heuristic random search algorithm named state transition algorithm is proposed. For continuous function optimization problems, four special transformation operators called rotation, translation, expansion and axesion are designed. Adjusting measures of the transformations are mainly studied to keep the balance of exploration and exploitation. Convergence analysis is also discussed about the algorithm based on random search theory. In the meanwhile, to strengthen the search ability in high dimensional space, communication strategy is introduced into the basic algorithm and intermittent exchange is presented to prevent premature convergence. Finally, experiments are carried out for the algorithms. With 10 common benchmark unconstrained continuous functions used to test the performance, the results show that state transition algorithms are promising algorithms due to their good global search capability and convergence property when compared with some popular algorithms.
keywords: random search. State transition algorithm intermittent exchange global optimization

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