A Multi-Stage Differential-Multifactorial Evolutionary Algorithm for Ingredient Optimization in the Copper Industry

Ingredient optimization plays a pivotal role in the copper industry,for which it is closely related to the concentrate utilization rate,stability of furnace conditions,and the quality of copper production.To acquire a practical ingredient plan,which should exhibit long duration time with sufficient utilization and feeding stability for real applications,an ingredient plan optimization model is proposed in this study to effectively guarantee continuous production and stable furnace conditions.To address the complex challenges posed by this integer programming model,including multiple coupling feeding stages,intricate constraints,and significant non-linearity,a multi-stage differential-multifactorial evolution algorithm is developed.In the proposed algorithm,the differential evolutionary(DE)algorithm is improved in three aspects to efficiently tackle challenges when optimizing the proposed model.First,unlike traditional time-consuming serial approaches,the multifactorial evolutionary algorithm is utilized to optimize multiple complex models contained in the population of evolutionary algorithm caused by the feeding stability in a parallel manner.Second,a repair algorithm is employed to adjust infeasible ingredient lists in a timely manner.In addition,a local search strategy taking feedback from the current optima and considering the different positions of global optimum is developed to avoiding premature convergence of the differential evolutionary algorithm.Finally,the simulation experiments considering different planning horizons using real data from the copper industry in China are conducted,which demonstrates the superiority of the proposed method on feeding duration and stability compared with other commonly deployed approaches.It is practically helpful for reducing material cost as well as increasing production profit for the copper industry.

Surrogate-Assisted Particle Swarm Optimization Algorithm With Pareto Active Learning for Expensive Multi-Objective Optimization

For multi-objective optimization problems, particle swarm optimization(PSO) algorithm generally needs a large number of fitness evaluations to obtain the Pareto optimal solutions. However, it will become substantially time-consuming when handling computationally expensive fitness functions. In order to save the computational cost, a surrogate-assisted PSO with Pareto active learning is proposed. In real physical space(the objective functions are computationally expensive), PSO is used as an optimizer, and its optimization results are used to construct the surrogate models. In virtual space, objective functions are replaced by the cheaper surrogate models, PSO is viewed as a sampler to produce the candidate solutions. To enhance the quality of candidate solutions, a hybrid mutation sampling method based on the simulated evolution is proposed, which combines the advantage of fast convergence of PSO and implements mutation to increase diversity. Furthermore, ε-Pareto active learning(ε-PAL)method is employed to pre-select candidate solutions to guide PSO in the real physical space. However, little work has considered the method of determining parameter ε. Therefore, a greedy search method is presented to determine the value ofεwhere the number of active sampling is employed as the evaluation criteria of classification cost. Experimental studies involving application on a number of benchmark test problems and parameter determination for multi-input multi-output least squares support vector machines(MLSSVM) are given, in which the results demonstrate promising performance of the proposed algorithm compared with other representative multi-objective particle swarm optimization(MOPSO) algorithms.

An Optimized Oxygen System Scheduling With Electricity Cost Consideration in Steel Industry

As an essential energy resource in steel industry, oxygen is widely utilized in many production procedures. With different demands of the oxygen amount, a gap between the generation and consumption always occurs. Therefore, its related optimization and scheduling work along with the electricity cost to fill the gap has a great impact on daily production and efficient energy utilization in steel plant. Considering an oxygen system in a steel plant in China, a nonlinear programming model for oxygen system scheduling is proposed in this study, which concerns not only the practical characteristics of the energy pipeline network, but also the electricity cost acquired by a fitting regression modeling between the load of air separation units U+0028 ASU U+0029 and its corresponding electricity consumption. A set of constraints is formulated for restricting the practical adjusting capacity and filling the imbalance gap of oxygen. To solve the proposed scheduling model with electricity cost consideration, a particle swarm optimization U+0028 PSO U+0029 algorithm is then adopted. To verify the effectiveness of the proposed approach, a large number of experiments employing the real data from this plant are carried out, both for the fitting regression and the scheduling optimization phases. And the results demonstrate that such a practice-based solution successfully resolves the oxygen scheduling problem and simultaneously minimizes the electricity cost, which will be beneficial for the enterprise. © 2017 Chinese Association of Automation.

Variational Inference Based Kernel Dynamic Bayesian Networks for Construction of Prediction Intervals for Industrial Time Series With Incomplete Input

Prediction intervals(PIs)for industrial time series can provide useful guidance for workers.Given that the failure of industrial sensors may cause the missing point in inputs,the existing kernel dynamic Bayesian networks(KDBN),serving as an effective method for PIs construction,suffer from high computational load using the stochastic algorithm for inference.This study proposes a variational inference method for the KDBN for the purpose of fast inference,which avoids the timeconsuming stochastic sampling.The proposed algorithm contains two stages.The first stage involves the inference of the missing inputs by using a local linearization based variational inference,and based on the computed posterior distributions over the missing inputs the second stage sees a Gaussian approximation for probability over the nodes in future time slices.To verify the effectiveness of the proposed method,a synthetic dataset and a practical dataset of generation flow of blast furnace gas(BFG)are employed with different ratios of missing inputs.The experimental results indicate that the proposed method can provide reliable PIs for the generation flow of BFG and it exhibits shorter computing time than the stochastic based one.