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.

Causality Diagram-based Scheduling Approach for Blast Furnace Gas System

Rational use of blast furnace gas(BFG) in steel industry can raise economic profit, save fossil energy resources and alleviate the environment pollution. In this paper, a causality diagram is established to describe the causal relationships among the decision objective and the variables of the scheduling process for the industrial system, based on which the total scheduling amount of the BFG system can be computed by using a causal fuzzy C-means(CFCM) clustering algorithm. In this algorithm,not only the distances among the historical samples but also the effects of different solutions on the gas tank level are considered.The scheduling solution can be determined based on the proposed causal probability of the causality diagram calculated by the total amount and the conditions of the adjustable units. The causal probability quantifies the impact of different allocation schemes of the total scheduling amount on the BFG system. An evaluation method is then proposed to evaluate the effectiveness of the scheduling solutions. The experiments by using the practical data coming from a steel plant in China indicate that the proposed approach can effectively improve the scheduling accuracy and reduce the gas diffusion.

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.

The inverse maximum dynamic flow problem

We consider the inverse maximum dynamic flow (IMDF) problem.IMDF problem can be described as: how to change the capacity vector of a dynamic network as little as possible so that a given feasible dynamic flow becomes a maximum dynamic flow.After discussing some characteristics of this problem,it is converted to a constrained minimum dynamic cut problem.Then an efficient algorithm which uses two maximum dynamic flow algorithms is proposed to solve the problem.