A multiobjective particle swarm optimization algorithm for load scheduling in electric smelting furnaces

Electric smelting furnaces, applied in the smelting process of infusible mineral, are highly energy-intensive. In China, they waste a huge amount of electric energy, but yield a small quantity of valuable metals due to the lack of optimized load scheduling strategies. In this paper, we design a multiobjective load scheduling method to minimize the electricity cost and maximize the production output and product quality. Firstly a load scheduling model is developed based on a least square support vector machine, which is a robust empirical model with simple formulation and low sensitivity to external disturbance. We utilize a modified multiobjective particle swarm optimization algorithm to solve the optimization model. The proposed algorithm adopts a supervised population initialization that reuses the past optimal solutions and digs out new candidate solutions to guide the current optimization. An elaborate constraint-handing strategy is devised, which repairs the infeasible solutions that violate the maximum demand constraint and reserve the ones that violate one production constraint but performing excellently on the other production targets. The case study on a typical magnesia-smelting plant shows that the proposed multi-objective load scheduling model and algorithm can achieve an increase of about 14.5% in the production output, an improvement of about 0.46% of the magnesia in the product, and a slight saving in electricity cost.