Multiobjective Production Planning Optimization Using Hybrid Evolutionary Algorithms for Mineral Processing

The production planning optimization for mineral processing is important for non-renewable raw mineral resource utilization. This paper presents a nonlinear multiobjective programming model for a mineral processing production planning (MPPP) for optimizing five production indices, including its iron concentrate output, the concentrate grade, the concentration ratio, the metal recovery, and the production cost. A gradient-based hybrid operator is proposed in two evolutionary algorithms named the gradient-based NSGA-II (G-NSGA-II) and the gradient-based SPEA2 (G-SPEA2) for MPPP optimization. The gradient-based operator of the proposed hybrid operator is normalized as a strictly convex cone combination of negative gradient direction of each objective, and is provided to move each selected point along some descent direction of the objective functions to the Pareto front, so as to reduce the invalid trial times of crossover and mutation. Two theorems are established to reveal a descent direction for the improvement of all objective functions. Experiments on standard test problems, namely ZDT 1-3, CONSTR, SRN, and TNK, have demonstrated that the proposed algorithms can improve the chance of minimizing all objectives compared to pure evolutionary algorithms in solving the multiobjective optimization problems with differentiable objective functions under short running time limitation. Computational experiments in MPPP application case have indicated that the proposed algorithms can achieve better production indices than those of NSGA-II, T-NSGA-FD, T-NSGA-SP, and SPEA2 in the case of small number of generations. Also, those experimental results show that the proposed hybrid operators have better performance than that of pure gradient-based operators in attaining either a broad distribution or maintaining much diversity of obtained non-dominated solutions.