A Genetic Algorithms Based Multi-Objective Optimization Approach Applied to Hydrometallurgical Circuit for Ocean Nodules


Several hydrometallurgical processes have been studied for the extraction of metals from lean ores utilizing various flow sheet options. Of particular significance is the grade of the ore being treated, the energy consumed and associated costs, options for byproduct recovery, and the relative price of the products. A process scheme needs to be optimized for simultaneously maximizing metal throughput and minimizing the direct operating costs incurred within constraints set for the operating variables. This leads to a multi-objective optimization problem. The range of input grades for raw material, which a flowsheet can handle, needs to be worked out based on an optimization exercise. A lean manganese-bearing resource such as polymetallic sea nodules has been chosen in this article for the development of an optimization approach based on which the input raw nodules grades are to be treated by a particular flowsheet. Only the chemical consumption costs have been adopted in this article as a measure of direct operating costs. A linear simulation model for the flowsheet has been developed, keeping a set of design parameters constant. The solutions generated by using a sequential modular approach become inputs to an optimization procedure based on a multi-objective genetic algorithm belonging to the differential evolution family. The variables considered in the optimization task are the grade of nodules and reactivity of different species inside the reactor. A nickel equivalent (t/h function) has been suggested as a measure of productivity, as it indirectly enhances the input manganese ore grade through a price ratio effect. This productivity function was maximized with the simultaneous minimization of direct chemical costs. Pareto optimal solutions were generated with grades of nodules and reactivity in the leach reactor as decision variables. The effect of the price ratio on the Pareto optimal solutions was also investigated. The various cases investigated clarifies the methodology for choosing an appropriate ore grade range for a given process flowsheet. Appropriate decisions regarding the nature of raw material to be used for a given flowsheet are then found on the basis of the Pareto optimal solutions.