Two-Level Production Plan Decomposition Based on a Hybrid MOEA for Mineral Processing

This paper addresses the integrated multiobjective production planning and decomposing (P&D) problem for mineral processing. A novel multiobjective 0–1 mixed integer nonlinear programming model is presented for the simultaneous P&D problem (O-model). In order to reduce the computational cost for solving O-model, a rolling horizon-based two-level decomposition approach is proposed to separate O-model into an upper level model (H-model) and a lower level model (L-model). An interactive partition (IP) and multiobjective gradient (MO-G)-based hybrid evolutionary multiobjective (EMO) algorithm named as IG-NSGA-II/IG-SPEA2, which takes the popular NSGA-II/SPEA2 as the basic EA, is proposed to solve both H-model and L-model, where an IP technique is designed to generate the efficient feasible combinational nodes, an ideal solution technique is provided for fathoming the infeasible nodes, an improved multiobjective gradient-based operator is developed to accelerate the evolution process in each selected node, and a cut with all continuous variables is constructed to exclude the previous feasible combination if it is not desired for the decision makers (DMs). The experimental results demonstrate that the presented two-level decomposition strategy can effectively integrate both levels. Moreover, the proposed hybrid method can effectively reduce the combinatorial space so as to concentrate the computing resource on the subspace of most interest, and can generate better feasible solutions than the pure EA in the full-space under computation time limits.

I. Introduction

Production planning and decomposing (or scheduling) are two important decision making levels for mineral process industry. The limited nonrenewable raw mineral resource and their rising price are forcing the enterprises to improve their production efficiency by careful P&D. The purpose of production planning for mineral processing is to allocate production resources (i.e., the raw minerals and the processing equipments, etc.) so as to achieve the desired production targets over a long time horizon [1]. Production plan decomposition of mineral processing, on the other hand, is to determine the resources (e.g., the raw ore combinations and allocation) for each short-term period over the entire planning horizon.