Elsevier

Computers & Chemical Engineering

Volume 108, 4 January 2018, Pages 349-359
Computers & Chemical Engineering

A biobjective DC programming approach to optimization of rougher flotation process

https://doi.org/10.1016/j.compchemeng.2017.10.001Get rights and content

Highlights

  • •

    The problem of optimizing the rougher flotation process and determining the best operating conditions.

  • •

    A general bi-objective DC programming framework.

  • •

    A particular implementation of the framework for optimizing the copper concentrate grade and recovery.

  • •

    Computational evaluation of the framework via a case study for a Mongolian mineral processing plant.

Abstract

New economic and environmental challenges have recently led to a growing interest in modern mathematical optimization and modeling techniques in order to improve the froth flotation performance. An important issue is that most of corresponding mathematical optimization models are non-convex and involve multiple criteria; hence, conventional convex optimization methods cannot guarantee finding global (Pareto) optimal solutions. We propose a deterministic biobjective mathematical programming framework, combined with experimental design and regression analysis, to optimizing flotation performance and determining the optimal operating conditions that meet specific needs. The framework aims at maximizing concentrate grade and recovery and is based on some well-known and advanced approaches including an epsilon-constraint method, DC programming, an exact penalty method, and the special global search strategy. To demonstrate the effectiveness of the proposed approach, we present a case study for the rougher flotation process of copper-molybdenum ores performed at the Erdenet Mining Corporation Mineral Processing Plant (Mongolia).

Section snippets

Problem statement and preliminaries

Let us consider the following general DC programming problemPwhere the set S is convex and the functions fi(x) are DC (difference of convex) functions, i.e. they can be represented as the difference of two convex functions: fi(x) = gi(x) − hi(x), gi(x), hi(x) are convex functions, x ∈ S, i ∈ I ∪ {0}.

We suppose that the feasible set of the problem (P) is not empty:D:={x∈S∣fi(x)⩽0,i∈I}≠∅,and the optimal value of Problem (P) is finite:V(P):=infx{f0(x)∣x∈D}>−∞.

The general optimization problem (P) is a

Methodology

In this section we describe the main components and a general scheme of our approach that consists in solving a bi-objective non-convex optimization problem with DC objective functions and box constraints. We carefully describe all components of the proposed approach and design its implementation for a particular problem of determining the best operating conditions of the rougher flotation process.

Case study

In this section we carry out a case study to both maximize the metallurgical performance (concentrate grade and recovery) and determine the best operating conditions (e.g. reagent dosages) of the rougher flotation process at the Erdenet Mining Corporation Mineral Processing Plant (Erdenet, Mongolia).

Erdenet Mining Corporation is a joint Russian-Mongolian enterprise founded (together with the city of Erdenet) in 1974 and aimed at the commercial exploitation of Asia's largest porphyry

Conclusion

This work was motivated by the problem of improving efficiency and quality of the froth flotation process used in the mineral processing industry. For many years, the flotation process has been controlled empirically by human operators whose decisions may lead to poor performance and the decrease of the concentrate production profitability. In some cases an increase of even several percent in recovery and/or concentrate grade may have a significant economic effect and convert previously

Acknowledgments

The work was supported by the Russian Science Foundation under research project No. 15-11-20015. The authors thank the Erdenet Mining Corporation for providing actual operating data.

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