# Design of Flotation Circuits Using Tabu-Search Algorithms: Multispecies, Equipment Design, and Profitability Parameters

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Escuela de Ingeniería Química, Pontificia Universidad Católica de Valparaíso, Valparaíso 2340000, Chile

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Departamento de Ingeniería Metalurgica y Minas, Universidad Católica del Norte, Antofagasta 1240000, Chile

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Departamento de Ingeniería Química y Procesos de Minerales, Universidad de Antofagasta, Antofagasta 1240000, Chile

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Author to whom correspondence should be addressed.

Received: 31 January 2019 / Revised: 8 March 2019 / Accepted: 9 March 2019 / Published: 15 March 2019

(This article belongs to the Special Issue Modeling, Design and Optimization of Multiphase Systems in Minerals Processing)

The design of a flotation circuit based on optimization techniques requires a superstructure for representing a set of alternatives, a mathematical model for modeling the alternatives, and an optimization technique for solving the problem. The optimization techniques are classified into exact and approximate methods. The first has been widely used. However, the probability of finding an optimal solution decreases when the problem size increases. Genetic algorithms have been the approximate method used for designing flotation circuits when the studied problems were small. The Tabu-search algorithm (TSA) is an approximate method used for solving combinatorial optimization problems. This algorithm is an adaptive procedure that has the ability to employ many other methods. The TSA uses short-term memory to prevent the algorithm from being trapped in cycles. The TSA has many practical advantages but has not been used for designing flotation circuits. We propose using the TSA for solving the flotation circuit design problem. The TSA implemented in this work applies diversification and intensification strategies: diversification is used for exploring new regions, and intensification for exploring regions close to a good solution. Four cases were analyzed to demonstrate the applicability of the algorithm: different objective function, different mathematical models, and a benchmarking between TSA and Baron solver. The results indicate that the developed algorithm presents the ability to converge to a solution optimal or near optimal for a complex combination of requirements and constraints, whereas other methods do not. TSA and the Baron solver provide similar designs, but TSA is faster. We conclude that the developed TSA could be useful in the design of full-scale concentration circuits.

*Keywords:*design; flotation circuits; Tabu-search algorithm; multispecies