A hybrid augmented Lagrangian multiplier method for the open pit mines long-term production scheduling problem optimization

To improve the quality of decision making in the mining operation, it is essential to find global optimum in problems with large dimensional scales. It is widely accepted that Long-term production scheduling (LTPS) problem is playing key role in mining projects to improve their performance by considering availability constraints while maximizing the project total profits during the period. Since production scheduling problems are NP-hard, there is need of improving scheduling methodologies to get good solution. This paper presents a hybrid model between augmented Lagrangian relaxation (ALR) and Genetic algorithm (GA) to solve the LTPS problem. We propose to apply the ALR method on the LTPS problem which to improve its performance speeding up the convergence and also, GA is used to update the Lagrangian multipliers. The results from case study show that the ALR method is effective in solving large-scale problem and generation a feasible solution then the traditional linearization method. Furthermore, the proposed hybrid strategy based on GA showed better performance in comparison to the available methods.

[1]  Lou Caccetta,et al.  An Application of Branch and Cut to Open Pit Mine Scheduling , 2003, J. Glob. Optim..

[2]  Birol Elevli Open pit mine design and extraction sequencing by use of OR and AI concepts , 1995 .

[3]  Tsuyoshi Adachi,et al.  Surface Mining Technologies, Today and Future. Optimum Production Scale and Scheduling of Open Pit Mines Using Revised 4-D Network Relaxation Method. , 2001 .

[4]  Salih Ramazan,et al.  Traditional and New MIP Models for Production Scheduling With In-Situ Grade Variability , 2004 .

[5]  Natashia Boland,et al.  A strengthened formulation and cutting planes for the open pit mine production scheduling problem , 2010, Comput. Oper. Res..

[6]  Robert Underwood,et al.  A scheduling algorithm for open pit mines , 1996 .

[7]  Daniel Bienstock,et al.  A New LP Algorithm for Precedence Constrained Production Scheduling , 2009 .

[8]  Ambros M. Gleixner,et al.  LP-based disaggregation approaches to solving the open pit mining production scheduling problem with block processing selectivity , 2009, Comput. Oper. Res..

[9]  E. Moosavi,et al.  Improvement of Lagrangian relaxation performance for open pit mines constrained long-term production scheduling problem , 2014 .

[10]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[11]  Sadamichi Mitsumori Optimum Production Scheduling of Multicommodity in Flow Line , 1972, IEEE Trans. Syst. Man Cybern..

[12]  Sei-ichiro Kamata,et al.  A New Algorithm for , 1999 .

[13]  Ted K. Ralphs,et al.  Integer and Combinatorial Optimization , 2013 .

[14]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[15]  José Mario Martínez,et al.  On Augmented Lagrangian Methods with General Lower-Level Constraints , 2007, SIAM J. Optim..

[16]  Ambros M. Gleixner,et al.  Solving Large-scale Open Pit Mining Production Scheduling Problems by Integer Programming , 2008 .

[17]  Bin Zhang,et al.  Dynamic optimization of cutoff grade in underground metal mining , 2010 .

[18]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[19]  B. Denby,et al.  Genetic algorithms for flexible scheduling of open pit operations , 1998 .

[20]  B. Tolwinski Scheduling production for open pit mines , 1998 .

[21]  Javad Gholamnejad,et al.  A new mathematical programming model for long-term production scheduling considering geological uncertainty , 2012 .

[22]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[23]  Alexandre Boucher,et al.  Multivariate Block-Support Simulation of the Yandi Iron Ore Deposit, Western Australia , 2012, Mathematical Geosciences.

[24]  Mark Gershon,et al.  Optimal mine production scheduling: evaluation of large scale mathematical programming approaches , 1983 .

[25]  Yong He,et al.  A hybrid intelligent optimization method for multiple metal grades optimization , 2011, Neural Computing and Applications.

[26]  K. Dagdelen,et al.  Fundamental tree algorithm in optimising production scheduling for open pit mine design , 2005 .

[27]  M. Kumral,et al.  A simulated annealing approach to mine production scheduling , 2005, J. Oper. Res. Soc..

[28]  H. Askari-Nasab,et al.  Mixed integer linear programming formulations for open pit production scheduling , 2011 .

[29]  Maksud Ibrahimov,et al.  Scheduling in iron ore open-pit mining , 2014 .

[30]  Claude Lemaréchal,et al.  Lagrangian Relaxation , 2000, Computational Combinatorial Optimization.

[31]  Philip Wolfe,et al.  Validation of subgradient optimization , 1974, Math. Program..

[32]  M. Jünger,et al.  50 Years of Integer Programming 1958-2008 - From the Early Years to the State-of-the-Art , 2010 .

[33]  Marshall L. Fisher,et al.  The Lagrangian Relaxation Method for Solving Integer Programming Problems , 2004, Manag. Sci..

[34]  Alexandra M. Newman,et al.  Tailored Lagrangian Relaxation for the open pit block sequencing problem , 2014, Ann. Oper. Res..

[35]  Alexandra M. Newman,et al.  MineLib: a library of open pit mining problems , 2013, Ann. Oper. Res..

[36]  Arthur M. Geoffrion,et al.  Lagrangian Relaxation for Integer Programming , 2010, 50 Years of Integer Programming.

[37]  Thys B Johnson,et al.  OPTIMUM OPEN PIT MINE PRODUCTION SCHEDULING , 1968 .