Comparing MIQCP Solvers to a Specialised Algorithm for Mine Production Scheduling

This paper investigates the performance of several out-of-the-box solvers for mixed-integer quadratically constrained programmes (MIQCPs) on an open pit mine production scheduling problem with mixing constraints. We compare the solvers BARON, Couenne, SBB, and SCIP to a problem-specific algorithm on two different MIQCP formulations. The computational results presented show that general-purpose solvers with no particular knowledge of problem structure are able to nearly match the performance of a hand-crafted algorithm.

[1]  Tobias Achterberg,et al.  Constraint integer programming , 2007 .

[2]  Robert E. Bixby,et al.  MIP: Theory and Practice - Closing the Gap , 1999, System Modelling and Optimization.

[3]  Christopher Fricke.  Applications of integer programming in open pit mining , 2006 .

[4]  Martin Grötschel,et al.  Polyhedral and Computational Investigations for Designing Communication Networks with High Survivability Requirements , 1995, Oper. Res..

[5]  Klaus Schittkowski,et al.  A trust region SQP algorithm for mixed-integer nonlinear programming , 2007, Optim. Lett..

[6]  T. Koch,et al.  Solving Steiner Tree Problems in Graphs to Optimality , 1998 .

[7]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[8]  Thorsten Koch,et al.  Solving Steiner tree problems in graphs to optimality , 1998, Networks.

[9]  Jeff T. Linderoth,et al.  FilMINT: An Outer-Approximation-Based Solver for Nonlinear Mixed Integer Programs , 2008 .

[10]  Salih Ramazan,et al.  The new Fundamental Tree Algorithm for production scheduling of open pit mines , 2007, Eur. J. Oper. Res..

[11]  Stefan Vigerske,et al.  LaGO: a (heuristic) Branch and Cut algorithm for nonconvex MINLPs , 2008, Central Eur. J. Oper. Res..

[12]  Leo Liberti,et al.  Branching and bounds tighteningtechniques for non-convex MINLP , 2009, Optim. Methods Softw..

[13]  Behrooz Karimi,et al.  Long-term open pit mine production planning: a review of models and algorithms , 2008 .

[14]  Gérard Cornuéjols,et al.  An algorithmic framework for convex mixed integer nonlinear programs , 2008, Discret. Optim..

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

[16]  Nikolaos V. Sahinidis,et al.  Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming , 2002 .

[17]  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..