Angus Kenny
ABSTRACT
Many large-scale combinatorial problems contain too many variables and constraints for conventional mixed-integer programming (MIP) solvers to manage. To make the problems easier for the solvers to handle, various meta-heuristic techniques can be applied to reduce the size of the search space, by removing, or aggregating, variables and constraints. A novel meta-heuristic technique is presented in this paper called merge search, which takes an initial solution and uses the information from a large population of neighbouring solutions to determine promising areas of the search space to focus on. The population is merged to produce a restricted sub-problem, with far fewer variables and constraints, which can then be solved by a MIP solver. Merge search is applied to a complex problem from open-pit mining called the constrained pit (CPIT) problem, and compared to current state-of-the-art results on well known benchmark problems minelib [7] and is shown to give better quality solutions in five of the six instances.
- Jacques F Benders. 1962. Partitioning procedures for solving mixed-variables programming problems. Numerische mathematik 4, 1 (1962), 238--252. Google Scholar
Digital Library
- Daniel Bienstock and Mark Zuckerberg. 2010. Solving LP Relaxations of Large-Scale Precedence Constrained Problems. In Integer Programming and Combinatorial Optimization, Friedrich Eisenbrand and F. Bruce Shepherd (Eds.). Number 6080 in Lecture Notes in Computer Science. Springer Berlin Heidelberg. Google ScholarDigital Library
- Christian Blum, Pedro Pinacho, Manuel Lopez-Ibanez, and Jose A. Lozano. 2016. Construct, Merge, Solve & Adapt A new general algorithm for combinatorial optimization. Computers & Operations Research 68 (2016), 75 -- 88. Google ScholarDigital Library
- Barbara Chapman, Gabriele Jost, and Ruud Van Der Pas. 2008. Using OpenMP: portable shared memory parallel programming. Vol. 10. MIT press. Google ScholarDigital Library
- Renaud Chicoisne, Daniel Espinoza, Marcos Goycoolea, Eduardo Moreno, and Enrique Rubio. 2012. A new algorithm for the open-pit mine production scheduling problem. Operations Research 60, 3 (2012), 517--528. Google ScholarDigital Library
- Jacques Desrosiers and Marco E. Lübbecke. 2005. A Primer in Column Generation. Springer US, Boston, MA, 1--32.Google Scholar
- Daniel Espinoza, Marcos Goycoolea, Eduardo Moreno, and Alexandra N. Newman. 2012. Minelib: A Library of Open Pit Mining Problems. Annals of Operations Research 206(1) (2012), 91--114. http://mansci-web.uai.cl/minelib/Google Scholar
- Dorit S. Hochbaum and Anna Chen. 2000. Performance Analysis and Best Implementations of Old and New Algorithms for the Open-Pit Mining Problem. Operations Research 48, 6 (Dec. 2000), 894--914. Google ScholarDigital Library
- Enrique Jélvez, Nelson Morales, Pierre Nancel-Penard, Juan Peypouquet, and Patricio Reyes. 2016. Aggregation heuristic for the open-pit block scheduling problem. European Journal of Operational Research 249, 3 (2016), 1169--1177.Google ScholarCross Ref
- Angus Kenny, Xiaodong Li, Andreas T. Ernst, and Dhananjay Thiruvady. 2017. Towards Solving Large-scale Precedence Constrained Production Scheduling Problems in Mining. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO '17). ACM, 1137--1144. Google ScholarDigital Library
- Scott Kirkpatrick, C Daniel Gelatt, and Mario P Vecchi. 1983. Optimization by simulated annealing, science 220, 4598 (1983), 671--680.Google Scholar
- C. Meagher, R. Dimitrakopoulos, and D. Avis. 2014. Optimized open pit mine design, pushbacks and the gap problem-a review. Journal of Mining Science 50, 3 (May 2014), 508--526.Google ScholarCross Ref
- Gonzalo Ignacio Muñoz Martínez. 2012. Modelos de optimización lineal entera y aplicaciones a la minería. (2012).Google Scholar
- Napoleão Nepomuceno, Plácido Pinheiro, and André L. V. Coelho. 2008. A Hybrid Optimization Framework for Cutting and Packing Problems. Springer Berlin Heidelberg, Berlin, Heidelberg, 87--99.Google Scholar
- Jean-Claude Picard. 1976. Maximal closure of a graph and applications to combinatorial problems. Management science 22, 11 (1976), 1268--1272. Google ScholarDigital Library
- Franz Rothlauf. 2011. Optimization Problems. Springer Berlin Heidelberg, Berlin, Heidelberg, 7--44.Google Scholar
- E-G Talbi. 2002. A taxonomy of hybrid metaheuristics. Journal of heuristics 8, 5 (2002), 541--564. Google ScholarDigital Library
- Dhananjay Thiruvady, Davaatseren Baatar, Andreas T. Ernst, Angus Kenny, Mohan Krishnamoorthy, and Gaurav Singh. 2018. Mixed Integer Programming Based Merge Search for Open Pit Block Scheduling. Computers & Operations Research (under review) (2018).Google Scholar
Index Terms
- A merge search algorithm and its application to the constrained pit problem in mining
Recommendations
An improved merge search algorithm for the constrained pit problem in open-pit mining
GECCO '19: Proceedings of the Genetic and Evolutionary Computation ConferenceConventional mixed-integer programming (MIP) solvers can struggle with many large-scale combinatorial problems, as they contain too many variables and constraints. Meta-heuristics can be applied to reduce the size of these problems by removing or ...
Towards solving large-scale precedence constrained production scheduling problems in mining
GECCO '17: Proceedings of the Genetic and Evolutionary Computation ConferencePit planning and long-term production scheduling are important tasks within the mining industry. This is a great opportunity for optimisation techniques, as the scale of a lot of mining operations means that a small percentage increase in efficiency can ...
A New Algorithm for the Open-Pit Mine Production Scheduling Problem
For the purpose of production scheduling, open-pit mines are discretized into three-dimensional arrays known as block models. Production scheduling consists of deciding which blocks should be extracted, when they should be extracted, and what to do with ...
Comments