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An improved merge search algorithm for the constrained pit problem in open-pit mining

Published: 13 July 2019 Publication History

Abstract

Conventional 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 aggregating variables or constraints. Merge search algorithms achieve this by generating populations of solutions, either by heuristic construction [4], or by finding neighbours to an initial solution [12]. This paper presents a merge search algorithm that improves the population generation heuristic in [12] and utilises a variable grouping heuristic that exploits the common information across a population to aggregate groups of variables in order to create a reduced subproblem. The algorithm is tested on some well known benchmarks for a complex problem called the constrained pit (CPIT) problem and it is compared to results produced by a merge search algorithm previously used on the same problem and the results published on the minelib [9] website.

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Daniel Bienstock and Mark Zuckerberg. 2010. Solving LP pelaxations 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.
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Andreas Bley, Natashia Boland, Christopher Fricke, and Gary Froyland. 2010. A strengthened formulation and cutting planes for the open pit mine production scheduling problem. Computers & Operations Research 37, 9 (Sept. 2010), 1641--1647.
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Christian Blum, Pedro Pinacho, Manuel López-Ibáñez, and José A. Lozano. 2016. Construct, Merge, Solve & Adapt A new general algorithm for combinatorial optimization. Computers & Operations Research 68 (2016), 75 -- 88.
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Barbara Chapman, Gabriele Jost, and Ruud Van Der Pas. 2008. Using OpenMP: portable shared memory parallel programming. Vol. 10. MIT press.
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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/
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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.
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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.
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Angus Kenny, Xiaodong Li, and Andreas T. Ernst. 2018. A merge search algorithm and its application to the constrained pit problem in mining. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO '18). ACM, 8.
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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.
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Scott Kirkpatrick, C Daniel Gelatt, and Mario P Vecchi. 1983. Optimization by simulated annealing. science 220, 4598 (1983), 671--680.
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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.
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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).
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Dhananjay Thiruvady, Christian Blum, and Andreas T Ernst. 2019. Maximising the net present value of project schedules using CMSA and parallel ACO. In International Workshop on Hybrid Metaheuristics. Springer, 16--30.

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      cover image ACM Conferences
      GECCO '19: Proceedings of the Genetic and Evolutionary Computation Conference
      July 2019
      1545 pages
      ISBN:9781450361118
      DOI:10.1145/3321707
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      Published: 13 July 2019

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      Author Tags

      1. applied computing
      2. hybrid algorithms
      3. merge search
      4. mine planning
      5. mixed integer programming

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      GECCO '19
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      GECCO '19: Genetic and Evolutionary Computation Conference
      July 13 - 17, 2019
      Prague, Czech Republic

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