Benchmarks for the Coal Processing and Blending Problem

In this paper we present a challenging problem that many decision makers in coal mining industry face. The coal processing and blending problem (CPBP) builds upon the traditional blending problem known in operations research (OR) by including decision variables around coal processing, novel constraints as well as arbitrary user-defined profit functions which express price bonuses and penalties. The added complexity turns the traditional blending problem into a challenging black-box optimisation problem. We give an informal and mathematical description of this problem and present nine real-world problem instances as benchmark. Finally, we provide preliminary results for solving the problem by using a Genetic Algorithm (GA) and compare the results with those from a commercial Linear Programming (LP) solver. The results show that the GA significantly outperforms the LP solver in many problem instances while being marginally worse in others.

[1]  Wilfred Candler,et al.  Coal blending - with acceptance sampling , 1989, Comput. Oper. Res..

[2]  Vishal Gupta,et al.  Coal preparation plant optimization: A critical review of the existing methods , 2006 .

[3]  Marco Molinaro,et al.  Bounding the gap between the McCormick relaxation and the convex hull for bilinear functions , 2015, Math. Program..

[4]  Franz Rothlauf,et al.  Representations for genetic and evolutionary algorithms , 2002, Studies in Fuzziness and Soft Computing.

[5]  Tughrul Arslan,et al.  Elitist selection schemes for genetic algorithm based printed circuit board inspection system , 2005, 2005 IEEE Congress on Evolutionary Computation.

[6]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[7]  Günther R. Raidl,et al.  Decomposition based hybrid metaheuristics , 2015, Eur. J. Oper. Res..

[8]  Atul Sharma,et al.  An experimental study of the effect of coal blending on ash deposition , 2004 .

[9]  R. K. Ursem Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[10]  Mohammed Alfaki,et al.  Strong formulations for the pooling problem , 2013, J. Glob. Optim..

[11]  E. Weinberger,et al.  Correlated and uncorrelated fitness landscapes and how to tell the difference , 1990, Biological Cybernetics.

[12]  M. Chakraborty,et al.  Multi criteria genetic algorithm for optimal blending of coal , 2012 .

[13]  Parag C. Pendharkar,et al.  Nonlinear programming and genetic search application for production scheduling in coal mines , 2000, Ann. Oper. Res..

[14]  Zbigniew Michalewicz,et al.  The travelling thief problem: The first step in the transition from theoretical problems to realistic problems , 2013, 2013 IEEE Congress on Evolutionary Computation.

[15]  D. E. Goldberg,et al.  Simple Genetic Algorithms and the Minimal, Deceptive Problem , 1987 .

[16]  J. Speight,et al.  Chemistry and technology of coal , 2012 .

[17]  C. A. Haverly Studies of the behavior of recursion for the pooling problem , 1978, SMAP.

[18]  Bernard Manderick,et al.  The Genetic Algorithm and the Structure of the Fitness Landscape , 1991, ICGA.

[19]  Urszula Lorenz,et al.  Hard coal for energetic purposes: price-quality relationships; international coal market observations and Polish practice , 2003 .

[20]  Mohammed Alfaki,et al.  Models and Solution Methods for the Pooling Problem , 2012 .

[21]  H. Christopher Frey,et al.  Coal blending optimization under uncertainty , 1995 .

[22]  Hanif D. Sherali,et al.  Models for a coal blending and distribution problem , 1993 .

[23]  L. Shih Planning of fuel coal imports using a mixed integer programming method , 1997 .

[24]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation) , 2006 .