Optimization Approaches for a Complex Dairy Farm Simulation Model
This paper describes the optimization of a complex
dairy farm simulation model using two quite different methods of
optimization, the Genetic algorithm (GA) and the Lipschitz
Branch-and-Bound (LBB) algorithm. These techniques have been
used to improve an agricultural system model developed by Dexcel
Limited, New Zealand, which describes a detailed representation of
pastoral dairying scenarios and contains an 8-dimensional parameter
space. The model incorporates the sub-models of pasture growth and
animal metabolism, which are themselves complex in many cases.
Each evaluation of the objective function, a composite 'Farm
Performance Index (FPI)', requires simulation of at least a one-year
period of farm operation with a daily time-step, and is therefore
computationally expensive. The problem of visualization of the
objective function (response surface) in high-dimensional spaces is
also considered in the context of the farm optimization problem.
Adaptations of the sammon mapping and parallel coordinates
visualization are described which help visualize some important
properties of the model-s output topography. From this study, it is
found that GA requires fewer function evaluations in optimization
than the LBB algorithm.
[1] R.P.S. Hart, M.T. Larcombe, R.A. Sherlock, and L.A. Smith,
Optimization techniques for a computer simulation of a pastoral dairy
farm, Computers and Electronics in Agriculture, 19 (1998), 129-153.
[2] M.C. Fu , Optimization via simulation: a review, Annals of Operations
Research, 53 (1994), 199-247.
[3] D.G.Mayer, B. P. Kinghorn, and A.A. Archer, Differential evolution - an
easy and efficient evolutionary algorithm for model optimisation,
Agricultural Systems, 83 (2005), 315-328.
[4] A.E. Dooley, W.J. Parker, and H.T. Blair, Modelling of transport costs
and logistics for on-farm milk segregation in New Zealand dairying,
Computers and Electronics in Agriculture, 48 (2005), 75-91.
[5] The Treasury. (2007, November 25). Available:
http://www.treasury.govt.nz/economy/overview/2007/07.htm#_tocPrim
ary_Industries
[6] R.A. Sherlock, K.P. Bright and P.G. Neil, An Object-Oriented Simulation
Model of a Complete Pastoral Dairy Farm, Proceeding of the
international conference on Modelling and Simulation Modelling and
Simulation Society of Australia (1997),Hobart.
[7] E. Post, Adventures with portability. Third LCI International Conference
on Linux Clusters: The HPC Revolution 2002, Florida (2002), USA.
[8] D.G. Mayer, J.A. Belward, and K. Burrage , Robust parameter settings of
evolutionary algorithms for the optimisation of agricultural systems
models, Agricultural Systems, 69 (2001), 199-213
[9] J. H. Holland, Adaptation in Natural and Artificial Systems. Ann Arbor,
Michigan: The University of Michigan Press, 1975.
[10] S.J. Mardle, S. Pascoea and M. Tamizb, An investigation of genetic
algorithms for the optimization of multi-objective fisheries bioeconomic
models, International Transaction in Operational Research,7.(2000), 33 -
49
[11] M.J. Chen, K.N. Chen, and C.W. Lin, Optimization on response surface
models for the optimal manufacturing conditions of dairy tofu, Journal of
Food Engineering, 68 (2005), 471- 480.
[12] L.G. Barioni, C.K.G. Dake, and W.J. Parker, Optimizing rotational
grazing in sheep management systems, Environment International, 25,
617 (1999), 819-825.
[13] R.G. Strongin, On the convergence of an algorithm for finding a global
extremum, Engineering Cybernetics 11 (1973), 549-555.
[14] Y.D. Sergeyev, D. Famularo, and P. Pugliese, Index branch-and-bound
algorithm for Lipschitz univariate global optimization with multiextremal
constraints, Journal of Global Optimization, 21, (2001) 317-341.
[15] R. Horst, P.M. Pardalos, and Thoai N.V., Introduction to Global
Optimization, Kluwer Academic Publishers, Amsterdam, 1995
[16] E. Gourdin, P. Hansen and B. Jaumard, Global optimization of
Multivariate Lipschitz Functions: Survey and Computational
Comparison, Les cahier du GERAD, 1994.
[17] P. Hansen and B. Jaumard, Lipschitz optimization In R. Horst and P. M.
Pardalos (eds.) Handbook of Global Optimization (pp 407- 487).
Dordrecht/Boston/London: Kluwer Academic Publishers, 1995
[18] L. Padula and M.A. Arbib, System Theory, W.B. Saunders, Philadelphia,
1974.
[19] S. J. R. Woodward, Dynamical systems models and their application to
optimising grazing management, In R.M. Peart and R.B. Curry (eds.),
Agricultural Systems Modelling and Simulation, Marcel Dekker, 1997.
[20] W. Gropp, E. Lusk, and A. Skjellum, Using MPI: Portable Parallel
Programming with the Message Passing Interface, The MIT Press,
Massachusetts, 1994.
[21] J.W. Sammon, A non-linear mapping for data analysis. IEEE
Transactions on computers, 5 (1969), 401-409.
[1] R.P.S. Hart, M.T. Larcombe, R.A. Sherlock, and L.A. Smith,
Optimization techniques for a computer simulation of a pastoral dairy
farm, Computers and Electronics in Agriculture, 19 (1998), 129-153.
[2] M.C. Fu , Optimization via simulation: a review, Annals of Operations
Research, 53 (1994), 199-247.
[3] D.G.Mayer, B. P. Kinghorn, and A.A. Archer, Differential evolution - an
easy and efficient evolutionary algorithm for model optimisation,
Agricultural Systems, 83 (2005), 315-328.
[4] A.E. Dooley, W.J. Parker, and H.T. Blair, Modelling of transport costs
and logistics for on-farm milk segregation in New Zealand dairying,
Computers and Electronics in Agriculture, 48 (2005), 75-91.
[5] The Treasury. (2007, November 25). Available:
http://www.treasury.govt.nz/economy/overview/2007/07.htm#_tocPrim
ary_Industries
[6] R.A. Sherlock, K.P. Bright and P.G. Neil, An Object-Oriented Simulation
Model of a Complete Pastoral Dairy Farm, Proceeding of the
international conference on Modelling and Simulation Modelling and
Simulation Society of Australia (1997),Hobart.
[7] E. Post, Adventures with portability. Third LCI International Conference
on Linux Clusters: The HPC Revolution 2002, Florida (2002), USA.
[8] D.G. Mayer, J.A. Belward, and K. Burrage , Robust parameter settings of
evolutionary algorithms for the optimisation of agricultural systems
models, Agricultural Systems, 69 (2001), 199-213
[9] J. H. Holland, Adaptation in Natural and Artificial Systems. Ann Arbor,
Michigan: The University of Michigan Press, 1975.
[10] S.J. Mardle, S. Pascoea and M. Tamizb, An investigation of genetic
algorithms for the optimization of multi-objective fisheries bioeconomic
models, International Transaction in Operational Research,7.(2000), 33 -
49
[11] M.J. Chen, K.N. Chen, and C.W. Lin, Optimization on response surface
models for the optimal manufacturing conditions of dairy tofu, Journal of
Food Engineering, 68 (2005), 471- 480.
[12] L.G. Barioni, C.K.G. Dake, and W.J. Parker, Optimizing rotational
grazing in sheep management systems, Environment International, 25,
617 (1999), 819-825.
[13] R.G. Strongin, On the convergence of an algorithm for finding a global
extremum, Engineering Cybernetics 11 (1973), 549-555.
[14] Y.D. Sergeyev, D. Famularo, and P. Pugliese, Index branch-and-bound
algorithm for Lipschitz univariate global optimization with multiextremal
constraints, Journal of Global Optimization, 21, (2001) 317-341.
[15] R. Horst, P.M. Pardalos, and Thoai N.V., Introduction to Global
Optimization, Kluwer Academic Publishers, Amsterdam, 1995
[16] E. Gourdin, P. Hansen and B. Jaumard, Global optimization of
Multivariate Lipschitz Functions: Survey and Computational
Comparison, Les cahier du GERAD, 1994.
[17] P. Hansen and B. Jaumard, Lipschitz optimization In R. Horst and P. M.
Pardalos (eds.) Handbook of Global Optimization (pp 407- 487).
Dordrecht/Boston/London: Kluwer Academic Publishers, 1995
[18] L. Padula and M.A. Arbib, System Theory, W.B. Saunders, Philadelphia,
1974.
[19] S. J. R. Woodward, Dynamical systems models and their application to
optimising grazing management, In R.M. Peart and R.B. Curry (eds.),
Agricultural Systems Modelling and Simulation, Marcel Dekker, 1997.
[20] W. Gropp, E. Lusk, and A. Skjellum, Using MPI: Portable Parallel
Programming with the Message Passing Interface, The MIT Press,
Massachusetts, 1994.
[21] J.W. Sammon, A non-linear mapping for data analysis. IEEE
Transactions on computers, 5 (1969), 401-409.
@article{"International Journal of Information, Control and Computer Sciences:50081", author = "Jagannath Aryal and Don Kulasiri and Dishi Liu", title = "Optimization Approaches for a Complex Dairy Farm Simulation Model", abstract = "This paper describes the optimization of a complex
dairy farm simulation model using two quite different methods of
optimization, the Genetic algorithm (GA) and the Lipschitz
Branch-and-Bound (LBB) algorithm. These techniques have been
used to improve an agricultural system model developed by Dexcel
Limited, New Zealand, which describes a detailed representation of
pastoral dairying scenarios and contains an 8-dimensional parameter
space. The model incorporates the sub-models of pasture growth and
animal metabolism, which are themselves complex in many cases.
Each evaluation of the objective function, a composite 'Farm
Performance Index (FPI)', requires simulation of at least a one-year
period of farm operation with a daily time-step, and is therefore
computationally expensive. The problem of visualization of the
objective function (response surface) in high-dimensional spaces is
also considered in the context of the farm optimization problem.
Adaptations of the sammon mapping and parallel coordinates
visualization are described which help visualize some important
properties of the model-s output topography. From this study, it is
found that GA requires fewer function evaluations in optimization
than the LBB algorithm.", keywords = "Genetic Algorithm, Linux Cluster, LipschitzBranch-and-Bound, Optimization", volume = "2", number = "2", pages = "248-7", }
