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hydroPSO: A Versatile Particle Swarm Optimisation R Package for Calibration of Environmental Models (EGU 2012)

Particle Swarm Optimisation (PSO) is a recent and powerful population-based stochastic optimisation technique inspired by social behaviour of bird flocking and shares few similarities with other evolutionary techniques such as Genetic Algorithms (GA). In PSO, however, each individual of the population, termed particle in PSO terminology, adjusts its flying trajectory on the multi-dimensional search-space according to its own experience (best-known previous position) and the one of all particles in swarm (best-known global position). PSO has recently received a surge of attention given its flexibility, ease of programming, low memory and CPU requirements, and efficiency. Albeit these advantages, PSO may still get trapped into sub-optimal solutions, experience swarm explosion or convergence problems and, thus, the development and enhancements to the canonical PSO are active areas of research. To date, several modifications to the “canonical” PSO have been proposed in the literature resulting into a large and dispersed collection of codes and algorithms which might well be used for similar if not identical purposes. In this work we present hydroPSO, a platform-independent R package implementing several enhancements to the canonical PSO that we consider of utmost importance to bring this technique to the attention of a broader community of scientists and practitioners. hydroPSO is model-independent, allowing the user to interface any model code with the calibration engine without having to invest considerable effort in customizing PSO to a new calibration problem. Some of the controlling options to fine-tune hydroPSO are: four alternative topologies, several types of inertia weight schemes, time-variant acceleration coefficients, time-variant maximum velocity, regrouping of particles when premature convergence is detected, different types of boundary conditions and many others. Additionally, hydroPSO implements recent PSO variants such as: Improved Particle Swarm Optimisation (IPSO), Fully Informed Particle Swarm (FIPS), and weighted FIPS (wFIPS). Finally, an advanced sensitivity analysis using the Latin Hypercube One-At-a-Time (LH-OAT) method and user-friendly plotting summaries facilitate the interpretation and assessment of the calibration/optimisation results. We validate hydroPSO against the standard PSO algorithm (SPSO-2007) employing five test functions commonly used to assess the performance of optimisation algorithms. Additionally, we illustrate how the performance of the optimization/calibration engine is boosted by using several of the fine-tune options included in hydroPSO. Finally, we show how to interface SWAT-2005 with hydroPSO to calibrate a semi-distributed hydrological model for the Ega River basin in Spain, and how to interface MODFLOW-2000 and hydroPSO to calibrate a groundwater flow model for the regional aquifer of the Pampa del Tamarugal in Chile.

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hydroPSO:                                                     A         Versatile Particle Swarm Optimisation                                                                                                                                                                 R          Package                                       for
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                                                hydroPSO:                                                     A         Versatile Particle Swarm Optimisation                                                                                                                                                                 R          Package                                       for                     Research
                                                                                                                                                                                                                                                                                                                                                                                                                Centre

                                                                                                                        Calibration of Environmental Models
                                                                                                                         Calibration of Environmental Models                                                                                                                                                                                                                                                   EGU2012-10950
                                                                                                                                                                                                                                                                                                                                                                                                               Session: HS3.3
                                                                                                                                      Mauricio Zambrano-Bigiarini and Rodrigo Rojas
                                                                                                                                      Mauricio Zambrano-Bigiarini and Rodrigo Rojas                                                                                                                                                                                                                             Apr 25th, 2012



    1) Motivation                                                                                                                                                                                                         5) Fine-tuning Options                                                      6) hydroPSO Main Functions
    Parameter optimisation techniques are generally                                                                                                                                                                                             hydroPSO                                           Function                                                             Short Description
                                                                                                                                                                                                                         PSO Parameter                                    Value(s)
    implemented in customised pieces of (proprietary)                                                                                                                                                                                            Option
                                                                                                                                                                                                                                                                                                   lhoat()                                      Sensitivity analysis using LH-OAT (van Griensven et al.,2006)
    software, which have to be strongly modified to set up the                                                                                                                                                                                                linear, non-linear, adaptive
                                                                                                                                                                                                                                                  use.IW      inertia weight factor (aiwf),        hydromod()                                   Run the model code to be calibrated
    calibration of alternative environmental models.                                                                                                                                                                             ω               IW.type      global-local    best   ratio,
                                                                                                                                                                                                                                                              random
                                                                                                                                                                                                                                                                                                   hydroPSO()                                   Platform- and model-independent PSO calibration engine
    The latter deprives the user of the flexibility to easily reuse                                                                                                                                                              c1           c1,use.TVc1,    linear, non-linear, global-local     read_results()                               Reading hydroPSO() results. It is a wrapper to:
                                                                                                                                                                                                                                               TVc2.type      best ratio
    existing calibration codes without having to invest                                                                                                                                                                                                                                                read_particles()                         Reading ”Particles.txt” output file
                                                                                                                                                                                                                                 c2           c2,use.TVc2,
                                                                                                                                                                                                                                                              linear, non-linear
    considerable time and effort.                                                                                                                                                                                                              TVc2.type                                               read_velocities()                        Reading ”Velocities.txt” output file
                                                                                                                                                                                                                            Boundary                          absorbing, invisible,
                                                                                                                                                                                                                            condition
                                                                                                                                                                                                                                              boundary.wall
                                                                                                                                                                                                                                                              reflecting, damping
                                                                                                                                                                                                                                                                                                       read_out()                               Reading ”Model_output.txt” output file
                                                                                                                                                                                                                           Regrouping             use.RG      TRUE/FALSE                               read_convergence()    Reading ”ConvergenceMeasures.txt” output file
    2) Aim                                                                                                                                                                                                                Initial positions     Xini.type     random, lhs                              read_GofPerParticle() Reading ”Particles_GofPerIter.txt” output file
                                                                                                                                                                                                                          Initial velocites     Vini.type     random, lhs, zero
    To present and illustrate the application of hydroPSO, a                                                                                                                                                                                                                                       plot_results()                               Plotting hydroPSO()results. It is a wrapper to:
                                                                                                                                                                                                                             Updates           best.update    synchronous, asynchronous
    new global optimisation R package specifically designed                                                                                                                                                                 Maximum           use.TVlambda,                                            plot_particles()                         Plotting sampled parameters (histograms, dotty plots, ...)
                                                                                                                                                                                                                                                            linear, non-linear
    to calibrate complex real-world environmental models.                                                                                                                                                                    velocity         TVlambda.type
                                                                                                                                                                                                                                                                                                       plot_velocities()                        Plotting evolution of particle velocities
                                                                                                                                                                                                                                                              gbest, lbest, vonNeumann,
                                                                                                                                                                                                                             Topology           topology                                               plot_out()                               Plotting model outputs against observations
                                                                                                                                                                                                                                                              random
                                                                                                                                                                                                                           PSO variant            method      pso, fips, wfips, ipso                   plot_convergence()                       Plotting convergence measures (optimum and swarm radious)
    3) hydroPSO: Key Features                                                                                                                                                                                                                                                                          plot_GofPerParticle() Plotting the evolution of the goodness-of-fit per each particle
                                                                                                                                                                                                                                                                                                   verification()            Runs the model code with one or more parameter sets
        ●
            Model-independent                                                                                                                                                                                                                                                                      test_functions()                             Six n-dimensional benchmark functions included: Sphere,
        ●
            Multi-platform (GNU/Linux, Windows, Mac OS X)                                                                                                                                                                                                                                                                                       Rosenbrock, Rastrigin, Griewank, Ackley and Schaffer F6.
        ●
            State-of-the-art Particle Swarm Optimisation (PSO) as                                                                                                                                                                                                                                                                               Useful to test the PSO configuration performance for different
            calibration engine                                                                                                                                                                                                                                                                                                                  types of calibration problems.
        ●
            Minimal user intervention to interface the model code
            with the calibration engine
                                                                                                                                                                                                                       Fig 02. Dotty plots showing the model performance versus parameter
                                                                                                                                                                                                                       values, for three selected parameters (SWAT-2005 case study). Vertical
                                                                                                                                                                                                                                                                                                      7) Case Studies
        ●
            Easy plotting of results                                                                                                                                                                                    red line indicates the optimum parameter value.                                     Application Feature                      SWAT-2005                                   Modflow-2005
        ●
            Sensitivity analysis by using the Latin-Hypercube One-                                                                                                                                                                                                                                        Platform                          GNU/Linux                                  Windows 7
                                                                                                            Fig 01. Interactions among the main hydroPSO functions. User-defined files ParamRanges.txt  and
            factor-At-a-Time (LH-OAT, van Griensven et al., 2006)                                           ParamFiles.txt  defines which parameters are to be calibrated and where they have to be modified,                                                                                             Type of model                     Semi-distributed, surface                  Fully-distributed, groundwater
                                                                                                            respectively. R functions out.FUN() and gof.FUN() are used along with observations to read model outputs                                                                                                                        hydrology
        ●
            Calibration engine validated against the Standard PSO                                           and to assess model performance, respectively. Light-blue shaded boxes indicate some user intervention.
            2007 (SPSO 2007, Clerc 2011)                                                                                                                                                                                                                                                                  hydroPSO-model                    Basic, through available R                 Advanced, through user-defined
                                                                                                                                                                                                                                                                                                          interface                         functions                                  R functions
        ●
            Several fine-tuning options and PSO variants to tackle
                                                                                                                                                                                                                                                                                                          Executable model code   Single file (swat2005.out)                           Sequential batch file (*.bat)
            different kinds of optimisation problems                                                                                                                                                                   Fig 03. Evolution of parameter values along number of model
                                                                                                                                                                                                                                                                                                          Simulated model outputs Continuous-time, single-site                         Steady-state, multi-site
        ●
            Open-source code (GPL >=2)                                                                                                                                                                                 evaluations for three selected parameters (SWAT-2005 case study).
                                                                                                                                                                                                                                                                                                          Goodness-of-fit measure Pre-defined Nash-Sutcliffe                           User-defined Gaussian
        ●
            Binaries, user manual, and vignette (tutorial) are                                                                                                                                                                                                                                                                    efficiency                                           Likelihood
            available on http://www.rforge.net/hydroPSO/
                                                                                                                                                                                                                                                                                                          8) Concluding Remarks
    4) Particle Swarm Optimisation (PSO)                                                                                                                                                                                                                                                              ●
                                                                                                                                                                                                                                                                                                           hydroPSO provides an efficient and ready-to-use global optimisation engine for the
                                                                                                                                                                                                                                                                                                           calibration of different environmental models
    PSO (Kennedy and Eberhart, 1995) is a                                                                                                                                                                                                                                                             ●
                                                                                                                                                                                                                                                                                                           hydroPSO allows to carry out a typical modelling exercise: sensitivity analysis, model
    population-based            stochastic                                                                                                                                                                                                                                                                 calibration and assessment of results
    optimisation technique inspired by                                                                                                                                                                                                                                                                ●
                                                                                                                                                                                                                                                                                                           For specific problems, a customised PSO configuration will have a significant impact on the
    the social behaviour of bird flocking.                                                                                                                                                                                                                                                                 optimisation results
                                                                                                                                                                                                                                                                                                      ●
                                                                                                                                                                                                                                                                                                           Results in two case studies show that hydroPSO is effective and efficient in finding optimal
    Each individual of the population adjuts its flying trajectory                                                                                                                                                                                                                                         solutions compared to intensive MCMC-based techniques
    around the multi-dimensional search space according to its                                                                                                                                                                                                                                        ●
                                                                                                                                                                                                                                                                                                           hydroPSO shows an outstanding flexibility to tackle several types of optimisation problems
    own flying experience (local search) and that of                                                                                                                                                                                                                                                       commonly faced by the modelling community (see point 7)
    neighbouring particles (global search):                                                                                                                                                                                                                                                           ●
                                                                                                                                                                                                                                                                                                           Given the versatility added by the R environment and the large amount of packages
                                         local search             global search                                                                                                                                                                                                                            available, we believe hydroPSO can be applied to a wide class of environmental models
                                                                                                                                                                                                                                                                                                           requiring some form of parameter optimisation
        V i t  1 =  V i t  c1 U 1t  P 1 − X it   c2 U 2t  G − X i t 
                                                                                                                                                                                                                                                                                                      9) Ongoing research:
                                   X i t 1 = X i t  V i t 1                                                                                                                                                         Fig 04. Evolution of the global optimum (Gaussian likelihood) and the          ●
                                                                                                                                                                                                                                                                                                          Multi-core/parallel support, to alleviate the computational burden
                                                                                                                                                                                                                       normalised swarm radious (δnorm) along the iterations (Modflow-2005
                                                                 ω : inertia weigth
                                                                                                                                                                                                                                                                                                          Multi-objective implementation, to tackle a wider class of optimisation problems
                                                            ●
●   X i t : i-th particle position at iteration t                                                                                                                                                                      case study).                                                                   ●

                                                            ●    c1 : cognitive aceleration coefficient
                                                                                                                                                                                                                                                                      References:
        t
●   V i : i-th particle velocity at iteration t
                                                            ●    c2 : social aceleration coefficient
●   P i : i-th particle best-known position
                                                             ● U 1 t, U 2 t: independent and uniformly      Fig 05. Gaussian likelihood response surface projected onto the parameter space (pseudo 3D-dotty                                                          ●
                                                                                                                                                                                                                                                                          Zambrano-Bigiarini, M., and R. Rojas (2012), hydroPSO: A model-independent particle swarm optimization software for calibration of environmental models,
●   G       : neighbourhood best-known position                                                             plots) for selected parameters. Panels show “behavioural” samples with L > 3.8x10-2. For a subset of                                                          Environmental Modelling & Software, submitted
                                                             distributed random vectors
                                                                                                            parameters (Modflow-2005 case study).                                                                                                                     ●
                                                                                                                                                                                                                                                                          Kennedy, J., and R. Eberhart (1995), Particle swarm optimization, in Proceedings IEEE International Conference on Neural Networks, 1995, vol. 4, pp. 1942–
                                                                                                                                                                                                                                                                          1948, doi: 10.1109/ICNN.1995.488968.
                                                                                                       Mauricio Zambrano-Bigiarini and Rodrigo Rojas
www.jrc.europa.eu
                                                                                                                                                                                                                                                                      ●
                                                                                                                                                                                                                                                                          Clerc, M., 2011. Standard particle swarm optimisation. http://clerc.maurice.free.fr/pso/SPSO_descriptions.pdf. [Online; last accessed Apr-2011].
                                                                                                       European Commission • Joint Research Centre • Institute for Environment and Sustainability                                                                     ●
                                                                                                                                                                                                                                                                          van Griensven, A., T. Meixner, S. Grunwald, T. Bishop, M. Diluzio, and R. Srinivasan (2006), A global sensitivity analysis tool for the parameters of multi-
                                                                                                                                                                                                                                                                          variable catchment models, Journal of Hydrology, 324 (1–4), 10–23, doi: 10.1016/j.jhydrol.2005.09.008.
                                                                                                       Tel. +39 0332 789588 • Email: mauricio.zambrano@jrc.ec.europa.eu

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  • 1. hydroPSO: A Versatile Particle Swarm Optimisation R Package for Joint hydroPSO: A Versatile Particle Swarm Optimisation R Package for Research Centre Calibration of Environmental Models Calibration of Environmental Models EGU2012-10950 Session: HS3.3 Mauricio Zambrano-Bigiarini and Rodrigo Rojas Mauricio Zambrano-Bigiarini and Rodrigo Rojas Apr 25th, 2012 1) Motivation 5) Fine-tuning Options 6) hydroPSO Main Functions Parameter optimisation techniques are generally hydroPSO Function Short Description PSO Parameter Value(s) implemented in customised pieces of (proprietary) Option lhoat() Sensitivity analysis using LH-OAT (van Griensven et al.,2006) software, which have to be strongly modified to set up the linear, non-linear, adaptive use.IW inertia weight factor (aiwf), hydromod() Run the model code to be calibrated calibration of alternative environmental models. ω IW.type global-local best ratio, random hydroPSO() Platform- and model-independent PSO calibration engine The latter deprives the user of the flexibility to easily reuse c1 c1,use.TVc1, linear, non-linear, global-local read_results() Reading hydroPSO() results. It is a wrapper to: TVc2.type best ratio existing calibration codes without having to invest     read_particles() Reading ”Particles.txt” output file c2 c2,use.TVc2, linear, non-linear considerable time and effort. TVc2.type     read_velocities() Reading ”Velocities.txt” output file Boundary absorbing, invisible, condition boundary.wall reflecting, damping     read_out() Reading ”Model_output.txt” output file Regrouping use.RG TRUE/FALSE     read_convergence() Reading ”ConvergenceMeasures.txt” output file 2) Aim Initial positions Xini.type random, lhs     read_GofPerParticle() Reading ”Particles_GofPerIter.txt” output file Initial velocites Vini.type random, lhs, zero To present and illustrate the application of hydroPSO, a plot_results() Plotting hydroPSO()results. It is a wrapper to: Updates best.update synchronous, asynchronous new global optimisation R package specifically designed Maximum use.TVlambda,     plot_particles() Plotting sampled parameters (histograms, dotty plots, ...) linear, non-linear to calibrate complex real-world environmental models. velocity TVlambda.type     plot_velocities() Plotting evolution of particle velocities gbest, lbest, vonNeumann, Topology topology     plot_out() Plotting model outputs against observations random PSO variant method pso, fips, wfips, ipso     plot_convergence() Plotting convergence measures (optimum and swarm radious) 3) hydroPSO: Key Features     plot_GofPerParticle() Plotting the evolution of the goodness-of-fit per each particle verification() Runs the model code with one or more parameter sets ● Model-independent test_functions() Six n-dimensional benchmark functions included: Sphere, ● Multi-platform (GNU/Linux, Windows, Mac OS X) Rosenbrock, Rastrigin, Griewank, Ackley and Schaffer F6. ● State-of-the-art Particle Swarm Optimisation (PSO) as Useful to test the PSO configuration performance for different calibration engine types of calibration problems. ● Minimal user intervention to interface the model code with the calibration engine Fig 02. Dotty plots showing the model performance versus parameter values, for three selected parameters (SWAT-2005 case study). Vertical 7) Case Studies ● Easy plotting of results red line indicates the optimum parameter value. Application Feature SWAT-2005 Modflow-2005 ● Sensitivity analysis by using the Latin-Hypercube One- Platform GNU/Linux Windows 7 Fig 01. Interactions among the main hydroPSO functions. User-defined files ParamRanges.txt  and factor-At-a-Time (LH-OAT, van Griensven et al., 2006) ParamFiles.txt  defines which parameters are to be calibrated and where they have to be modified, Type of model Semi-distributed, surface Fully-distributed, groundwater respectively. R functions out.FUN() and gof.FUN() are used along with observations to read model outputs hydrology ● Calibration engine validated against the Standard PSO and to assess model performance, respectively. Light-blue shaded boxes indicate some user intervention. 2007 (SPSO 2007, Clerc 2011) hydroPSO-model Basic, through available R Advanced, through user-defined interface functions R functions ● Several fine-tuning options and PSO variants to tackle Executable model code Single file (swat2005.out) Sequential batch file (*.bat) different kinds of optimisation problems Fig 03. Evolution of parameter values along number of model Simulated model outputs Continuous-time, single-site Steady-state, multi-site ● Open-source code (GPL >=2) evaluations for three selected parameters (SWAT-2005 case study). Goodness-of-fit measure Pre-defined Nash-Sutcliffe User-defined Gaussian ● Binaries, user manual, and vignette (tutorial) are efficiency Likelihood available on http://www.rforge.net/hydroPSO/ 8) Concluding Remarks 4) Particle Swarm Optimisation (PSO) ● hydroPSO provides an efficient and ready-to-use global optimisation engine for the calibration of different environmental models PSO (Kennedy and Eberhart, 1995) is a ● hydroPSO allows to carry out a typical modelling exercise: sensitivity analysis, model population-based stochastic calibration and assessment of results optimisation technique inspired by ● For specific problems, a customised PSO configuration will have a significant impact on the the social behaviour of bird flocking. optimisation results ● Results in two case studies show that hydroPSO is effective and efficient in finding optimal Each individual of the population adjuts its flying trajectory solutions compared to intensive MCMC-based techniques around the multi-dimensional search space according to its ● hydroPSO shows an outstanding flexibility to tackle several types of optimisation problems own flying experience (local search) and that of commonly faced by the modelling community (see point 7) neighbouring particles (global search): ● Given the versatility added by the R environment and the large amount of packages local search global search available, we believe hydroPSO can be applied to a wide class of environmental models requiring some form of parameter optimisation V i t  1 =  V i t  c1 U 1t  P 1 − X it   c2 U 2t  G − X i t  9) Ongoing research: X i t 1 = X i t  V i t 1 Fig 04. Evolution of the global optimum (Gaussian likelihood) and the ● Multi-core/parallel support, to alleviate the computational burden normalised swarm radious (δnorm) along the iterations (Modflow-2005 ω : inertia weigth Multi-objective implementation, to tackle a wider class of optimisation problems ● ● X i t : i-th particle position at iteration t case study). ● ● c1 : cognitive aceleration coefficient References: t ● V i : i-th particle velocity at iteration t ● c2 : social aceleration coefficient ● P i : i-th particle best-known position ● U 1 t, U 2 t: independent and uniformly Fig 05. Gaussian likelihood response surface projected onto the parameter space (pseudo 3D-dotty ● Zambrano-Bigiarini, M., and R. Rojas (2012), hydroPSO: A model-independent particle swarm optimization software for calibration of environmental models, ● G : neighbourhood best-known position plots) for selected parameters. Panels show “behavioural” samples with L > 3.8x10-2. For a subset of Environmental Modelling & Software, submitted distributed random vectors parameters (Modflow-2005 case study). ● Kennedy, J., and R. Eberhart (1995), Particle swarm optimization, in Proceedings IEEE International Conference on Neural Networks, 1995, vol. 4, pp. 1942– 1948, doi: 10.1109/ICNN.1995.488968. Mauricio Zambrano-Bigiarini and Rodrigo Rojas www.jrc.europa.eu ● Clerc, M., 2011. Standard particle swarm optimisation. http://clerc.maurice.free.fr/pso/SPSO_descriptions.pdf. [Online; last accessed Apr-2011]. European Commission • Joint Research Centre • Institute for Environment and Sustainability ● van Griensven, A., T. Meixner, S. Grunwald, T. Bishop, M. Diluzio, and R. Srinivasan (2006), A global sensitivity analysis tool for the parameters of multi- variable catchment models, Journal of Hydrology, 324 (1–4), 10–23, doi: 10.1016/j.jhydrol.2005.09.008. Tel. +39 0332 789588 • Email: mauricio.zambrano@jrc.ec.europa.eu