SCRF2010_10.Juan_PSO_uncertainty_SCRF_final

Annual Meeting 2010 Stanford Center for Reservoir forecasting Advances in Particle Swarm  Optimization and application to  history Matching: Stanford VI Juan Luis Fernández Martínez Stanford University UC Berkeley‐Lawrence Berkeley Lab Oviedo University Spain In collaboration with Tapan Mukerji, Amit Suman and Esperanza García‐Gonzalo (Oviedo University,Spain) INDEX • Advances in PSO design • Application of PSO to the History Matching Problem (Uncertainty analysis) • (TIP) Preliminary results on Differential Evolution SCRF 2010 I Advances in PSO design Work done in collaboration with Esperanza García-Gonzalo (University of Oviedo) SCRF 2010 The spring-mass analogy xi '' ( t ) + (1 − w ) ⋅ xi ' ( t ) + (φ1 + φ2 ) ⋅ xi ( t ) = φ1 ⋅ li ( t ) + φ2 ⋅ g ( t ) (Fernández Martínez et al, 2008) lik-xik xik-gk φ1 φ2 gk m=1 DISCRETIZATION 1-w in xi '' ( t ) , xi ' ( t ) xi k lik GPSO vi ( k + 1) = (1 − (1 − w ) ∆ t ) vi ( k ) + φ1 ∆ t ( xi ( k ) − g ( k ) + φ ∆ t ( xi ( k ) − li ( k ) ), xi ( k + 1) = xi ( k ) + vi ( k + 1) ∆ t (Fernández Martínez and García Gonzalo, 2008) SCRF 2010 PSO Analysis & Design Based on this mechanical analogy we have Shown that PSO BELONGS TO A FAMILY: • Design and stochastic stability analysis of a whole family of PSO optimizers: PSO, CC-PSO, CP-PSO (Fernández Martínez and García Gonzalo, Swarm Int., 2009), PP-PSO, RR-PSO (García Gonzalo and Fernández Martínez, 2010) Shown that PSO IS NOT HEURISTIC: • Full stochastic stability of the PSO family (Fernández Martínez and García Gonzalo, 2010) Designed a PSO Cloud Algorithm with variable time step (cooling and exploration) (Fernández Martínez et al, 2009, 2010) • Avoids tuning of the PSO parameters (automatic) SCRF 2010 Parameter tuning: the cloud of particles PSO ROSENBROCK φ CP ROSENBROCK 3.5 3.5 2.5 Đ 2.5 Đ 1.5 1 0.5 0.5 1.5 -1 ω -0.5 -1 -1 0.5 ω -0.5 0.5 ω ω CC ROSENBROCK PP ROSENBROCK 3.5 2.5 4 3.5 φ ¹ § 3 φ 2.5 2 1.5 1.5 1 0.5 0.5 -1 -3 -2.5 -2 -1.5 ω -1 -0.5 0.5 -3 ω SCRF 2010 -2.5 -2 -1.5 ω -1 -0.5 0.5 RR-PSO is very different _ φ = 14 / 3(ω − 1) SCRF 2010 The ∆t parameter v ( k + 1) = (1 − (1 − w ) ∆ t ) v ( k ) + φ1 ∆ t ( x ( k ) − g ( k ) + φ ∆ t ( x ( k ) − l ( k ) ), x ( k + 1) = x ( k ) + v ( k + 1) ∆ t ∆t>=1 INITIAL BIG EXPLORATION ∆t