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Unformatted text preview: ERE 284 Optimization: Deterministic and Stochastic Approaches MW 1:15pm Green 104 End Begin Optimization Optimization Most engineering disciplines require optimization. solve a problem with the least cost, in the minimum amount of time, making optimal use of resources and minimize failure. Optimum allocation of resources Optimum decisions Optimization: examples Transportation problem Factory F1 Stock S1 F2 S2 Retail outlets R1, demand d1 R2, d2 R3, d3 R4, d4 C12 cost Optimization: examples Travelling salesman problem Knapsack problem Optimization: examples Optimal filtering W I(t) O(t) = W*I Artificial Neural nets Pattern Recognition Optimization: examples Inverse Theory and Parameter estimation: Given noisy data, estimate optimal model parameters Modelbased inversion Optimization: examples Inverse problem? 2 2 = dx T d k And boundary conditions T(r1) = T1 T(r2) = T2 Given k, T1, T2, find T(x). Forward or direct problem. Optimization: examples Inverse problem? ) ( 2 2 r S dx T d = And boundary conditions T(r1) = T1 T(r2) = T2 Given T(x), find the source S(r). Optimization: examples Inverse problem C0 Conc. In reservoir J1, C1 J2, C2 Jn, Cn Optimization: examples Inverse problems in Earth sciences Seismic tomography Gravity and Magnetic anomalies Resistivity inversion Earthquake location Impedance inversion History Matching Optimization Mature Calculus of variation Operations research linear & nonlinear programming Statistics regression Inverse problems Optimization: ca 800 BC Dido  Founder Queen of Carthage as much land as could be enclosed by the skin of an ox Natural optimization Evolutionary optimization of organisms For ask now the animals, and they will teach you; ask the birds, and they will tell you Job 12:79 Genetic algorithms Particle Swarm optimization Ant colony optimization Optimization problem Basic ingredients Objective function f(x) Unknown Variables x Constraints c(x) Optimization problem Basic ingredients ) ( min x f Subject to C i (x) = 0 C j (x0 > 0 Optimization: examples...
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