Global Optimization for Real-World Applications
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Introduction
Global optimization (GO) helps you get the best solution of a problem. In case the objective has many local optima (see Fig 1), conventional iterative algorithms (usually derivative-based) easily get trapped into a local optimum (see the point A in Fig 1). However, GO can jump out of the local cave and lead to the global optimum (see the point T in Fig 1).
Two kinds of global optimization are mainly considered here:
(1) General global optimization, in which the objective function to be minimized is easy to evaluate, although its gradient information might be unavailable or unreliable (e.g., function with noise). Some algorithms for this kind of GO problems are listed as follows.
• Branch and bound approaches
• Point-to-point approaches
– ASA ( L. Ingber, 1993)
– Tabu search (F. Glover, 1989)
– Hit-and-run (R.L. Smith et al., 1993)
• Population-set based approaches
– GA ( John Holland,1970s)
– PSO (J. Kennedy, R. Eberhart, 1995)
– DE (R. Stone, K. Price, 1997)
– LDSE (C.T. Luo, B. Yu, 2011)
Two kinds of global optimization are mainly considered here:
(1) General global optimization, in which the objective function to be minimized is easy to evaluate, although its gradient information might be unavailable or unreliable (e.g., function with noise). Some algorithms for this kind of GO problems are listed as follows.
• Branch and bound approaches
• Point-to-point approaches
– ASA ( L. Ingber, 1993)
– Tabu search (F. Glover, 1989)
– Hit-and-run (R.L. Smith et al., 1993)
• Population-set based approaches
– GA ( John Holland,1970s)
– PSO (J. Kennedy, R. Eberhart, 1995)
– DE (R. Stone, K. Price, 1997)
– LDSE (C.T. Luo, B. Yu, 2011)
Fig 1. An overlook of global optimization
(2) Expensive global optimization, in which the objective function is very costly to evaluate (e.g., For a given design vector x, it requires a computation-intensive CFD-simulation process to get its corresponding performance L/D). Some algorithms for this kind of GO problems are listed as follows.
• Direct approaches
– DIRECT (D.R. Jones et al., 1993)
– MCS (W. Huyer, A. Neumaier, 1999)
• Metamodel-assisted approaches
– EGO (D. R. Jones et al., 1998)
– RBFGLOB (H.-M. Gutmann, 2001)
– CORS-RBF (R.G. Regis, C.A. Shoemaker, 2005)
– ARBF (K. Holmstrom, 2008)
– LDSEE (C.T. Luo et al., 2011)
• Direct approaches
– DIRECT (D.R. Jones et al., 1993)
– MCS (W. Huyer, A. Neumaier, 1999)
• Metamodel-assisted approaches
– EGO (D. R. Jones et al., 1998)
– RBFGLOB (H.-M. Gutmann, 2001)
– CORS-RBF (R.G. Regis, C.A. Shoemaker, 2005)
– ARBF (K. Holmstrom, 2008)
– LDSEE (C.T. Luo et al., 2011)
Fig 2. The objective function is expensive to evaluate
If you have an objective (e.g., cost function) f(x1, x2, ... ,xn) to be minimized, where the decision variables (x1, x2, ... ,xn) are constrained by some give conditions (e.g., quality requirements) g(x1, x2, ... ,xn)<=0.
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Last update: Oct. 20, 2011
