Hojjat Adeli and Nai-Tsang Cheng. Augmented Lagrangian Genetic Algorithm for Structural Optimization. Journal of Aerospace Engineering, 7(1):104-118, January 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to compute the most appropriate value of this parameter [149] 6 Hybrid methods Within this category we are considering methods that are coupled with another technique (normally a numerical optimization approach) to handle constraints in an EA. 6. 1 Lagrangian multipliers Adeli and Cheng [1] proposed a hybrid EA that integrates the penalty function method with the primal dual method. This approach is based on sequential minimization of the Lagrangian method, and uses a tness function of the form: tness = f( x) 1 j 2 (46) where i 0, i is a parameter ....

....of the Lagrangian method, and uses a tness function of the form: tness = f( x) 1 j 2 (46) where i 0, i is a parameter associated with the ith constraint, and m is the total number of constraints. Also: max[0; g j ( x) j ] 47) The proposal of Adeli and Cheng [1] was to de ne j in terms of the previously registered maximum violation of its associated constraint and scale it using a parameter . This parameter is de ned by the user and has to be greater than one. j is increased using also the parameter , whose value (kept constant through the entire ....

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Hojjat Adeli and Nai-Tsang Cheng. Augmented Lagrangian Genetic Algorithm for Structural Optimization. Journal of Aerospace Engineering, 7(1):104-118, January 1994.

....of any sort (linear, non linear, equality or inequality) into the fitness function as to guide the search properly. The approach most commonly used to incorporate constraints is the penalty function, and there have been many successful applications of this approach reported in the literature [1, 15, 35, 31, 12]. However, penalty functions have some well known limitations [41] from which the most remarkable is the difficulty to define good penalty factors. These penalty factors are normally generated by trial and error, although their definition may severely affect the results produced by the GA [41] ....

Hojjat Adeli and Nai-Tsang Cheng. Augmented Lagrangian Genetic Algorithm for Structural Optimization. Journal of Aerospace Engineering, 7(1):104--118, January 1994.

....so that they can participate in a meaningful way in the selection process used to determine the next generation. This is typically accomplished through normalization of the constraint violations which are then multiplied by a scalar which can remain constant[11] or dynamically change [2]. Depending on the method of constraint modification and the form of the penalty functions, the magnitudes of the components in the fitness equation can vary widely relative to one another. For example, some components may have very large magnitudes and vary in a highly non linear fashion, while ....

Adeli, H., Cheng, N.-T. Augmented Lagrangian Genetic Algorithm for Structural Optimization. Journal of Aerospace Engineering 1994; 7:104-18.

....N indices of S, in a random order, and t dom is the size of the comparison set. function selection Returns an individual from the current population S begin shuffle(random pop index) Re randomize random index array candidate 1 = random pop index[1] candidate 2 = random pop index[2]; candidate 1 dominated = false; candidate 2 dominated = false; for comparison set index = 3 to t dom 3 do Select t dom individuals randomly from S begin comparison individual = random pop index[comparison set index] if S[comparison individual] dominates S[candidate 1] then candidate ....

....problem into an unconstrained one, and the fitness function was re scaled because the GA always maximizes and this was a minimization problem. Three space trusses were used to illustrate their approach: a 12 bar truss, a 25 bar truss and a 72 bar truss. In a further paper by the same authors [2], a hybrid GA that integrated the penalty function method with the primal dual method was proposed. This approach is based on sequential minimization of the Lagrangian method, and eliminated the difficulties of the unpredictability of the penalty function coefficient. Adeli and Kumar [4] proposed ....

Hojjat Adeli and Nai-Tsang Cheng. Augmented lagrangian genetic algorithm for structural optimization. Journal of Aerospace Engineering, 7(1):104--18, jan 1994.

....that may not satisfy one of the constraints. 7 Hybrid methods Within this category we are considering methods that are coupled with another technique (normally a numerical optimization approach) to handle constraints in an evolutionary algorithm. 7. 1 Lagrangian multipliers Adeli and Cheng [1] proposed a hybrid GA that integrates the penalty function method with the primal dual method. This approach is based on sequential minimization of the Lagrangian method, and uses a fitness function of the form: fitness i = f i (X) 1 2 m X j=1 fl j Phi [OE j (X) j ] Psi 2 (36) ....

....of the form: fitness i = f i (X) 1 2 m X j=1 fl j Phi [OE j (X) j ] Psi 2 (36) where fl i 0, i is a parameter associated with the ith constraint, and m is the number of constraints. Also: OE j (X) j ] max[0; OE j (X) j ] 37) The proposal of Adeli and Cheng [1] was to define j in terms of the previously registered maximum violation of its associated constraint and scale it using a parameter fi which is defined by the user and has to be 1. fl j is increased using also the parameter fi, whose value (kept constant through the entire process) is ....

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Hojjat Adeli and Nai-Tsang Cheng. Augmented lagrangian genetic algorithm for structural optimization. Journal of Aerospace Engineering, 7(1):104--18, jan 1994.

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