Specific Optimization Algorithms

For certain types of non linear dynamical systems subject to stochastic loading, a method has been proposed based on the free-vibration response of the structure (Koo et al. 2005). In several cases, the output of this method will be a rough approximation of the design point which can be used as a starting point (a so-called warm solution) for a specific optimization algorithm. 

J. P. Stewart, subsequently left Dewar s labs to work as an independent researcher. Stewart felt that the development of AMI had been potentially non-optimal, from a statistical point of view, because (i) the optimization of parameters had been accomplished in a stepwise fashion (thereby potentially accumulating errors), (ii) the search of parameter space had been less exhaustive than might be desired (in part because of limited computational resources at the time), and (iii) human intervention based on the perceived reasonableness of parameters had occurred in many instances. Stewart had a somewhat more mathematical philosophy, and felt that a sophisticated search of parameter space using complex optimization algorithms might be more successful in producing a best possible parameter set within the Dewar-specific NDDO framework. 

Linear Models. Variable selection approaches can be applied in combination with both linear and nonlinear optimization algorithms. Exhaustive analysis of all possible combinations of descriptor subsets to find a specific subset of variables that affords the best correlation with the target property is practically impossible because of the combinatorial nature of this problem. Thus, stochastic sampling approaches such as genetic or evolutionary algorithms (GA or EA) or simulated annealing (SA) are employed. To illustrate one such application we shall consider the GA-PLS method, which was implemented as follows (136). 

The most important part of process optimization is linking the process flowsheeting tool to the optimization algorithm. With an equation-based architecture, the unit equations (material and energy balances, operating constraints, and specifications) are constraints in a general nonlinear programming formulation. The main problems are... 

Solution method refers to the method applied to solve the proposed model e.g. (commercial) standard solvers [standard] (such as CPLEX or CONOPT), a specific optimization method [specific], a hierarchical decomposition approach [decomp.j, or a heuristioal procedure [heur.]. For simulation models, often a finite set of scenarios is evaluated and compared [seen.]. But also genetic algorithms are sometimes used for simulation optimzation [GA]. ... 

This section outlines the principles of optimization methods that are based on material density perturbations with the purpose of (1) illustrating another area for the application of perturbation theory formulations, and (2) promoting the use of these potentially powerful perturbation-based optimization methods. The perturbation theory foundations of optimization methods, and their relation with the variational formulation of these methods, have already been described in previous reviews (/, 56). Our presentation is restricted to a specific type of control variable—the material densities— and is given in terms of sensitivity functions. Moreover, we present only the conditions for the optimum and do not consider optimization algorithms. 

The program has a modular design where fitness functions, constraint functions, evaluation schemes, and optimization algorithms can easily be modified or varied. Furthermore the suitability of different algorithms can be analyzed for the specific optimization problem. The individual components are presented in the following section. 

Understand the advantages of performing optimization and converging recycle calculations and design specifications simultaneously, as implemented using an infeasible path optimization algorithm. 

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