Features of the Algorithm

So far we have described all the inputs to the explanation-based learning procedure. We must now describe a few of the basic feature of the algorithm itself. 

The most distinctive feature of the algorithm is its use of a population of potential solutions, so it is reasonable to ask why it might be more effective to work with many potential solutions when conventional methods require only one. To answer this question, and to appreciate how the genetic algorithm works, we consider a simple example. 

A last feature of the algorithm that is worth discussing is its extendibil-ity to other types of constraints. Additional specifications for the pathways or mechanisms under construction might arise from thermodynamics, kinetics, yield or productivity restrictions, biological regulation, etc. The question is whether such additional constraints can easily be incorporated into the synthesis procedure. 

The maximum number of walkers that can be used scales exponentially with the dimensionality of the free energy that has to be reconstructed. In practical applications, the number of walkers can be used for reconstructing a free energy in two, three and for dimensions is of the order of 10, 100 and 1000, respectively. This feature of the algorithm allows to reconstruct free energies as a function of several variables in a clock time that depends only on the maximum number of available processors. 

Inspect the objective function and select the variable with the largest positive coefficient to bring into the basis, i.e., make nonzero. If there are no positive coefficients, the maximum has been reached (automatic stopping feature of the algorithm). 

In this chapter, a surrogate assisted evolutionary algorithm (SAEA) that eliminates some of the problems discussed above is proposed. Its performance on a number of mathematical benchmarks is reported and compared with the results of NSGA-II. The features of the algorithm are discussed in Sec. 5.2 and the results are presented in Sec. 5.3. Summarized in Sec. 5.4 are the findings and some of the ongoing developments. 

An outline of a scalar direct MP2 algorithm is shown in Figure 9.1, and the major features of the algorithm are summarized in Table 9.1. The algorithm is a modified version of a previously published direct MP2 algorithm designed... 

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