Heuristic evaluation function

Providing Sense of Purpose. Planning is more than just a heuristic evaluation function that measures complexity. The ultimate goal of synthesis is to prepare the complex from things simple. Thus... 

Direct search methods use only function evaluations. They search for the minimum of an objective function without calculating derivatives analytically or numerically. Direct methods are based upon heuristic rules which make no a priori assumptions about the objective function. They tend to have much poorer convergence rates than gradient methods when applied to smooth functions. Several authors claim that direct search methods are not as efficient and robust as the indirect or gradient search methods (Bard, 1974 Edgar and Himmelblau, 1988 Scales, 1986). However, in many instances direct search methods have proved to be robust and reliable particularly for systems that exhibit local minima or have complex nonlinear constraints (Wang and Luus, 1978). 

It is helpful to contrast the view we adopt in this book with the perspective of Hill (1986). In that case, the normative example is some separable system such as the polyatomic ideal gas. Evaluation of a partition function for a small system is then the essential task of application of the model theory. Series expansions, such as a virial expansion, are exploited to evaluate corrections when necessary. Examples of that type fill out the concepts. In the present book, we establish and then exploit the potential distribution theorem. Evaluation of the same partition functions will still be required. But we won t stop with an assumption of separability. On the basis of the potential distribution theorem, we then formulate additional simplified low-dimensional partition function models to describe many-body effects. Quasi-chemical treatments are prototypes for those subsequent approximate models. Though the design of the subsequent calculation is often heuristic, the more basic development here focuses on theories for discovery of those model partition functions. These deeper theoretical tools are known in more esoteric settings, but haven t been used to fill out the picture we present here. 

Typical GA applications can require many function evaluations to find a good answer. This is true of all global optimization methods, and not just GA. A typical run for a problem with n variables will use a population of lOn, run for 100 generations, and be repeated 10 times, for a total of 10,000 function evaluations. If your function is expensive to evaluate, it may be best to look for some heuristic that allows you to locate the minima of interest more quickly than GA will. 

For fair and realistic comparison, the pure GA and FA are run for the same number of function evaluations (iVpg) - 10000. The hybrid meta-heuristic algorithms are run for NpE = 1250. 

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