ABSTRACT
Fitness computation is a crucial part of any population-based evolutionary strategy. In Genetic Programming (GP) each individual of a population is evaluated by comparing the output they return when fed some input with the expected output. The mapping input/output form the test cases, it describes the "behaviour" an individual should have when presented an instance of a problem. However, there exist situations in which the mapping is given as a function an individual should implement, thus consisting in combinations of several variables of the problem. This paper addresses the issue of efficiently computing the fitness of an individual evaluated on such test sets exponentially large in the number of variables. The inspiration came from digital electronics and more specifically the ESPRESSO-MV algorithm, accepting multi-valued variables. The proposed datastructure represents subsets of the solution space, hence allowing to compute the number of passed test cases as a single operation rather than enumerating all of them. The heuristics used rely on the Unate Recursive Paradigm (URP), some of the proposed algorithms are new while others come directly from ESPRESSO-MV.
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Index Terms
Espresso to the rescue of genetic programming facing exponential complexity
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