In this paper we empirically evaluate several local search (LS) mechanisms that heuristically edit classification rules and rule sets to improve their performance. Two kinds of operators are studied, (1) rule-wise operators, which edit individual rules, and (2) a rule set-wise operator, which takes the rules from N parents (N > or = 2) to generate a new offspring, selecting the minimum subset of candidate rules that obtains maximum training accuracy. Moreover, various ways of integrating these operators within the evolutionary cycle of learning classifier systems are studied. The combinations of LS operators and policies are integrated in a Pittsburgh approach framework that we call MPLCS for memetic Pittsburgh learning classifier system. MPLCS is systematically evaluated using various metrics. Several datasets were employed with the objective of identifying which combination of operators and policies scale well, are robust to noise, generate compact solutions, and use the least amount of computational resources to solve the problems.