Memetic algorithms (MAs) represent an emerging field that has attracted increasing research interest in recent times. Despite the popularity of the field, we remain to know rather little of the search mechanisms of MAs. Given the limited progress made on revealing the intrinsic properties of some commonly used complex benchmark problems and working mechanisms of Lamarckian memetic algorithms in general non-linear programming, we introduce in this work for the first time the concepts of local optimum structure and generalize the notion of neighborhood to connectivity structure for analysis of MAs. Based on the two proposed concepts, we analyze the solution quality and computational efficiency of the core search operators in Lamarckian memetic algorithms. Subsequently, the structure of local optimums of a few representative and complex benchmark problems is studied to reveal the effects of individual learning on fitness landscape and to gain clues into the success or failure of MAs. The connectivity structure of local optimum for different memes or individual learning procedures in Lamarckian MAs on the benchmark problems is also investigated to understand the effects of choice of memes in MA design.