How to implement a local search with different operators?

I suggest you take a look at Variable Neighborhood Search (VNS) method. The Wikipedia page has some useful pseudo codes.

My answer to OP EDIT: First, I think there is no good or bad algorithm, it depends on how you use the different features.

Getting back to your question, of course VNS is not the only way to have multiple operators. You can implement multiple operators in many meta-heuristics, e.g., in an Iterated Local Search, Simulated Annealing, Tabu Search, etc. One way to do so is to define a probability for each operator, and each time you pick the operator based on the probability.