Solving Parallel Machine Scheduling Problems with Variable Depth Local Search

We present new local search heuristics for the problem of scheduling jobs on identical parallel machines with the goal of minimizing total weighted completion time. Our proposed algorithm is a local search method based on combining a variable number of insertion moves. We develop an efficient heuristic for finding a profitable sequence of insertion moves. In a computational study, we compare the performance of new and old neighborhoods, and various search frameworks including steepest descent, multi-start tabu search, and iterated local search. Experimental results show that a version of the new variable depth sequential insertions neighborhood implemented within an iterated local search framework is the most effective heuristic among those that we implemented.