Problem of scheduling on a single machine to minimize total weighted tardiness of jobs can be described as follows: there are n jobs to be processed, each job has an integer processing time, a weight and a due date. The objective is to minimize the total weighted tardiness of jobs. The problem belongs to the class of NP-hard problems. Some new properties of the problem associated with the blocks have been presented and discussed. These properties allow us to propose a new fast local search procedure based on a tabu search approach with a specific neighborhood which employs blocks of jobs and a compound moves technique. A compound move consists in performing several moves simultaneously in a single iteration of algorithm and allows us to accelerate the convergence to good solutions. In the algorithm, we use an idea which decreases the complexity for the search of neighborhood from O(n3) to O(n2). Additionally, the neighborhood is reduced by using some elimination criteria. The method presented in this paper is deterministic one and has not any random element, as distinct from other effective but non-deterministic methods proposed for this problem, such as tabu search of Crauwels et al., iterated dynasearch of Congram et al. and enhanced dynasearch of Grosso et al. Computational experiments on the benchmark instances from OR-Library are presented and compared with the results yielded by the best algorithms discussed in the literature. These results show that the algorithm proposed allows us to obtain the best known results for the benchmarks in a short time. The presented properties and ideas can be applied in any local search procedures.
