Parallel Algorithm with Blocks for a Single-Machine Total Weighted Tardiness Scheduling Problem

Abstract

In this paper, the weighted tardiness single-machine scheduling problem is considered. To solve it an approximate (tabu search) algorithm, which works by improving the current solution by searching the neighborhood, is used. Methods of eliminating bad solutions from the neighborhood (the so-called block elimination properties) were also presented and implemented in the algorithm. Blocks allow a significant shortening of the process of searching the neighborhood generated by insert type moves. The designed parallel tabu search algorithm was implemented using the MPI (Message Passing Interface) library. The obtained speedups are very large (over 60,000×) and superlinear. This may be a sign that the parallel algorithm is superior to the sequential one as the sequential algorithm is not able to effectively search the solution space for the problem under consideration. Only the introduction of diversification process through parallelization can provide an adequate coverage of the entire search process. The current methods of parallelization of metaheuristics give a speedup which strongly depends on the problem’s instances, rarely greater than number of used parallel processors. The method proposed here allows the obtaining of huge speedup values (over 60,000×), but only when so-called blocks are used. The above-mentioned speedup values can be obtained on high performance computing infrastructures such as clusters with the use of MPI library.

Optimal solving of a scheduling problem using quantum annealing metaheuristics on the D-Wave quantum solver

“…These algorithms are time-consuming, so in practice, typically examples of small size (at the level of several dozen tasks) can be solved on classical computers with their help. The following metaheuristics have been widely used to support the solution algorithms since the 1990s: tabu search (Bożejko et al [4], Uchroński [16]), dynamic programming (Rostami et al [15]), simulated annealing (Potts and Van Wassenhove [13]), genetic algorithm (Crauwels et al [5]) ant colony optimization algorithm (Den Basten et al [6]). Extensive reviews of the literature on scheduling problems with due dates have also been presented by Adamu and Adewumi [1].…”

“…The results obtained are listed in the table IX. The first column shows the name of the instance from the [17] repository, while the following columns show the number of generated H nodes until the optimum is determined by each of the tested algorithms and the total computation time of the D-Wave machine performing the QAdB&B algorithm and execution time of the B&B-BF algorithm on the CPU.…”

Optimal solving of a scheduling problem using quantum annealing metaheuristics on the D-Wave quantum solver

“…These algorithms are time-consuming, so in practice, typically examples of small size (at the level of several dozen tasks) can be solved on classical computers with their help. The following metaheuristics have been widely used to support the solution algorithms since the 1990s: tabu search (Bożejko et al [4], Uchroński [16]), dynamic programming (Rostami et al [15]), simulated annealing (Potts and Van Wassenhove [13]), genetic algorithm (Crauwels et al [5]) ant colony optimization algorithm (Den Basten et al [6]). Extensive reviews of the literature on scheduling problems with due dates have also been presented by Adamu and Adewumi [1].…”

“…The results obtained are listed in the table IX. The first column shows the name of the instance from the [17] repository, while the following columns show the number of generated H nodes until the optimum is determined by each of the tested algorithms and the total computation time of the D-Wave machine performing the QAdB&B algorithm and execution time of the B&B-BF algorithm on the CPU.…”