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.
Highlights
Problems of scheduling tasks on a single machine with cost goal functions, despite the simplicity of formulation, mostly belong to the class of the most difficult (NP-hard) discrete optimization problems
The proposed tabu search algorithm has been parallelized using the Message Passing Interface (MPI) library using the scheme of independent search processes with different starting points (MSSS according to Voß [19] classification) On the cluster platform, there were parallel noncooperative processes implemented with mechanism for diversifying startup solutions based on the Scatter Search idea
Tabu search method using block properties allows the solution of the problem faster than classic tabu search metaheuristic without using these properties, and with huge speedups
Summary
Problems of scheduling tasks on a single machine with cost goal functions, despite the simplicity of formulation, mostly belong to the class of the most difficult (NP-hard) discrete optimization problems. One should determine the order of performing tasks, minimizing the sum of delay costs It is undoubtedly one of the most studied problems of scheduling theory. Single-machine scheduling problems with random execution times or desired completion dates are considered in the literature (Rajba and Wodecki [10], Bozejko et al [11,12]). We propose the use of a parallel algorithm, tabu search multiple-walk version based on the MPSS model (Multiple starting Points Single Strategy). The paper presents a new method of generating sub-neighborhoods based on the elimination properties of the block in a solution. The properties of blocks are used to eliminate solutions from the neighborhood
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