Abstract
This paper addresses the problem of makespan minimization on unrelated parallel machines with sequence dependent setup times. The symbiotic organisms search (SOS) algorithm is a new and popular global optimization technique that has received wide acceptance in recent years from researchers in continuous and discrete optimization domains. An improved SOS algorithm is developed to solve the parallel machine scheduling problem. Since the standard SOS algorithm was originally developed to solve continuous optimization problems, a new solution representation and decoding procedure is designed to make the SOS algorithm suitable for the unrelated parallel machine scheduling problem (UPMSP). Similarly, to enhance the solution quality of the SOS algorithm, an iterated local search strategy based on combining variable numbers of insertion and swap moves is incorporated into the SOS algorithm. More so, to further improve the SOS optimization speed and performance, the longest processing time first (LPT) rule is used to design a machine assignment heuristic that assigns processing machines to jobs based on the machine dynamic load-balancing mechanism. Subsequently, the machine assignment scheme is incorporated into SOS algorithms and used to solve the UPMSP. The performances of the proposed methods are evaluated by comparing their solutions with other existing techniques from the literature. A number of statistical tests were also conducted to determine the variations in performance for each of the techniques. The experimental results showed that the SOS with LPT (SOS-LPT) heuristic has the best performance compared to other tested method, which is closely followed by SOS algorithm, indicating that the two proposed algorithms’ solution approaches are reasonable and effective for solving large-scale UPMSPs.
Highlights
This paper considers the implementation and application of an improved symbiotic organisms search optimization algorithm, to solve the parallel machine scheduling problem with the objective of minimizing makespan
The proposed approach resulting from the research, involves a two stage solution, which includes the use of the longest processing time first heuristic to generate an initial schedule of jobs to machine assignment for n jobs on m machines, and the employment of the improved symbiotic organisms search (SOS) algorithm (SOS-LPT) to perform a global search update on the generated job sequence
In order to apply SOS-LPT to solve the unrelated parallel machine scheduling problem, a new encoding scheme was designed to increase the effectiveness of the SOS algorithm to handle the one-to-one mapping between candidate solution and individual organisms
Summary
The parallel machine scheduling problem (PMSP) is one of the most intensively studied problems in combinatorial optimization, probably because of its considerable theoretical interests and as a representative of many real world problems such as, production lines; hospital management systems (e.g. nurses or doctors’ scheduling problems); university management. Inspired by the recent trend in the performance achievements and applications of the SOS algorithm into different research domains, in this work an improved SOS algorithm is developed to solve the unrelated parallel machine scheduling problem with the main objective of minimizing makespan. The LPT is a common dispatching heuristic employed to generate schedules for the PMSP, whereas the SOS is a new population based metaheuristic algorithm that has a wide range of applications in engineering and scientific computing. The SOS algorithm finds the sequence of the partial schedules to minimize the total setup time These techniques and their applications to solve the parallel machine scheduling problem entail the following: Longest processing time first heuristic. 2: While(termCondition < maxIt) // termCondition is the user defined termination condition
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