Permutation-Based Genetic, Tabu, and Variable Neighborhood Search Heuristics for Multiprocessor Scheduling With Communication Delays

Abstract

The multiprocessor scheduling problem with communication delays that we consider in this paper consists of finding a static schedule of an arbitrary task graph onto a homogeneous multiprocessor system, such that the total execution time (i.e. the time when all tasks are completed) is minimum. The task graph contains precedence relations as well as communication delays (or data transferring time) between tasks if they are executed on different processors. The multiprocessor architecture is assumed to contain identical processors connected in an arbitrary way, which is defined by a symmetric matrix containing minimum distances between every two processors. The solution is represented by a feasible permutation of tasks. In order to obtain the objective function value (i.e. schedule length, makespan), the feasible permutation has to be transformed into the actual schedule by the use of some heuristic method. For solving this NP-hard problem, we develop basic tabu search and variable neighborhood search heuristics, where various types of reduced Or-opt-like neighborhood structures are used for local search. A genetic search approach based on the same solution space is also developed. Comparative computational results on random graphs with up to 500 tasks and 8 processors are reported. On average, it appears that variable neighborhood search outperforms the other metaheuristics. In addition, a detailed performance analysis of both the proposed solution representation and heuristic methods is presented.

Variable neighbourhood search: methods and applications

“…Joly and Frein (2008) use VNS to tackle an industrial car sequencing problem considering paint and assembly shop objectives. Davidović et al (2005) use VNS heuristics for multiprocessor scheduling with communication delays. Higgins et al (2006) apply VNS to the scheduling of brand production and shipping within a sugar supply chain and Lejeune (2006) also consider supply chain planning.…”

A Permutation-Based Differential Evolution Algorithm Incorporating Simulated Annealing for Multiprocessor Scheduling with Communication Delays

“…In our experiments, we select the ogra100 problem with different edge densities , which is defined as the number of edges divided by the number of edges of a completely connected graph with the same number of nodes [5]. For each density, the mean deviations from the optimal schedule for 10 runs are recorded in Table1 for DE with and without SA selection strategy respectively.…”

“…Due to the intractability, many classical heuristics have been proposed to find out sub-optimal solution of the problem, the idea behind these heuristic algorithms is to tradeoffs the solution quality and the complexity [1][2][3][4][5]. Recently meta-heuristics search approaches have also made some accomplishment on solving the problem [1][2] [3].…”

Variable neighbourhood search: methods and applications

“…Good results were obtained in Estellon et al (2006Estellon et al ( , 2008 by applying VNS-related heuristics for real-life car sequencing problems. Davidović et al (2005) use VNS heuristics for multiprocessor scheduling with communication delays. Higgins et al (2006) apply VNS to the scheduling of brand production and shipping within a sugar supply chain and Lejeune (2006) also consider supply chain planning.…”