Minimizing total tardiness on one machine is NP-hard
Mathematics of Operations Research
Minmax earliness/tardiness scheduling in identical parallel machine system using genetic algorithms
ICC&IE '94 Proceedings of the 17th international conference on Computers and industrial engineering
`` Strong '' NP-Completeness Results: Motivation, Examples, and Implications
Journal of the ACM (JACM)
Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study
PPSN V Proceedings of the 5th International Conference on Parallel Problem Solving from Nature
IEEE Transactions on Parallel and Distributed Systems
Power-Aware Scheduling for AND/OR Graphs in Real-Time Systems
IEEE Transactions on Parallel and Distributed Systems
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
Parallel machine total tardiness scheduling with a new hybrid metaheuristic approach
Computers and Operations Research
A particle swarm optimization algorithm for the multiple-level warehouse layout design problem
Computers and Industrial Engineering
Computers and Industrial Engineering
A discrete particle swarm optimization algorithm for scheduling parallel machines
Computers and Industrial Engineering
Computers and Industrial Engineering
Power-aware scheduling for makespan and flow
Journal of Scheduling
An effective hybrid optimization approach for multi-objective flexible job-shop scheduling problems
Computers and Industrial Engineering
Computers and Operations Research
Computers and Industrial Engineering
Computers and Industrial Engineering
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Traditional research on machine scheduling focuses on job allocation and sequencing to optimize certain objective functions that are defined in terms of job completion times. With regard to environmental concerns, energy consumption becomes another critical issue in high-performance systems. This paper addresses a scheduling problem in a multiple-machine system where the computing speeds of the machines are allowed to be adjusted during the course of execution. The CPU adjustment capability enables the flexibility for minimizing electricity cost from the energy saving aspect by sacrificing job completion times. The decision of the studied problem is to dispatch the jobs to the machines as well as to determine the job sequence and processing speed of each machine with the objective function comprising of the total weighted job tardiness and the power cost. We give a formal formulation, propose two heuristic algorithms, and develop a particle swarm optimization (PSO) algorithm to effectively tackle the problem. Since the existing solution representations do not befittingly encode the decisions involved in the studied problem into the PSO algorithm, we design a tailored encoding scheme which can embed all decisional information in a particle. A computational study is conducted to investigate the performances of the proposed heuristics and the PSO algorithm.