Future Generation Computer Systems 29 (2013) 1901–1908 Contents lists available at ScienceDirect Future Generation Computer Systems journal homepage: www.elsevier.com/locate/fgcs An approximate ϵ -constraint method for a multi-objective job scheduling in the cloud L. Grandinetti a,∗ , O. Pisacane b , M. Sheikhalishahi a a Dipartimento di Elettronica, Informatica e Sistemistica, Università della Calabria, Via P. Bucci, 41C, Arcavacata di Rende (CS), Italy b Dipartimento di Ingegneria dell’Informazione, Università Politecnica delle Marche, Via B. Bianche, 12, Ancona (AN), Italy highlights • We formulate the multi-objective off-line job scheduling problem in the cloud. • We optimize the makespan, the total average waiting time and the used hosts. • We generate a set of test instances suitable for the problem. • We define an approximate ϵ -constraint method. • We compare the proposed solution approach with the weighted sum method. article info Article history: Received 13 July 2012 Received in revised form 26 March 2013 Accepted 8 April 2013 Available online 9 May 2013 Keywords: Jobs scheduling Operations management Cloud computing ϵ-constraint method Multi-objective optimization abstract Cloud computing is a hybrid model that provides both hardware and software resources through com- puter networks. Data services (hardware) together with their functionalities (software) are hosted on web servers rather than on single computers connected by networks. Through a device (e.g., either a computer or a smartphone), a browser and an Internet connection, each user accesses a cloud platform and asks for specific services. For example, a user can ask for executing some applications (jobs) on the machines (hosts) of a cloud infrastructure. Therefore, it becomes significant to provide optimized job scheduling approaches suitable to balance the workload distribution among hosts of the platform. In this paper, a multi-objective mathematical formulation of the job scheduling problem in a homo- geneous cloud computing platform is proposed in order to optimize the total average waiting time of the jobs, the average waiting time of the jobs in the longest working schedule (such as the makespan) and the required number of hosts. The proposed approach is based on an approximate ϵ -constraint method, tested on a set of instances and compared with the weighted sum (WS) method. The computational results highlight that our approach outperforms the WS method in terms of a number of non-dominated solutions. © 2013 Elsevier B.V. All rights reserved. 1. Introduction Cloud computing is a revolutionary paradigm suitable to change the way of accessing both hardware and software in order to produce, price, provide and deliver services and computational resources to users. Users can run their applications (jobs) without paying for software licenses, using well equipped machines (hosts) and high performance computational resources. This paper addresses a multi-objective job scheduling problem in a homogeneous cloud infrastructure considering the minimiza- tion of the total average waiting time of the jobs, of the total wait- ing time of the jobs belonging to the longest working schedule ∗ Corresponding author. Tel.: +39 3351244747. E-mail addresses: lugran@unical.it (L. Grandinetti), pisacane@dii.univpm.it (O. Pisacane), alishahi@unical.it (M. Sheikhalishahi). (makespan) and the number of used hosts. It takes into account an off-line job scheduling scenario and, therefore, the number of jobs to run and their resource requirements are known a-priori. The main contributions are as follows: • a multi-objective formulation of the off-line job scheduling problem in a homogeneous cloud computing platform; • an approximate ϵ -constraint method for solving the problem; • a detailed experimental analysis for evaluating the quality of the proposed approach. With reference to the last contribution, first we implement an instance generator in order to determine a set of problems con- sidered during the experimental phase. Then, we implement an alternative solution approach based on the weighted sum (WS) method. Finally, we compare the two approaches on the set of gen- erated instances. 0167-739X/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.future.2013.04.023