Customer satisfaction is crucially affected by energy consumption in mobile devices. One of the most energy-consuming parts of an application is images. This paper, first, investigates that there is a correlation between energy consumption and image quality as well as image file size. Therefore, these two can be considered as a proxy for energy consumption. In the next step, we focused on proposing a multi-objective strategy to enhance image quality and reduce image file size based on the quantisation table (QT) in JPEG image compression. To this end, we have used two general multi-objective approaches: scalarisation and Pareto-based. In this paper, we embed our strategy into five scalarisation algorithms, including energy-aware multi-objective genetic algorithm (EnMOGA), energy-aware multi-objective particle swarm optimisation (EnMOPSO), energy-aware multi-objective differential evolution (EnMODE), energy-aware multi-objective evolutionary strategy (EnMOES), and energy-aware multi-objective pattern search (EnMOPS). Also, two Pareto-based methods, including a non-dominated sorting genetic algorithm (NSGA-II) and a reference-point-based NSGA-II (NSGA-III) are used for the embedding scheme, and two Pareto-based algorithms, EnNSGAII and EnNSGAIII, are presented. With our proposed scalarisation method, user’s preferences can be set before starting the optimisation process and the algorithm generates only one solution based on the preference, while our Pareto-based approaches generate a set of solutions so that a user can select one of the preferred solutions after the optimisation process.Experimental studies show that the performance of the baseline algorithm is improved by embedding the proposed strategy into metaheuristic algorithms. In particular, EnMOGA, EnMOPS, and EnNSGA-II can perform competitively, among others. From the results, the baseline algorithm in all cases and in comparison to all algorithms yields the worst results. Among the scalarisation methods, EnMOGA and EnMOPS can achieve the first rank in 6 and 7 out of 13 cases and the second rank in 7 and 5 cases in terms of objective function. Also, EnMOES achieved the fifth or worst rank among the scalarisation algorithms. Regarding the Pareto-based algorithms, the table shows that EnNSGAII outperforms EnNSGAIII in 10 out of 13 cases in terms of hyper-volume measure, while it fails in 3 cases. Furthermore, we statistically verify the proposed algorithm’s effectiveness based on the Wilcoxon-signed rank test. Finally, a sensitivity analysis of the parameters is provided. The source code for reproducing the results is available in: https://github.com/SeyedJalaleddinMousavirad/MultiobjectiveJPEGImageCompression.