Cloud Computing provides an effective platform for executing large-scale and complex workflow applications with a pay-as-you-go model. Nevertheless, various challenges, especially its optimal scheduling for multiple conflicting objectives, are yet to be addressed properly. The existing multi-objective workflow scheduling approaches are still limited in many ways, e.g., encoding is restricted by prior experts' knowledge when handling a dynamic real-time problem, which strongly influences the performance of scheduling. In this paper, we apply a deep-Q-network model in a multi-agent reinforcement learning setting to guide the scheduling of multi-workflows over infrastructure-as-a-service clouds. To optimize multi-workflow completion time and user's cost, we consider a Markov game model, which takes the number of workflow applications and heterogeneous virtual machines as state input and the maximum completion time and cost as rewards. The game model is capable of seeking for correlated equilibrium between make-span and cost criteria without prior experts' knowledge and converges to the correlated equilibrium policy in a dynamic real-time environment. To validate our proposed approach, we conduct extensive case studies based on multiple well-known scientific workflow templates and Amazon EC2 cloud. The experimental results clearly suggest that our proposed approach outperforms traditional ones, e.g., non-dominated sorting genetic algorithm-II, multi-objective particle swarm optimization, and game-theoretic-based greedy algorithms, in terms of optimality of scheduling plans generated. INDEX TERMS Multi-objective workflow scheduling, deep-Q-network (DQN), multi-agent reinforcement learning (MARL), infrastructure-as-a-service (IaaS) cloud, quality-of-service (QoS).

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A novel method of crystal growth by introducing jet flow to the pyramidal-restriction long-seed growth system of potassium dihydrogen phosphate (KH 2 PO 4 , KDP) in rotating crystal method, namely, the jet-rotating crystal method, is proposed. To evaluate the prospect of this new method, three-dimensional (3D) time-dependent numerical simulations of flow and mass transfer involved in the jet-rotating crystal method are conducted. Compared with the rotating crystal method, the jet-rotating crystal method can improve the magnitude and distribution homogeneity of the prismatic face supersaturation and obtain high-quality KDP crystals. The supersaturation on the prismatic face as a function of rotation rate, jet velocity, and crystal size is investigated. The effects of solution flow on mass transfer are analyzed in detail. A further improvement in the magnitude and distribution homogeneity of the prismatic face supersaturation can be observed through designing the jet flow pipes to swing periodically in vertical plane. Besides, the role of natural and forced convection in mass transport is discussed, which indicates that the effects of natural convection can be neglected when the jet velocity is equal to or greater than 0.6 m s -1 .