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FCS | 前沿研究:云计算中基于多目标强化学习的期限约束科学工作流调度 |
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论文标题:A Multi-objective reinforcement learningalgorithm for deadline constrained scientific workflow scheduling in clouds
期刊:Frontiers of Computer Science
作者:Yao QIN, Hua WANG, Shanwen YI, Xiaole LI, Linbo ZHAI
发表时间:15 Oct 2021
DOI:10.1007/s11704-020-9273-z
微信链接:点击此处阅读微信文章
原文信息
• 标题:
A Multi-objective reinforcement learningalgorithm for deadline constrained scientific workflow scheduling in clouds
• 原文链接:
https://journal.hep.com.cn/fcs/EN/10.1007/s11704-020-9273-z
• 引用格式:
Yao QIN, Hua WANG, Shanwen YI, Xiaole LI, Linbo ZHAI. A multi-objective reinforcement learning algorithm for deadline constrained scientific workflow scheduling in clouds. Front. Comput. Sci., 2021, 15(5): 155105
• 公众号推文链接:
云计算中基于多目标强化学习的期限约束科学工作流调度
1导读
云计算可为云用户提供按需服务而受到欢迎,成为当今重要的计算范式之一。随着云计算的普及,云数据中心的能耗问题日益突出:到2030年,云数据中心的用电量将占全球用电量的3%-13%。据悉,亚马逊的数据中心将19%的预算用于云计算的能耗上。数据中心的高能耗不仅增加了运营成本,而且加速了全球气候变暖。研究表明,工作流已成为数据中心的主要能耗源,科学有效的工作流调度方法可有效降低能耗和运行成本。因此,科学工作流调度问题越来越受到研究人员的重视。
为了解决云计算带来的问题,研究人员将工作流调度问题转化成多目标优化问题,通过多目标优化算法科学地降低工作流调度中的能耗和运行成本。然而,大多数现有的多目标工作流调度优化方法忽略了对权重的选择,导致解决方案质量的下降。虽然部分关键路径(PCP)策略被广泛用在期限约束的工作流调度问题中,但其不能准确地反映每个时间步长的工作流调度情况。针对PCP中存在的问题,本文提出了MPCP方法,以解决期限约束下的工作流调度问题。
首先,设计了一种基于多目标强化学习的期限约束科学工作流调度算法,基于Chebyshev标量函数刻画强化学习过程中的Q值,实现了对目标的权重选择;其次,提出了可准确反应每个时间步长的工作流调度情况的MPCP方法。结果表明,本文提出的方法在给定的期限内可以最小的成本和最低的能耗实现对工作流的科学调度。
2模型细节
在DCMORL中,时间步长i的可用动作集用
表示,状态空间
表示调度阶段每种虚拟机类型的利用率。
表示每个虚拟机类型在第i个时间步长的利用率,n表示虚拟机类型的序号。
为了保证工作流能够在期限内被执行,首先为工作流中的每个未执行任务分配子期限,并分别定义最早开始时间和最晚结束时间。定义任务
的最早开始时间为
,其数学描述为:
![](data:image/png;base64,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)
上式中,
表示任务
的所有父任务的集合,
表示任务
的可能执行时间,其计算如下:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAR0AAABBCAYAAADsUXBDAAAdL0lEQVR4Ae3dB7TsVNUHcBQFLICAIlZUik8piopdUEBFRRBUOipiAQUr9oYg1V5BsD0UUEGQKhasSBHBBijV3kXsYIF863c+93huSDKZmcy9972bvdbcuZmcnJzsnOyz93+XLFP01HOg50DPgVnkwDKzeK7+VD0Heg70HCh6odNPgp4DPQdmlQO90JlVdvcn6znQc6AXOv0cGHDgxBNPLH7xi18Mtsf955RTTil+9KMfjXt4f9xSzoFe6CzlN7jN5f3qV78qHvWoRxWPfvSji5/97GdtDmlsc/DBBxd3vOMdi8WLFze263cuTA70Qmee3fdf/vKXxY9//ONZG9Wf/vSnYtGiRcUTn/jE4vrrr+/svCeccEKxzDLLFMccc0xnffYdLR0c6IXOPLmPN954Y/HGN76x2HDDDYuPfvSjszaqZz7zmUkr6VLgxOAPOeSQ4mY3u9msCtE4d/89fznQC515cG8InO222664293uVnzrW9+aMaJ//vOfxZ///Ofi3//+d3HdddcVf/vb3waff/3rX4WP45E2//jHP9J+x9mn/d///vf0f95W+x/84AdT1Uac7053ulPx7Gc/e8Y19Rtzz4F8PplXts0T8yXmzn/+85+pDLQXOlNh62idvv3tb08Pf5VZ9etf/7p42tOeVtzznvcs7nOf+xQbbbTR4ENIPfShDy1uuOGGZMZ4wO9973sXD3jAA1Lbe9zjHqnt/e53vyTQtthiizS5YnQveMELipVXXjkJqvit6+83vOENxQorrFD8/ve/77rrvr8xOfC9732vMDdifmywwQZpfvk2v/xuvl122WVjnqH5sF7oNPNn6nuvueaa4ta3vnXx6le/uvZcRx55ZBJKH/jABwqYjw/A98EPfnCx7rrrpuN22GGHYvXVVy/OO++8AjAMpyGEAiNac801i0c+8pGDc1jN7nCHOxS77LLL4Leqf5yTV2tc+s53vjNVbWrccc32cd/97neL/fffP2kRXZ/b/b7qqqtmfGgsdXTEEUeke/KpT30qzY8999wzbX/zm99M2zvuuGOx3HLLFddee21dFxP93gudidg3+cEf+chH0g2/9NJLazs74IADUpvLL798Rpt99903CQ3mFeFz+umnp/0EyoorrliYPEFPecpTiuc///mxmcw4QO+HP/zhwW/lf6jbyy677EQYE9WdNpWPpXyehbD9rGc9Ky0EXV7r5z73uWLjjTcubnnLW6b54X7G59hjj6091TbbbFO8/OUvH+x/whOeUKyxxhoDM/1973tfwhYHDTr+pxc6HTN01O6e/OQnJ42EiVRHzKvb3/72CdPJ21xxxRXFlVdemcyrc889d7DLqmryvfWtbx385v9TTz11sP3BD34wtaEZlYkQ++Mf/1iEsLNC80J9+ctfLjdttb3JJpskoRjYU6uDlpJGhO4FF1yQFgGmMD764O8kdNppp6X7x+uoP9v5h/ZTR+eff37CCe0Pjfdxj3vcoLl5ks+dwY6O/umFTkeMHKcbHiPxLFaaOiKMYDebb775oAmNJxcygx3//ecTn/hEmpBnnXVWeddg+yUveUlx85vfvPjJT34y+C3++etf/1q8+93vLtZee+2Exzz1qU8trI7ib8Yhq/zyyy9f/OEPfxjn8CX6mM9//vPFM57xjHQ/xELhI6cBs3dc4iy4613vmvoat484zsJlgXr9618fP039uxc6U2dx/Ql+/vOfpwd/7733rm0Eu+F23muvvdJEFekL8HvLW95SewyBYiI1RReb/LCkphXXykxLmZRe8YpXpPFMC5icdHzTPv74449P1w936YK+9rWvpf5otJPSZz/72dTXJLjdqGPohc6oHOuwPS8C4SA+p46+9KUvpTZrrbVW8cAHPrC4173ulbYBtHUEMOaBaDLZHv7whyeTra6NoEFCicCYlN72trelMVPrFyJZVG53u9sll3QX18+xAMdhGpcB5NhuApLzMbzpTW9K92Y201Z6oZPfgVn+X0wOofPOd76z9sxsa22+/e1vpxgKZhXPVJ1nwWRbZZVVCiZRExE6vFd1OMtFF12UzvvJT36yqZtW+1yfa1ioQofG+IhHPKIVr9o0OvzwwxM/8bTu0wQk5+d40pOeVIkX5m3a/m/unX322WmuNgWb9kKnLUen0I73waR517veVds7+/82t7nNIEVBENcll1xS2/7iiy9OfR500EG1bex42MMellzsdY2OPvro1E8XK6Drc51VoHXd+ZeW33kAV1pppeJlL3tZZ5f0nve8J2k6VQBygMlNQHIMJII3H/OYx8RPE33/5S9/STFlNGShIHXUC506zszC72E61ZlXTJ911llnRnxNPiwCqEyBHxBoTbTpppsmjahuRQqTAGg5KR144IFJ6NDWFhpF1PfHP/7xzi5dfA2c73e/+91EfXIi6OdVr3rVRP3kB/N0whybqBc6TdyZ8j6uVBoA4LeKrFY8TPvss8+M3dycgGATukyCDE2kq6++urxrxragQAFgv/3tb2f8HhtwIcGHQQQgU8w3d/unP/3ptOsrX/lKIeq4Kc7I+F1nlacs+l9av/HJtbvXQdzo6JxzzikOPfTQhPVIdeEdbGMW8V7q86ijjooux/o+88wzUz+EWBXRhI477rh0v+FIuWPCNUjqFdMjVzAWLyEgL3rRi4rvf//7CatkppdpiRI6EPYmN3D54uq22Z2YOdcUplBd4Jy4GJPrM5/5zIyhCuiDx1SBhZtttllx97vfvRFE1hntSt/lgMM4kZQL6RSIiUUwEnZc6fAibnwTDtDMw0Uji4cp+ojv7bffPmlVMV45Pcw/E3lpp/e+972JzxdeeGG61Ne+9rVJ2HAEPOc5z0lhCXjLG8lD6Z6cfPLJQ9ny+Mc/vlh11VUrF56hB/+3ASHnfFULBoEj1ME9JkDuf//7J+HjUB7VrbfeujjppJOS4FlttdUKjgckYdlxNB44FgeIvnJaIoSOSSrWQdzIV7/61Xz8Y/0P0Lzvfe+bHh4P0lyRlYO2AdQtk3HJADcp2PBf/OIX08eDSpN57GMfWz6k+OEPf5jaS3+AJTRRrMD6rSIBic4tPmj99dcfBBbKDxNjctvb3jY9JI7lheNNEfNRRdRtkbNBJiFvjn6XdvrCF76Q+Ojh8xBKOWAW02J9R5Z/CH8PbR4tXMcf94GH0lxgKtMw8s83vvGNukPT7zSr9dZbL42tyuwVziG2Ktzyxuc32q6AxJe+9KWpH9cgfQIx925xi1ukOCTbggzNk9CCUqOiWDJqJMsrsnr/5je/iXFP/C0+xWoOva/z4Ex8kiEdEAx3vvOd07WVM3oJRpPIiubBV2DLh9kD+AMi5kSLeOUrX1lI6nRNAgSbiPlFqNQF/Nm/0047pXOXBT2w8la3ulV6cJzDWE2uqjgUAYEmYv4g4beEQteztBMBy4QicPbbb7+bzDV8ePOb3zxgg7CIthiLZGDlQ/DRcfmHsGsippm5Yn4ZV3mRsugJZpSzl3sdmUvudZWpTDMnqEJzotVxWJRp3ms6ADgPh9W0a7JahCbRdd9t+5MBLk+qKUivbV+jtrOqWiVHJRhOrp3xdFGxq0BnEbl4LKAtiKbkN4mHC5nMP+ktoWl40G3PZj2lJv4zmZj+BIn7iHgimdJVpFqChTxIqEAZj7SvUuhQh6j+HgRAo0lCqtZpBFRFba1q2sbHsX6PycilpsSB/bQW+3zbpprZznEB47jLXe6STKu4kK6/gV5U/cAbuu5/WH/bbrttUpHrTJNhx0+yP1zZ+D8K0bTy5FGgNnyiinbdddekyeV2vba014VOooHhMkwdBK+UFjOpV6oLvuaat2RhGhGCBdKogjzz4YzgnIDfIddEiz/jjDPSdi47KoWOjkwKDBEB6yQwEHa5Va1McAZlFXxyFY9JJFBNoW6Chw1qRdSGPa9/2dG2CRdtc7WQGm9FDJuxfN4utoFkztGlS3OUcb34xS9O5w/beZRjJ21LyI8aQ0J4uM8hZNwjNViqBNdPf/rTdG3A1Jy+/vWvz1hc8n0L6X9gKyzM4irYkzAH3M41USIsJFEDiSyIOCOVDDwv8BoChTBifhEqnm+mGnLv4U0Wtne84x2FfL6gSqFjp0hUnXOP0gJ08vSnPz39Vs42tl+hJjag/+PDQ6QPwWzcg/6HRdivTottF2E7Vl1gaBBMgeTPV8nYF98uvqkWTbRr+gZQNyVdNh076T4TDx/mQugYO0+Y84d3Zdj1ABQFfykAJtIY/lCXUwXsBiLPJVg/7Hrmcj9AlsD2UMI/5oNHFT8IwOc+97kJIxQRf9hhhw2EBg2IYOHZZHrxBCNCxTMUssE9N0e23HLLlJw8VNPRCfDLZMxjQUwuv+WgoLYBSr7mNa9JA4g/bFaaEqEhi3W33XaLXcULX/jCFIMSqpl4D+oYAYRIf/YtidtEsAWA6yTEgwAYZf7NNnGV4imNa66ItkXLjAnTNA5xJDwxvBZ1/LJCWjB40aoAx6b+F8o+MAIQWYwMK6BpYZ0rnngG43nscgy1ms7OO++cii/lalEInTI4FEFG5XgS0i7C6Hk2wpfvAoBMNIywHQk3gi4oUu5pAlUkzFpwkuA5sSlALKppPt6q46p+45L24FcFMlW17/K3173udalQVpeeuXHGJ/6GAA/PQ10f6h3DwPJ7WW5LiFn1qkyuctuFuh1m/TAv49LIn0qhQxWioZST1JgyHk4mV06KPbHf4p1JBAlVkaSsIiskcyxAp6o2IciqMCTt4UQRS6IfDwNQeBzJLBjLdUWUbdV4/OZ64CBtPgGe1/UVv9PkeLDmA7kvOZBfNSbYF9d8Ux4VTLCnZg5YwFkM73//+4cGcjb3tOTtrRQ6gCRChGs0iCASFs+9y5OVk6REv8ua5toGOnGd1amMUTdXyYM6ijKegX5XtXO84Lo64VZ1TNVvgGpCh23dRB/60IdSO22HfepSG/L+PeD4RtPqqefAQuFApdDhXfBQCXEXsUoAMIfgHmUTSi4OAcMrJRBIO8dSsesoYm8kPNZRvCGh/EqWvD0gLo8LyPeN8n+kI+RCtup4pqKgqjafpsp++iYoYUkPetCDJhaaVWPtf+s5MF85UCl0qHwEB/NKtKMAMqpglZeCSaVtHkUpL6NsguUMEEJNkxJWXUe0Dv3WCR3CTslGcSCTUgidumzvSfsvH88TKFSAoI4YjXKbfrvnwNLKgUqhI8gH5sJDMYwCe8kzVQGITdgKwHJYUmJoOhGtWR5HlPHsIq4BeErADdN0CDo8afPRto7wRtSpd1QJFeip58BC4sBNhA7shsnykIc8pBUf+PA9sLSFMlWt4nI8BAXCgZqIMNFvOe8njglhxxSclMSoOFdT3WHnWLx4cco7kXsy7JNrfnXjEybgvG1jZOr66X/vObAkceAmQkeMBXBWmn0b4kEChpY1G65gXo4yCRT0oA2rbBfFqHxXERA595jRLGIMHmZ5PQSo66E1EVJ1FJnATe+AciyXuuS8Np+m8+Xj4LkSdNlTNQfcQ97CSYlHtama3aT998e358BNhA4AlFAQMdyGmEn561Ec4+bCK8qZ0PaFMMnTHarOEwWuyiH00VYgonF67xNX7x577JFKOxA4zEPZsSInmUzPe97zUixMni0b/fiO0pxd1OrJ+23zv5inLot2tznnktIGnif1povEUFq3kH14YhvYYEnh0ZI4zhlCh0dFAR4PM1C16eZYgRTV0hbgTMD4fOxjH0sFf/xeLnUgoEwgn33aNeEeBJe3S+aJhTmDox6MqFd5YfFyMNHRVjVp+7JhI0BNuzrXtDQKY4o4o/w80/4/XmhXBdJP+9zzuX9eU+kWgkOHxQ61vQ4pHNIyvFiuaW637a9vNx4HZggdMTY0BukK4kykMdQRUwZuwXsk5F2QW3zgNfaVb6y6vdrr3/5h2bTiguoC58QA8XA5V7nEo8A8Yf15ZTrJaHWgM+8cUJcgnW2KNIi5yr2a7ettcz5eTeEZ5bSaNscOa2MxMzfawgfD+uv3j86BGUJn9MOne4S0CLhNORhx2FmZZsw7rmlEuFk1q0w62pcJ3gb4HXbecfaHltULnf9xj3nMbC8vWv9rMdl/oSU3vTtssjP0RzdxYF4LnSiy1RZfigul0cB0Iq+L2Se5rlwdTfs8Ez6On83vKEkaOWpdnVs9JO54OVXexgDf8gGCA+EjvYSw44FkxtgfpQjytnk4RFfjq+vHQsHUNe5pEY1WKRX5hfOVhHHUOVFizIQymCLuL+cMCMG3+6cqJCdK0yuLoq/Z/J7XQgcjmGImSF1KRRWz1HpRuBxJ6eD+r3twBOlttdVWVd3Mym8wLjFRXSd8Snz1UHmAmaDe5AhUB6T6TdVAxNy1jWcEknds8UbC9OItDuNUFxyXeRGf1YSvMZ9lr09iDou2VxFvVM8YQLppbONed/k4i9Gw94vjgXsHu3R/5SDaVq6W2W7e21Y+Zj7RvBc6hIaYmCgE3YZ5PB7SMbwJkflSTt2IPqzu6vfygM0FeWhgSYpidQWW5tdhtTPpgOs5qXNjgjq/tzrkmfw8aXlVP2kaypDMFqkBrWB4E1nZtZuEANV4I3F4FOJo6VpDYuJLrYGnCkGx0JrzTYulMQswVf4l4AfbrilK+6p1o5/y/R/leqfRdt4LHRetsj3wz+pUFXCYMwZ+o/CXY4DdVRqS3z2QVvS6tyHkfU7rf65+GhnBMw0C7ONbOSFWGALVnTYkMz8EnjgkkzZPxFWiQu7dbJB7S/vYfffdG0+nng/ByPvJhB5H4wFW846aU23J/aIJmjuTnDs/H68lbdvip6AXrdIiBJNUSbApXMCimseWEVbwydDeVAKwAE8LG8uvY5T/lwih44LYpdzgw4pWR6BfXgi8zBBAohtal2JRbj+tbRNfuUomVtdkosG1XGdOuRAuP6wRr5Qn4sIW6t6bnvfbxf9WaEIvwh/KfYoho3Vpw6RQlU6e3zimqVpPwijaVIzEJ/NKpTzn9g4obncmUFmgl8fctO1YZq7SvXl4ibrZdZ7Wpv6EjuRv1yTE3b/5RkuM0AnGxaoc2+VvAWWwiABKy/ttD+uj6php/BaJpt7p1TUFIMsUCbKqN/FFmITVnzCcC4qa2HVjZCaIdPfgcwBYNHxyQTrKuD2k6kYNI1qNMro0Cd5UQaQ8pJNWe4zrzYvHucZFixYNip0PG1vsF3lPS2SizXda4oTOfGfoKOOLqOs2tXdG6VfbwCxoOuobBcjYlKumNIl4pvD6jXrOSdsHJtH0HnZCR/hDFwsHDVMeYNuCa96KwBTqilRu4CTJCZgvgn5UippQo3p6Rz1PF+17odMFF8fsgxlj1c6B3DG7uslhXsKmb14otr8ATvgOXKKK4FxAR68MnisSzGnMTaYxIRqvO550nEwzwHkdT/L+CWKxQ/jYFal2CSNitlkUaLyAYQGxzsPM8oKENuQe492wOk5t+pp2m17oTJvDDf3Hi+imEZPCTW4VD5IO0lS6I2r2ElZdENMR/jJK6VIeHA9OXWUBOAyA1VsGuiAF/QniNnW1xT0xrepSacYZD1MI8KvUizep0DIJIRoYrZP3qglIzs+pL/XCR+F3fnz+PwHrvKK243XH+f5J/++FzqQcnOD4MK+6etBjKIBPwZCjuJXjlUNN5WGj/zbfzDvxIm1NF32G0Kl7K4UASkJJ2dguSOVJmk4boROlVJq0sFHHxP3u5QRB++67b/ImxvYo37S/YaEGo/QnoBav81dCjXJ8U9te6DRxZ8r7AkiuKgEyyanFbQCEq2KbCJeq1RDIbJLV5dvlybll4La8zVQT/Z0fU76e8jH2RwWCukDOk046KY2xrih8fr42bmIuaq89aoNhWRi4tetA9twTWHVt5eu3LTSB9zIi5XnFxjGPxPkAkaWPNBEvXz7OvK1Qk5x/akepzInaXk/eX9P/vdBp4s6U93nnV5u4lFGHEcXBym8ttUqbSFUucPEhVdUceUWswLAUbl3BdEqZUOe5ZOXHqTKQvz5IGw+0iYsICWUl9txzz1T2RKStY8oaS4ChyuVWUeBUEQzHcyWw0/UQmq6BIBeBy6XNxIyYlXJ/HjDmDDMmyMOrP2ZcmcQOMcWC8NL9wx+OAPxhihCMgi/hNMM0qKgtJdZG2RUm1jiEDxaMOhBZjpmX+dlP+8wTpHnOYIpenOj8EVi49957J3zPm1LwFf5UxZdxxtsLnXG41tExVh2BgQK4uiQekLJqTPtwHjWvy2QyrbzyyulhKe8z6QQHOtaD5QER52SF9mDZTyitscYaA43BisrDFCComBMBiYI2eWa8ysgkLnuCCBPjjlfYlscSdbM9IDxd4rZErDN9CLBNNtkkRaI7n+BQfeXBc3l/ss2N0Zssg+AYAkar6nIrsaI/10RDAfICoL2PnHAVuc2cVRscJqUtPg0jgphWyn1PkBMCzG4fWg8saRgFiFxVD0oskHtnnEi6RNQvl3cHtHYuc5ETIV6u6V5z3dM6Iz8x9g0bz7D9vdAZxqEp7weKAhOrtI9xTm3SwnNMeoFvVnsPiAA0v+VxO/onjKyC9on0tWpWkRK2MBAUMUARuWwFFeQWqrvJ6R3pOQhpgjtHrLK0nVzL0C/tA8ZhZa0i0bu0Mf0QWOXMfKVQ8oJyrrnOMxjaQV7+BEis7yogm2ZD07HfuKNOU4zTw8sbFoRfhOMwYtrJe9MvrZcJRwj5+G1Y/hXNJO6t6PLyPGK68Yjl/YQ5SbDkpn0EOvoWOCklAwkwdD/zAMZh19W0vxc6TdyZhX3yY0yuWIkmPSXgDxDLVKEBiHnxEVHrXGU8h9AB+mrPLKtazay2Jl2AqLSbPF+MuzfP16KFiIbO1XEeOqZdCCbCoSoexYPDg2NcVUQbYq6V9zNzjDFPaxEDU+dtog3he553Jyvbb3W4jcA9ZlAZL9Ke1nTOOeekIYshghUNi56P65MbSJC5LjyOD+E3LG/K/RZ64f75rkoTMg4liCX3hsmnX3yuqs9tsZCEHKU/3DuLQfm6Y/yjfvdCZ1SOddzeQ0j9pZ7PVyK0CJlYRWlGkbphItI6chyGmcD0yUncSaycVl/mWGA+ebvAddrWmI5jmRbMNzgLsirXPVT2M8XyeB/CmDnh2kYlGJLrgQkhWA0h1LZcCVMz59+o52/TnqlG42HOIdHQtJkqzItZKBE4NB/3jcbcFfVCpytOTtBPmB5NcTQTdD/xoRIc85weuBCNBCnzwCSg5ls9eTpgG46hfYQQIJjibRtWV5iQFVV8UO4dYWI5l7yqUQjITLsIUl0AeF1FzAUaDawiiHYBmxqHREnnL30UnzTKQ0p760qLyMfPjKLdBgH7Y3GjRRGMYSYS2pFxr6CdKg3IokjLYUIbJyxsUuqFzqQc7Oh4JouVyJshQq3tqOuJuyFkopwDs8Y4FY9CQGORzISESc2kUp+I+xdexQXPHUu9jxggD70Jr51jcqGjzwiazE2lYRfBXQwbI9CAvQROnfufaSemJbANfYfZN+w8VfsJGEC8+8ZjiBdtAOCqvrr8jSklMZZ5BeujsYTHEAhOs6PxCQLkcQt3vd+YYghf3EtCyFt7Q0hNMs5e6EzCvY6PNVEBfuH16bj7sbszHh4OZCLzZvEaBcESJGmG8KDB8AQFNsJ0AdiG+eE4HiwPaN3DLi/Jg9wmqZJ2xPvD62W1psFUmQ3OSwPioSL4uiCCCwCvXwsHXrVJq+ji3MP6MDZePAsEnpTfhkKAwGsIopxfzKscpBeG4P5ZPLqgXuh0wcW+j6lwgNkCdxD70kQq6BEk+YNSbg9Hsnpb3es8dOVj2mzzqMGO+rd5tOHW/7fphU57XvUt54ADMAmrdRPRtLibI/6kqq10DKt9lXenqn3b32hWhE4VKN62j4XWrhc6C+2OL4XXC7CG5bQxxbq+fCYHzYkJ0lM7DvRCpx2f+lY9B3oOdMSBXuh0xMi+m54DPQfacaAXOu341LfqOdBzoCMO/B/lbFPR5sOiVAAAAABJRU5ErkJggg==)
定义最晚结束时间为
,其数学描述为:
![](data:image/png;base64,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)
本文基于分配任务和关键父级的概念构建了MPCP方法。将非计划任务分为两类:分配任务和未分配任务。任务
的关键父级
定义为:
![](data:image/png;base64,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)
未分配任务的子期限
定义为:
![](data:image/png;base64,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)
上式中的
表示通道P的子期限。
根据每个任务的子期限,可用的动作集
可表示为:
![](data:image/png;base64,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)
上式中
表示任务
的可能完成时间,其计算方式为:
![](data:image/png;base64,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)
在强化学习中,通常基于奖励向量优化多目标问题。因此,本文定义奖励向量为
,而
定义为:
![](data:image/png;base64,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)
上式中
表示在不考虑期限情况下的最小执行成本,
表示虚拟机类型
的单价。
定义为:
![](data:image/png;base64,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)
式中
表示在不考虑期限情况下的最小能耗,
表示任务
的能量消耗。
在工作流被调度之前,首先要对工作流中的任务进行分级。任务
的级别由
表示,即
![](data:image/png;base64,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)
式中
表示任务
在所有虚拟机类型中的平均执行时间。在强化学习框架下,实现对工作流调度问题的优化。
3 主要贡献
本文的主要贡献有:
(1)制定调度问题,而后基于切比雪夫标量函数设计DCMORL,降低了选择权重的难度。与其他方法相比,Chebyshev标量化函数可在更大的范围内找到解。
(2)为了满足期限约束,提出了一个改进的PCP策略(MPCP)。 MPCP 中的sub-deadlines在调度阶段会定期更新。
(3)提出了一种衡量解决方案质量的指标。
(4)实验表明,DCMORL在执行成本、能耗和超容量方面比其他算法更具优势。
4 实验结果
为了评价算法的性能,本文将所提算法DCMORL与IC-PCPD2, CEAS,S-CEDA和HPSO这四种算法作比较。实验结果表明,在大多数情况下,DCMORL的性能获得了很大的提升。以CyberShake结构为例,其实验结果如图1,2,3所示。图1展示了CyberShake结构工作流执行成本,从图中可看出,执行成本随着期限因子的增加而下降:当a=1.5时,CDMORL的执行成本分别比IC-PCPD2、CEAS、S-CEDA和HPSO的低52.50%、51.57%、41.43%和29.40%;当a上升到4时,DCMORL的执行成本分别比IC-PCPD2、CEAS、S-CEDA和HPSO的降低38.25%、36.97%、13.43%和18.75%。
图2给出了能量消耗的对比图,从图中可看出,能量消耗总体上随着期限因子的增加而下降:当增加时,更多的任务将在具有较低电源电压的虚拟机上执行,其能耗也随之降低。当a=1.5时,DCMORL的能耗比CEAS、S-CEDA和HPSO的低41.48%、28.00%和13.83%。当a上升到4时,DCMORL的能耗分别比CEAS、S-CEDA和HPSO的低36.31%、17.22%和9.93%。
图3展示了不同期限因子下的超容量值(超容量指标用于评估Pareto逼近集的质量)。DCMORL产生的超容量值大于S-CEDA和HPSO产生的超容量值。主要原因是DCMORL根据超容量值选择权重元组,而S-CEDA和HPSO只是将权重设置为相等的值。
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Abstract
Recently, a growing number of scientific applications have been migrated into the cloud. To deal with the problems brought by clouds, more and more researchers start to consider multiple optimization goals in workflow scheduling. However, the previous works ignore some details, which are challenging but essential. Most existing multi-objective workflow scheduling algorithms overlook weight selection, which may result in the quality degradation of solutions. Besides, we find that the famous partial critical path (PCP) strategy, which has been widely used to meet the deadline constraint, can not accurately reflect the situation of each time step. Workflow scheduling is an NP-hard problem, so self-optimizing algorithms are more suitable to solve it.
In this paper, the aim is to solve a workflow scheduling problem with a deadline constraint. We design a deadline constrained scientific workflow scheduling algorithm based on multi-objective reinforcement learning (RL) called DCMORL. DCMORL uses the Chebyshev scalarization function to scalarize its Q-values. This method is good at choosing weights for objectives. We propose an improved version of the PCP strategy calledMPCP. The sub-deadlines in MPCP regularly update during the scheduling phase, so they can accurately reflect the situation of each time step. The optimization objectives in this paper include minimizing the execution cost and energy consumption within a given deadline. Finally, we use four scientific workflows to compare DCMORL and several representative scheduling algorithms. The results indicate that DCMORL outperforms the above algorithms. As far as we know, it is the first time to apply RL to a deadline constrained workflow scheduling problem.
解读:胡亚洲 郑州大学
审核:张琨 合肥工业大学
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Frontiers of Computer Science
Frontiers of Computer Science (FCS)是由教育部主管、高等教育出版社和北京航空航天大学共同主办、SpringerNature 公司海外发行的英文学术期刊。本刊于 2007 年创刊,双月刊,全球发行。主要刊登计算机科学领域具有创新性的综述论文、研究论文等。本刊主编为周志华教授,共同主编为熊璋教授。编委会及青年 AE 团队由国内外知名学者及优秀青年学者组成。本刊被 SCI、Ei、DBLP、INSPEC、SCOPUS 和中国科学引文数据库(CSCD)核心库等收录,为 CCF 推荐期刊;两次入选“中国科技期刊国际影响力提升计划”;入选“第4届中国国际化精品科技期刊”;入选“中国科技期刊卓越行动计划项目”。
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