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        "author": "Zhan Lin",
        "author_email": "dy403164418@gmail.com",
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        "description": "Usage: Users are required to provide classes Algs and Simulator to SIM. Algs should inherit from algs. In the following example, we provide piecewise_linear(Algs) and SIM_Resolve_First(Simulator) to SIM. SIM.update() will solve the model, while SIM.avg(n) return simulation results.\r\n\r\nExample:\r\n\r\nfrom SIM import *\r\n\r\nfrom SIM_Resolve_First import *\r\n\r\nfrom piecewise_linear import *\r\n\r\ncase = SIM_Resolve_First()\r\n\r\nalgs = piecewise_linear()\r\n\r\nsim = SIM(case,algs)\r\n\r\nsim.update()\r\n\r\n#sim.train_mab()\r\n\r\nprint sim.avg(1000)\r\n\r\n\r\nStructure of Algs and Simulator:\r\n\r\nSIM:\r\n\r\nThe only requirement of Simulator is having a function sim() to return a realization. If there are any parameters, they should be implemented in set_para(). SIM_Resolve_First.py and SIM_ALP.py are examples.\r\n\r\nAlgs:\r\n\r\nInterfaces you should provide include lift_value(),relation(),strategy() and update(). Also, lifting method should be described in the class.\r\n\r\nExample of Piecewise Linear:\r\n\r\nfor t in range(self.T):\r\n\r\n            for j in range(self.J):\r\n\r\n                for k in range(self.div_num):\r\n\r\n                    self.div_axis[t,j,k] = self.low_bound[t,j] + (self.up_bound[t,j]-self.low_bound[t,j])/float(self.div_num - 1) * k\r\n\r\n                    self.xi[t,j,k] = self.script.add_var(0,self.div_axis[t,j,k])\r\n\r\n        for t in range(self.T):\r\n\r\n            for j in range(self.J):\r\n\r\n                left = {}\r\n\r\n                for k in range(self.div_num):\r\n\r\n                    left[self.xi[t,j,k]] = 1\r\n\r\n                right = {}\r\n\r\n                right[self.constant] = 1\r\n\r\n                self.script.add_lin_equ(left,right)\r\n\r\n                for k in range(self.div_num):\r\n\r\n                    self.script.add_lin_greater({self.xi[t,j,k]:1},{self.constant:0})\r\n\r\n        for t in range(self.T):\r\n\r\n            for j in range(self.J):\r\n\r\n                left = {self.xi[t,j]:1}\r\n\r\n                right = {}\r\n\r\n                for k in range(self.div_num):\r\n\r\n                    right[self.xi[t,j,k]] = self.div_axis[t,j,k]\r\n\r\n                self.script.add_lin_equ(left,right)\r\n\r\nlift_value(data):\r\n\r\nreturn lift value for a realization.\r\n\r\nrelation():\r\n\r\nset up dependence self.P for items. For example, if decision X(t,j) depends on first three elements of lifted vector, then self.P[t,j] = {1,2,3}\r\n\r\nstrategy(t,history,x):\r\n\r\nreturn strategy at stage t with history and optimized decision variable x.\r\n\r\nupdate():\r\n\r\nupdate lifting methods.\r\n\r\npiecewise_linear.py and tri_linear.py are examples of Algs.",
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