𝑡−1 (11) 𝑟𝑡 = ∑ 𝑟 + 𝑟𝑎𝑐𝑐 . 𝑖=0We use the following two agent algorithms to the environment in our study. The first algorithm iscalled Deep Q-Networks (DQN). It is an extension of Q-learning that uses deep neural networks toapproximate the Q-value function. This works with discrete observation space and discrete actionspace. The key equation for DQN involves updating the weights of the neural network to minimizethe loss function, which is typically the mean squared error between the predicted Q-values and thetarget Q-values. The function for DQN can be expressed as [20] 𝑄(𝑠𝑡 , 𝑎𝑡
| xi = 0, 1 ≤ i ≤ n} can be found, such that wi · xi ≤ S − W and xi ∈ {0, 1}. i=1Optimization AlgorithmIn this section, an optimization algorithm that makes use of 0−1 integer programming is describedto address the OTP problem. Consider that the catalog of the starting school contains p courses,denoted a1 , . . . , ap , and the catalog of the destination school contains q courses, denoted b1 , . . . , bq .Let cr[i] denote the credit hours associated with course i. To determine the set of courses that willbe included in the curriculum at the starting school, a p × 1 binary-valued assignment matrix isdefined as follows, 1; if course
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