Batch Production Control With Differentiable Integer Batch Sizing
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Solution Overview
Problem
Existing batch production systems face challenges in optimizing batch sizes for large-scale production due to integer constraints, which are not readily differentiable, making it difficult to scale reinforcement learning (RL) policies effectively.
Innovation Solution
The methodology employs reparameterization methods using Gumbel-Softmax estimators and straight-through estimators to represent discrete random variables, combined with a linear mapping to convert discretized vector representations of batch sizes into integers, enabling compatibility with continuous action-based RL methods like DDPG and SAC.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If reinforcement learning is used for batch size optimization, then productivity is improved, but the integer constraint on batch sizes makes the system difficult to implement and train
Solution Approach 1:
The patent transforms the discrete batch size parameter into a continuous relaxation using the Gumbel-Softmax distribution. This allows the batch size to be treated as a continuous variable during training, enabling gradient-based optimization while still producing discrete integer values during execution. The continuous relaxation is achieved by parameterizing the batch size selection as a categorical distribution and applying the Gumbel-Softmax trick to obtain differentiable samples.
Solution Approach 2:
The patent introduces the Gumbel-Softmax estimator as an intermediary between the neural network policy and the discrete batch size action. This intermediary layer provides a differentiable approximation of the discrete sampling process, allowing gradients to flow through what would otherwise be a non-differentiable operation. The straight-through estimator is used as another intermediary to pass gradients through the discretization operation during backpropagation.
2Manufacturing precision
If discrete batch sizes are used, then manufacturing precision is maintained, but the lack of differentiability prevents effective reinforcement learning training
Solution Approach 1:
The patent changes the parameterization of batch size from a direct discrete integer to a continuous distribution parameterized by logits. The neural network outputs logits that parameterize a categorical distribution, and the Gumbel-Softmax transformation converts these continuous parameters into discrete-like samples that are differentiable with respect to the logits. This maintains the discrete nature of batch sizes while enabling gradient-based training.
Solution Approach 2:
The patent makes the batch size selection dynamic and differentiable during training by using the Gumbel-Softmax relaxation. The batch size becomes a dynamic variable that can be optimized through gradient descent, rather than a static discrete parameter. The straight-through estimator enables this dynamic behavior by allowing gradients to pass through the discretization operation, effectively making the discrete selection process differentiable during training.
Data Source
AI summary
A computer-implemented method for supporting execution of batch production by a production system includes, over a sequence of steps: acquiring a system state defined by a shop floor status, inventory status and a demand of the product types, and processing the system state using a reinforcement learned policy including a deep learning model to output a control action defining an integer batch size of a selected product type. The control action is determined by using learned parameters of the deep learning model to compute logits for a categorical distribution of predicted product types and a categorical distribution of predicted batch sizes from the system state. The logits are processed to transform the categorical distribution of predicted product types into an encoding of the selected product type and reduce the categorical distribution of predicted batch sizes into an integer batch size, for producing a next batch on the shop floor.