9 research outputs found
An Expandable Machine Learning-Optimization Framework to Sequential Decision-Making
We present an integrated prediction-optimization (PredOpt) framework to
efficiently solve sequential decision-making problems by predicting the values
of binary decision variables in an optimal solution. We address the key issues
of sequential dependence, infeasibility, and generalization in machine learning
(ML) to make predictions for optimal solutions to combinatorial problems. The
sequential nature of the combinatorial optimization problems considered is
captured with recurrent neural networks and a sliding-attention window. We
integrate an attention-based encoder-decoder neural network architecture with
an infeasibility-elimination and generalization framework to learn high-quality
feasible solutions to time-dependent optimization problems. In this framework,
the required level of predictions is optimized to eliminate the infeasibility
of the ML predictions. These predictions are then fixed in mixed-integer
programming (MIP) problems to solve them quickly with the aid of a commercial
solver. We demonstrate our approach to tackling the two well-known dynamic
NP-Hard optimization problems: multi-item capacitated lot-sizing (MCLSP) and
multi-dimensional knapsack (MSMK). Our results show that models trained on
shorter and smaller-dimensional instances can be successfully used to predict
longer and larger-dimensional problems. The solution time can be reduced by
three orders of magnitude with an average optimality gap below 0.1%. We compare
PredOpt with various specially designed heuristics and show that our framework
outperforms them. PredOpt can be advantageous for solving dynamic MIP problems
that need to be solved instantly and repetitively
An integer programming based algorithm for the resource constrained project scheduling problem
Ankara : The Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent Univ., 2005.Thesis (Master's) -- Bilkent University, 2005.Includes bibliographical references leaves 48-54.In this thesis, we study the problem of scheduling the activities of a single project in
order for all resource and precedence relationships constraints to be satisfied with an
objective of minimizing the project completion time. To solve this problem, we propose
an Integer Programming based approximation algorithm, which has two phases. In the
first phase of the algorithm, a subproblem generation technique and enumerative cuts
used to tighten the formulation of the problem are presented. If an optimal solution is
not found within a predetermined time limit, we continue with the second phase that
uses the cuts and the lower bound obtained in the first phase. In order to evaluate the
efficiency of our algorithm, we used the benchmark instances in the literature and
compared the results with the best known solutions available for these instances.
Finally, the computational results are reported and discussed.Büyüktahtakın, İsmet EsraM.S
Learning Optimal Solutions via an LSTM-Optimization Framework
In this study, we present a deep learning-optimization framework to tackle
dynamic mixed-integer programs. Specifically, we develop a bidirectional Long
Short Term Memory (LSTM) framework that can process information forward and
backward in time to learn optimal solutions to sequential decision-making
problems. We demonstrate our approach in predicting the optimal decisions for
the single-item capacitated lot-sizing problem (CLSP), where a binary variable
denotes whether to produce in a period or not. Due to the dynamic nature of the
problem, the CLSP can be treated as a sequence labeling task where a recurrent
neural network can capture the problem's temporal dynamics. Computational
results show that our LSTM-Optimization (LSTM-Opt) framework significantly
reduces the solution time of benchmark CLSP problems without much loss in
feasibility and optimality. For example, the predictions at the 85\% level
reduce the CPLEX solution time by a factor of 9 on average for over 240,000
test instances with an optimality gap of less than 0.05\% and 0.4\%
infeasibility in the test set. Also, models trained using shorter planning
horizons can successfully predict the optimal solution of the instances with
longer planning horizons. For the hardest data set, the LSTM predictions at the
25\% level reduce the solution time of 70 CPU hours to less than 2 CPU minutes
with an optimality gap of 0.8\% and without any infeasibility. The LSTM-Opt
framework outperforms classical ML algorithms, such as the logistic regression
and random forest, in terms of the solution quality, and exact approaches, such
as the (, S) and dynamic programming-based inequalities, with respect to
the solution time improvement. Our machine learning approach could be
beneficial in tackling sequential decision-making problems similar to CLSP,
which need to be solved repetitively, frequently, and in a fast manner