Integrated machine learning and optimization approaches

This dissertation focuses on the integration of machine learning and optimization. Specifically, novel machine learning-based frameworks are proposed to help solve a broad range of well-known operations research problems to reduce the solution times. The first study presents a bidirectional Long Short-Term Memory framework to learn optimal solutions to sequential decision-making problems. Computational results show that the framework significantly reduces the solution time of benchmark capacitated lot-sizing problems without much loss in feasibility and optimality. 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 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 infeasibility. In the second study, an extendable prediction-optimization framework is presented for multi-stage decision-making problems to address the key issues of sequential dependence, infeasibility, and generalization. Specifically, an attention-based encoder-decoder neural network architecture is integrated with an infeasibility-elimination and generalization framework to learn high-quality feasible solutions. The proposed framework is demonstrated to tackle the two well-known dynamic NP-Hard optimization problems: multi-item capacitated lot-sizing and multi-dimensional knapsack. The results show that models trained on shorter and smaller-dimension instances can be successfully used to predict longer and larger-dimension problems with the presented item-wise expansion algorithm. The solution time can be reduced by three orders of magnitude with an average optimality gap below 0.1%. The proposed framework can be advantageous for solving dynamic mixed-integer programming problems that need to be solved instantly and repetitively. In the third study, a deep reinforcement learning-based framework is presented for solving scenario-based two-stage stochastic programming problems, which are computationally challenging to solve. A general two-stage deep reinforcement learning framework is proposed where two learning agents sequentially learn to solve each stage of a general two-stage stochastic multi-dimensional knapsack problem. The results show that solution time can be reduced significantly with a relatively small gap. Additionally, decision-making agents can be trained with a few scenarios and solve problems with a large number of scenarios. In the fourth study, a learning-based prediction-optimization framework is proposed for solving scenario-based multi-stage stochastic programs. The issue of non-anticipativity is addressed with a novel neural network architecture that is based on a neural machine translation system. Furthermore, training the models on deterministic problems is suggested instead of solving hard and time-consuming stochastic programs. In this framework, the level of variables used for the solution is iteratively reduced to eliminate infeasibility, and a heuristic based on a linear relaxation is performed to reduce the solution time. An improved item-wise expansion strategy is introduced to generalize the algorithm to tackle instances with different sizes. The results are presented in solving stochastic multi-item capacitated lot-sizing and stochastic multi-stage multi-dimensional knapsack problems. The results show that the solution time can be reduced by a factor of 599 with an optimality gap of only 0.08%. Moreover, results demonstrate that the models can be used to predict similarly structured stochastic programming problems with a varying number of periods, items, and scenarios. The frameworks presented in this dissertation can be utilized to achieve high-quality and fast solutions to repeatedly-solved problems in various industrial and business settings, such as production and inventory management, capacity planning, scheduling, airline logistics, dynamic pricing, and emergency management

Stochastic multi-period multi-product multi-objective Aggregate Production Planning model in multi-echelon supply chain

In this paper a multi-period multi-product multi-objective aggregate production planning (APP) model is proposed for an uncertain multi-echelon supply chain considering financial risk, customer satisfaction, and human resource training. Three conflictive objective functions and several sets of real constraints are considered concurrently in the proposed APP model. Some parameters of the proposed model are assumed to be uncertain and handled through a two-stage stochastic programming (TSSP) approach. The proposed TSSP is solved using three multi-objective solution procedures, i.e., the goal attainment technique, the modified ε-constraint method, and STEM method. The whole procedure is applied in an automotive resin and oil supply chain as a real case study wherein the efficacy and applicability of the proposed approaches are illustrated in comparison with existing experimental production planning method

Processing second-order stochastic dominance models using cutting-plane representations

This is the post-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2011 Springer-VerlagSecond-order stochastic dominance (SSD) is widely recognised as an important decision criterion in portfolio selection. Unfortunately, stochastic dominance models are known to be very demanding from a computational point of view. In this paper we consider two classes of models which use SSD as a choice criterion. The first, proposed by Dentcheva and Ruszczyński (J Bank Finance 30:433–451, 2006), uses a SSD constraint, which can be expressed as integrated chance constraints (ICCs). The second, proposed by Roman et al. (Math Program, Ser B 108:541–569, 2006) uses SSD through a multi-objective formulation with CVaR objectives. Cutting plane representations and algorithms were proposed by Klein Haneveld and Van der Vlerk (Comput Manage Sci 3:245–269, 2006) for ICCs, and by Künzi-Bay and Mayer (Comput Manage Sci 3:3–27, 2006) for CVaR minimization. These concepts are taken into consideration to propose representations and solution methods for the above class of SSD based models. We describe a cutting plane based solution algorithm and outline implementation details. A computational study is presented, which demonstrates the effectiveness and the scale-up properties of the solution algorithm, as applied to the SSD model of Roman et al. (Math Program, Ser B 108:541–569, 2006).This study was funded by OTKA, Hungarian National Fund for Scientific Research, project 47340; by Mobile Innovation Centre, Budapest University of Technology, project 2.2; Optirisk Systems, Uxbridge, UK and by BRIEF (Brunel University Research Innovation and Enterprise Fund)

A comparison of sample-based Stochastic Optimal Control methods

In this paper, we compare the performance of two scenario-based numerical methods to solve stochastic optimal control problems: scenario trees and particles. The problem consists in finding strategies to control a dynamical system perturbed by exogenous noises so as to minimize some expected cost along a discrete and finite time horizon. We introduce the Mean Squared Error (MSE) which is the expected $L^2$-distance between the strategy given by the algorithm and the optimal strategy, as a performance indicator for the two models. We study the behaviour of the MSE with respect to the number of scenarios used for discretization. The first model, widely studied in the Stochastic Programming community, consists in approximating the noise diffusion using a scenario tree representation. On a numerical example, we observe that the number of scenarios needed to obtain a given precision grows exponentially with the time horizon. In that sense, our conclusion on scenario trees is equivalent to the one in the work by Shapiro (2006) and has been widely noticed by practitioners. However, in the second part, we show using the same example that, by mixing Stochastic Programming and Dynamic Programming ideas, the particle method described by Carpentier et al (2009) copes with this numerical difficulty: the number of scenarios needed to obtain a given precision now does not depend on the time horizon. Unfortunately, we also observe that serious obstacles still arise from the system state space dimension