The growing penetration of utility-scale energy storage resources (ESRs) into power grids has heightened the need for their effective integration into the unit commitment (UC) problem. Since ESRs require binary variables to prevent simultaneous charging and discharging, their inclusion increases the computational complexity of UC, necessitating efficient models. While our prior work introduced a systematic formulation tightening approach based on constraint-to-vertex conversion that proved effectiveness for conventional generators, its reliance on manual parameterization (expressing numerical coefficients in terms of generator parameters) limits scalability. In this paper, to overcome the above challenges, a novel formulation tightening method that leverages machine learning (ML) is developed to enhance and automate the tightening process for ESRs. To address the limitations of manual analysis in ensuring generalizability and flexibility, a novel ML model is developed to map ESR parameters to the numerical coefficients of tightened constraints, thereby identifying their underlying mathematical relationships. The framework also fully automates the tightening process, improving its applicability. Simulations on the IEEE 118-bus and Polish 2383-bus systems demonstrate a substantial reduction in solution time (up to 64%) without compromising solution quality, validating the effectiveness of the tightened constraints. Given its generalizability and applicability, this method holds significant promise for tightening complex Mixed Binary Linear Programming problems in power systems and beyond.

Microgrid is a small-scale grid where generation is close to the demand allowing more penetration of renewables, like photovoltaic (PV). However, the intermittent nature of PV power generation poses a significant challenge in microgrid operation, especially on days with highly variable weather conditions. In this paper, a deep reinforcement Q-learning long short-term memory (QLSTM) model is developed to predict the operation strategy of a microgrid for the next day at a 15-minute time interval. To address the uncertainty of PV power and demand, the previous three days' PV and load data are added as inputs to the model since weather conditions on consecutive days may depend on similar atmospheric conditions. Also, to address the effect of propagation of error in the long forecasting horizon with multiple steps, a moving window training method is implemented. The moving window will be shifted by 15 minutes at each step once the actual PV and load data are available till the end of the day. The model is tested in a microgrid consisting of combined cooling, heating and power, heat pump, PV, battery, and heating and cooling energy storage systems. Results show that our model outperforms gated recurrent unit, LSTM, and Q-learning for testing data from different months. Also, it shows better performance than MATLAB 2023 Optimization Toolbox (the branch-and-bound method) which uses forecasted data, especially on a day with highly variable weather conditions.

Job-shop scheduling is an important but difficult combinatorial optimization problem for low-volume and high-variety manufacturing, with solutions required to be obtained quickly at the beginning of each shift. In view of the increasing demand for customized products, problem sizes are growing. A promising direction is to take advantage of Machine Learning (ML). Direct learning to predict solutions for job-shop scheduling, however, suffers from major difficulties when problem scales are large. In this paper, a Deep Neural Network (DNN) is synergistically integrated within the decomposition and coordination framework of Surrogate Lagrangian Relaxation (SLR) to predict good-enough solutions for subproblems. Since a subproblem is associated with a single part, learning difficulties caused by large scales are overcome. Nevertheless, the learning still presents challenges. Because of the high-variety nature of parts, the DNN is desired to be able to generalize to solve all possible parts. To this end, our idea is to establish “surrogate” part subproblems that are easier to learn, develop a DNN based on Pointer Network to learn to predict their solutions, and calculate the solutions of the original part subproblems based on the predictions. Moreover, a masking mechanism is developed such that all the predictions are feasible. Numerical results demonstrate that good-enough subproblem solutions are predicted in many iterations, and high-quality solutions of the overall problem are obtained in a computationally efficient manner. The performance of the method is further improved through continuous learning.Note to Practitioners—Scheduling is important for the planning and operation of job shops, and high-quality schedules need to be obtained quickly at the beginning of each shift. To take advantage of ML, in this paper, a DNN is integrated within our recent decomposition and coordination approach to learn to predict “good-enough” solutions to part subproblems. To be able to predict solutions for parts of various characteristics“, surrogate” part subproblems that are easier to learn are established, and a generic “pointer network” is developed to learn to predict their solutions. To satisfy the constraints of the surrogate part subproblems, the pointer network is enhanced with a novel “masking mechanism” such that all the predictions are feasible. The solutions to the original part subproblems are calculated based on the predictions. Testing results demonstrate that subproblem solutions are efficiently obtained based on predictions, and the high-quality solutions of the overall problem are thus efficiently obtained. Through continuous learning, the performance of the method is further improved. Python codes and datasets are submitted together with the paper.

Job shops are an important production environment for low-volume high-variety manufacturing. Its scheduling has recently been formulated as an integer linear programming (ILP) problem to take advantages of popular mixed-integer linear programming (MILP) methods, e.g., branch-and-cut. When considering a large number of parts, MILP methods may experience difficulties. To address this, a critical but much overlooked issue is formulation tightening. The idea is that if problem constraints can be transformed to directly delineate the problem convex hull in the data preprocessing stage, then a solution can be obtained by using linear programming (LP) methods without combinatorial difficulties. The tightening process, however, is fundamentally challenging because of the existence of integer variables. In this article, an innovative and systematic approach is established for the first time to tighten the formulations of individual parts, each with multiple operations, in the data preprocessing stage. It is a major advancement of our previous work on problems with binary and continuous variables to integer variables. The idea is to first link integer variables to binary variables by innovatively combining constraints so that the integer variables are uniquely determined by the binary variables. With binary and continuous variables only, it is proved that the vertices of the convex hull can be obtained based on vertices of the LP problem after relaxing binary requirements. These vertices are then converted to tightened constraints for general use. This approach significantly improves our previous results on tightening individual operations. Numerical results demonstrate significant benefits on solution quality and computational efficiency. This approach also applies to other complex ILP and MILP problems with similar characteristics and fundamentally changes the way how such problems are formulated and solved.Note to Practitioners—Scheduling is an important but difficult problem in planning and operation of job shops. The problem has been recently formulated in an integer linear programming (ILP) form to take advantage of popular mixed-integer linear programming methods. Given an ILP problem, there must exist a linear programming (LP) formulation so that all of its vertices are also the vertices to the ILP problem. If such an LP problem can be found in the data preprocessing stage, then the corresponding ILP problem is tight and can be solved by using an LP method without difficulties. In this article, an innovative and systematic approach is established to tighten the formulations of individual parts, each with one or multiple operations. It is a major advancement of our previous work on problems with binary and continuous variables by novel exploitation of the relationship between integer and binary variables in job-shop scheduling. The resulting tightened constraints are characterized by part parameters and the length of the scheduling horizon and can be easily adjusted for other data sets. Results demonstrate significant benefits on solution quality and computational efficiency. This approach also applies to other complex ILP and MILP problems with similar characteristics and fundamentally changes the way how such problems are formulated and solved.

With the emergence of the Internet of Things that allows communications and local computations and with the vision of Industry 4.0, a foreseeable transition is from centralized system planning and operation toward decentralization with interacting components and subsystems, e.g., self-optimizing factories. In this article, a new “price-based” decomposition and coordination methodology is developed to efficiently coordinate a system consisting of distributed subsystems such as machines and parts, which are described by mixed-integer linear programming (MILP) formulations, in an asynchronous way. The novel method is a dual approach, whereby the coordination is performed by updating Lagrangian multipliers based on economic principles of “supply and demand.” To ensure low communication requirements within the method, exchanges between the “coordinator” and subsystems are limited to “prices” (Lagrangian multipliers) broadcast by the coordinator and to subsystem solutions sent at the coordinator. Asynchronous coordination, however, may lead to convergence difficulties since the order in which subsystem solutions arrive at the coordinator is not predefined as a result of uncertainties in communication and solving times. Under realistic assumptions of finite communication and solve times, the convergence of our method is proven by innovatively extending the Lyapunov stability theory. Numerical testing of generalized assignment problems through simulation demonstrates that the method converges fast and provides near-optimal results, paving the way for self-optimizing factories in the future. Accompanying CPLEX codes and data are included.Note to Practitioners—In view of a foreseeable transition toward self-optimizing factories whereby machines and parts have communication and computational capabilities, a novel “price-based” distributed and asynchronous method to coordinate a system consisting of distributed subsystems is developed. Under realistic assumptions of finite communication and solve times, method convergence is proven. Numerical testing of generalized assignment problems through simulation demonstrates that the method converges fast and provides near-optimal results, paving the way for self-optimizing factories in the future. Accompanying CPLEX codes and data are included.

Many operation optimization problems such as scheduling and assignment of interest to the automation community are mixed-integer linear programming (MILP) problems. Because of their combinatorial nature, the effort required to obtain optimal solutions increases drastically as the problem size increases. Such operation optimization problems typically need to be solved several times a day and require short solving times (e.g., 5, 10, or 20 min). The goal is, therefore, to obtain near-optimal solutions with quantifiable quality in a computationally efficient manner. Existing MILP methods, however, suffer from slow convergence and may not efficiently achieve this goal. In this paper, motivated by fast convergence of augmented Lagrangian relaxation (LR), a novel advanced price-based decomposition and coordination “surrogate absolute-value LR” (SAVLR) approach is developed. Within the method, convergence of our recent surrogate LR (SLR), which has overcome all major difficulties of traditional LR, is significantly improved by penalizing constraint violations by adding “absolute-value” penalties. Moreover, such penalties are efficiently linearized in a standard way, thereby enabling the use of MILP solvers. By exploiting the beautiful property of exponential reduction of complexity of subproblems upon decomposition, subproblems are efficiently solved and their solutions are efficiently coordinated by updating Lagrangian multipliers. Convergence is then proved under novel adjustment of penalty coefficients. A series of generalized assignment problems is considered, and for these problems, superior performance of SAVLR over other state-of-the-art and state-of-the-practice methods is demonstrated. Accompanying CPLEX codes, whereby SAVLR is implemented, are also included.Note to Practitioners—Examples of important problems that arise in automation community include scheduling and assignment problems. Because of their combinatorial nature, the effort required to obtain optimal solutions increases drastically as the problem size increases. Existing mixed-integer linear programming (MILP) methods, however, may suffer from slow convergence and may not efficiently achieve this goal. The new method revolutionizes the way such problems can be solved with major improvements on the overall performance. It is based on our recent breakthrough “surrogate Lagrangian relaxation” (LR), which has overcome all major difficulties of traditional LR while exploiting the beautiful property of exponential reduction of complexity upon decomposition. To significantly improve convergence while maintaining linearity so as to use MILP solvers, our idea is to penalize violations of relaxed constraints by the infrequently used “absolute-value” penalty functions. Although not differentiable, absolute-value penalties have the advantage of being exactly linearizable through extra variables and constraints. The difficulties caused by those extra constraints, which couple subproblems, are resolved by adaptive adjustment of penalty coefficients. A series of generalized assignment problems is considered and superior performance of the new method against state-of-the-art and state-of-the-practice methods is demonstrated. Accompanying CPLEX codes whereby the new method is implemented are also included.

Fault management is critical for efficiently supporting the increasing microgrids' penetration in distribution networks but remains an open problem. No existing ride through methods can ride through symmetrical and asymmetrical faults without increasing the fault current magnitude, meanwhile balancing microgrid power and eliminating double frequency ripples in microgrid inverters. The paper bridges this gap by contributing a novel active fault management (AFM) method. The new contributions include: 1) the development of a new conceptual AFM to control multiple variables during voltage dips; 2) the optimization-based AFM to coordinate different objectives according to a guidance and 3) a combined optimization and feedback control, during which optimization method provides the optimal trade-offs among different objectives and the feedback control ensures accurate realization of chosen operation points. Simulations with different types of faults prove that the developed AFM can achieve better trade-offs and coordination among various control objectives in comparison to the conventional ride through method.

To reduce energy costs and emissions of microgrids, daily operation is critical. The problem is to commit and dispatch distributed devices with renewable generation to minimize the total energy and emission cost while meeting the forecasted energy demand. The problem is challenging because of the intermittent nature of renewables. In this paper, photovoltaic (PV) uncertainties are modeled by a Markovian process. For effective coordination, other devices are modeled as Markov processes with states depending on PV states. The entire problem is Markovian. This combinatorial problem is solved using branch-and-cut. Beyond energy and emission costs, to consider capital and maintenance costs in the long run, microgrid design is also essential. The problem is to decide device sizes with given types to minimize the lifetime cost while meeting energy demand. Its complexity increases exponentially with the problem size. To evaluate the lifetime cost including the reliability cost and the classic components such as capital and fuel costs, a linear model is established. By selecting a limited number of possible combinations of device sizes, exhaustive search is used to find the optimized design. The results show that the operation method is efficient in saving cost and scalable, and microgrids have lower lifetime costs than conventional energy systems. Implications for regulators and distribution utilities are also discussed.

Optimizing HVAC operation becomes increasingly important because of the rising energy cost and comfort requirements. In this paper, an innovative event-based approach is developed within the Lagrangian relaxation framework to minimize an HVAC's day-ahead energy cost. To solve the HVAC optimization problem based on events is challenging since with time-dependent uncertainties in weather, cooling load, etc., the optimal policy is not stationary. The nonstationary policy space is extremely large, and it is time consuming to find the optimal policy. To overcome the challenge, we develop an event-based approach to make the nonstationary optimal policy stationary in the planning horizon. The key idea is to augment state variables to include the time-dependent variables that make the optimal policy nonstationary and then define events based on the extended state variables. In addition, we develop within the Lagrangian relaxation framework a Q-learning method where Q-factors are used to evaluate event-action pairs and to obtain the optimal policy. Numerical results demonstrate that, as compared with time-based approaches, the event-based approach maintains similar levels of energy costs and human comfort, but reduces computational efforts significantly and has a much faster response to events.

The increasing pressure to meet demand are forcing semiconductor manufacturers to seek efficient scheduling methods. Lithography, with a limited number of expensive resources and the reentrant nature of the fabrication processes, is a major bottleneck. This paper presents a litho machine scheduling formulation for high-volume and low-variety manufacturing over a day, with novel modeling of resource setups, reticle expirations, and future stacking layer load balancing. The problem is believed to be NP hard. After linearization and simplification, it is solved by using the branch-and-cut method by exploiting problem linearity. Near-optimal solutions for practical problems, however, are still difficult to obtain efficiently. Through detailed analyses, it was discovered that the convex hull of the problem is difficult to delineate and many low-efficient branching operations are needed. A two-phase approach is therefore established. In the first phase, a simplified problem with certain complicating constraints dropped is efficiently solved by exploiting linearity to reduce ranges of decision variables. The problem with the full set of constraints is then solved in the second phase with a much reduced decision space. Numerical testing shows that this two-phase approach can generate near-optimal schedules within reasonable amounts of computation time. This two-phase approach is generic, and will have major implications on other semiconductor scheduling problems and beyond.