Search Results (16)

The growing adoption of electric buses in public transport has intensified the need for efficient scheduling algorithms. In the context of tactical planning, public transport operators must address two interdependent scheduling problems: the Single Depot Vehicle Scheduling Problem for Electric Buses (EB-SD-VSP) and the Crew Scheduling Problem for Electric Buses (EB-CSP). This study introduces a sequential approach, solving EB-SD-VSP via a Mixed-Integer Quadratic Programming (MIQP) model, and then using its solution to generate service blocks for the EB-CSP, which is then solved as a Mixed-Integer Linear Programming (MILP) model. The proposed sequential optimization approach ultimately solves the combined problem of Vehicle and Crew Scheduling for a fleet of Electric Buses (EB-SD-VCSP). Experiments on real-world bus line data from Athens, Greece demonstrate practical applicability of the approach. When compared to a baseline scenario where the services are executed with conventional buses, the proposed method can calculate efficient vehicle timetables and crew schedules for operations with electric buses. The results highlight the benefit of decomposing joint electric bus and crew planning into tractable subproblems while preserving solution quality. These findings offer a scalable tactical-level planning tool for transit agencies transitioning to electric fleets and suggest promising directions for future extensions to multi-depot and real-time scenarios. Full article

There has been tremendous interest in the development of DC microgrid systems which consist of interconnected DC renewable energy sources. However, operating a DC microgrid system optimally by minimizing operational cost and ensures stability remains a problem when the system’s model is not available. In this paper, a novel model-free approach to perform operation control of DC microgrids based on reinforcement learning algorithms, specifically Q-learning and Q-network, has been proposed. This approach circumvents the need to know the accurate model of a DC grid by exploiting an interaction with the DC microgrids to learn the best policy, which leads to more optimal operation. The proposed approach has been compared with with mixed-integer quadratic programming (MIQP) as the baseline deterministic model that requires an accurate system model. The result shows that, in a system of three nodes, both Q-learning (74.2707) and Q-network (74.4254) are able to learn to make a control decision that is close to the MIQP (75.0489) solution. With the introduction of both model uncertainty and noisy sensor measurements, the Q-network performs better (72.3714) compared to MIQP (72.1596), whereas Q-learn fails to learn. Full article

Market power, defined as the ability to raise prices above competitive levels profitably, continues to be a prime concern in the restructured electricity markets. Market power must be mitigated to improve market performance and avoid inefficient generation investment, price volatility, and overpayment in power systems. For this reason, involving market power in the transmission expansion planning (TEP) problem is essential for ensuring the efficient operation of the electricity markets. In this regard, a methodological bilevel stochastic framework for the TEP problem that explicitly includes the market power indices in the upper level is proposed, aiming to restrict the potential market power execution. A mixed-integer linear/quadratic programming (MILP/MIQP) reformulation of the stochastic bilevel model is constructed utilizing Karush−Kuhn−Tucker (KKT) conditions. Wind power and electricity demand uncertainty are incorporated using scenario-based two-stage stochastic programming. The model enables the planner to make a trade-off between the market power indices and the investment cost. Using comparable results of the IEEE 118-bus system, we show that the proposed TEP outperforms the existing models in terms of market power indices and facilitates open access to the transmission network for all market participants. Full article

Due to the high randomness and volatility of renewable energy sources such as wind energy, the traditional thermal unit commitment (UC) model is no longer applicable. In this paper, in order to reduce the possible negative effects of an inaccurate wind energy forecast, the chance-constrained programming (CCP) method is used to study the UC problem with uncertainty wind power generation, and chance constraints such as power balance and spinning reserve are satisfied with a predetermined probability. In order to effectively solve the CCP problem, first, we used the sample average approximation (SAA) method to transform the chance constraints into deterministic constraints and to obtain a mixed-integer quadratic programming (MIQP) model. Then, the quadratic terms were incorporated into the constraints by introducing some auxiliary variables, and some second-order cone constraints were formed by combining them with the output characteristics of thermal unit; therefore, a tighter mixed-integer second-order cone programming (MISOCP) formulation was obtained. Finally, we applied this method to some systems including 10 to 100 thermal units and 1 to 2 wind units, and we invoked MOSEK in MATLAB to solve the MISOCP formulation. The numerical results obtained within 24 h confirm that not only is the MISOCP formulation a successful reformulation that can achieve better suboptimal solutions, but it is also a suitable method for solving the large-scale uncertain UC problem. In addition, for systems of up to 40 units within 24 h that do not consider wind power and pollution emissions, the numerical results were compared with those of previously published methods, showing that the MISOCP formulation is very promising, given its excellent performance. Full article

With the rapid development of the sharing economy, more and more platform operators apply the sharing concept in manufacturing, which increases the efficiency of assets utilization. Considering the apparel industry, clothing enterprises or manufacturers may share their excess orders between each other via a manufacturing cloud platform. Under the traditional production mode, manufacturers focus on processing their individual orders. There may be a coexistence of insufficient and surplus production capabilities. Some manufacturers cannot meet their customer demands due to limited capabilities and some orders have to be rejected, while some other manufacturers may have excess capacities with insufficient demands. It results in loss of revenue, and it is not conducive to maintaining a good customer relationship. In this paper, we consider a shared system with multiple manufacturers that produce homogeneous products, and the manufacturers in the shared system can share customer orders with each other. Once any manufacturer cannot fulfill all of its orders, the unsatisfied ones will be shared with other manufacturers that have surplus capacities with the aim of improving the balance of resource utilization and risk resistance of all manufacturers on the platform. The entropy maximization theory is mainly adopted to facilitate the formulation of the objective function. We apply a Taylor expansion to reformulate the objective function and construct a mixed-integer quadratic programming (MIQP) model. We employ off-the-shelf solvers to solve small-scale problems, and also propose a two-stage constructive heuristic algorithm to solve large-scale problems. Numerical experiments are conducted to demonstrate the efficiency of the algorithm. Full article

The main purpose of the work was examining various methods of decomposition of a network optimization problem of simultaneous routing and bandwidth allocation based on Lagrangian relaxation. The problem studied is an NP-hard mixed-integer nonlinear optimization problem. Multiple formulations of the optimization problem are proposed for the problem decomposition. The decomposition methods used several problem formulations and different choices of the dualized constraints. A simple gradient coordination algorithm, cutting-plane coordination algorithm, and their more sophisticated variants were used to solve dual problems. The performance of the proposed decomposition methods was compared to the commercial solver CPLEX and a heuristic algorithm. Full article

The low voltage (LV) distribution systems are extended year by year due to the increase in energy demand. To overcome this issue, distribution system utilities have been focusing on designing and operating an appropriate distribution system with minimum capital and operational expenditure for supplying electricity to users. This article compares different algorithms to design an LVAC distribution system in a rural area, which focuses on minimizing the total length of lines and the power losses and balancing the loads among the three phases including the economic evaluation of the grid-connected PV system. Firstly, the shortest path (SP) algorithm is established to search for the minimization of the conductor used. Secondly, three different algorithms which are repeated phase sequence (RPABC), first fit bin packing (FFBP), and mixed-integer quadratic programming (MIQP) algorithms are developed to balance the load and minimize power losses. Next, a comparative result of three different algorithms is provided. Finally, the techno-economic analysis of the grid-connected PV system with different electricity tariffs with hybrid optimization of multiple energy resources (HOMER) software is studied in the planning period. To validate a proposed method, the 129-buses low voltage distribution in a rural village, in Cambodia, is tested. The simulation result confirms the optimal solution of the MIQP algorithm and PV system integration in designing a distribution system in a particular case study. Full article

COVID-19 is generally transmitted from person to person through small droplets of saliva emitted when talking, sneezing, coughing, or breathing. For this reason, social distancing and ventilation have been widely emphasized to control the pandemic. The spread of the virus has brought with it many challenges in locating people under distance constraints. The effects of wakes between turbines have been studied extensively in the literature on wind energy, and there are well-established interference models. Does this apply to the propagation functions of the virus? In this work, a parallel relationship between the two problems is proposed. A mixed-integer linear programming (MIP) model and a mixed-integer quadratic programming model (MIQP) are formulated to locate people to avoid the spread of COVID-19. Both models were constructed according to the distance constraints proposed by the World Health Organization and the interference functions representing the effects of wake between turbines. Extensive computational tests show that people should not be less than two meters apart, in agreement with the adapted Wells–Riley model, which indicates that 1.6 to 3.0 m (5.2 to 9.8 ft) is the safe social distance when considering the aerosol transmission of large droplets exhaled when speaking, while the distance can be up to 8.2 m (26 ft) if all the droplets in a calm air environment are taken into account. Full article

It is considered necessary to implement advanced controllers such as model predictive control (MPC) to utilize the technical flexibility of a building polygeneration system to support the rapidly expanding renewable electricity grid. These can handle multiple inputs and outputs, uncertainties in forecast data, and plant constraints, amongst other features. One of the main issues identified in the literature regarding deploying these controllers is the lack of experimental demonstrations using standard components and communication protocols. In this original work, the economic-MPC-based optimal scheduling of a real-world heat pump-based building energy plant is demonstrated, and its performance is evaluated against two conventional controllers. The demonstration includes the steps to integrate an optimization-based supervisory controller into a typical building automation and control system with off-the-shelf HVAC components and usage of state-of-art algorithms to solve a mixed integer quadratic problem. Technological benefits in terms of fewer constraint violations and a hardware-friendly operation with MPC were identified. Additionally, a strong dependency of the economic benefits on the type of load profile, system design and controller parameters was also identified. Future work for the quantification of these benefits, the application of machine learning algorithms, and the study of forecast deviations is also proposed. Full article

This paper considers the fast and effective solving method for the unit commitment (UC) problem with wind curtailment and pollutant emission in power systems. Firstly, a suitable mixed-integer quadratic programming (MIQP) model of the corresponding UC problem is presented by some linearization techniques, which is difficult to solve directly. Then, the MIQP model is solved by the outer approximation method (OAM), which decomposes the MIQP into a mixed-integer linear programming (MILP) master problem and a nonlinear programming (NLP) subproblem for alternate iterative solving. Finally, simulation results for six systems with up to 100 thermal units and one wind unit in 24 periods are presented, which show the practicality of MIQP model and the effectiveness of OAM. Full article

This paper proposes an active collision avoidance controller based on a hierarchical model predictive control framework for distributed electric drive vehicles (4IDEV) considering extreme conditions. In this framework, a two-layer strategy is developed. The upper layer is the path replanning controller based on nonlinear MPC (nMPC), from which a collision-free path including the optimal lateral displacement and yaw angle can be obtained in real-time while encountering the obstacles. The lower layer is the path tracking controller based on hybrid MPC (hMPC), and the coordinated control inputs (yaw moment and the front wheel steering angle) are solved by a Mixed-Integer Quadratic Programming (MIQP) with the piecewise affine (PWA) tire model considering tire saturation region. Moreover, to improve the lateral stability when tracking, the stable zone of lateral stability in the high-risk condition is analyzed based on the phase portrait method, by which the constraints of vehicle states and inputs are derived. The verification is carried out on the MATLAB and CarSim co-simulation platform, and the simulation results show that the proposed active collision avoidance controller can track the reference path accurately and prevent vehicle instability in extreme scenarios. Full article

This paper proposes a novel approach to optimize the main energy consumptions of heavy oil refining industries (ORI) in response to electricity price uncertainties. The whole industrial sub-processes of the ORI are modeled mathematically to investigate the joint power-heat flexibility potentials of the industry. To model the refinery processes, an input/output flow-based model is proposed for five main refining units. Moreover, the role of storage tanks capacity in the power system flexibility is investigated. To hedge against the electricity price uncertainty, an uncertain bound for the wholesale electricity price is addressed. To optimize the industrial processes, a dual robust mixed-integer quadratic program (R-MIQP) is adopted; therefore, the ORI’s operational strategies are determined under the worst-case realization of the electricity price uncertainty. Finally, the suggested approach is implemented in the south-west sector of the Iran Energy Market that suffers from a lack of electricity in hot days of summer. The simulation results confirm that the proposed framework ensures industrial demand flexibility to the external grids when a power shortage occurs. The approach not only provides demand flexibility to the power system, but also minimizes the operation cost of the industries. Full article

In this paper, the VVO (Volt/Var optimization) is proposed using simplified linear equations. For fast computation, the characteristics of voltage control devices in a distribution system are expressed as a simplified linear equation. The voltage control devices are classified according to the characteristics of voltage control and represented as the simplified linear equation. The estimated voltage of distribution networks is represented by the sum of the simplified linear equations for the voltage control devices using the superposition principle. The voltage variation by the reactive power of distributed generations (DGs) can be expressed as the matrix of reactance. The voltage variation of tap changing devices can be linearized into the control area factor. The voltage variation by capacitor banks can also be expressed as the matrix of reactance. The voltage equations expressed as simplified linear equations are formulated by quadratic programming (QP). The variables of voltage control devices are defined, and the objective function is formulated as the QP form. The constraints are set using operating voltage range of distribution networks and the control ranges of each voltage control device. In order to derive the optimal solution, mixed-integer quadratic programming (MIQP), which is a type of mixed-integer nonlinear programming (MINLP), is used. The optimal results and proposed method results are compared by using MATLAB simulation and are confirmed to be close to the optimal solution. Full article

In real life, many problems are instances of combinatorial optimization. Cross-functional team selection is one of the typical issues. The decision-maker has to select solutions among $\left(\begin{array}{c}k\\ h\end{array}\right)$ solutions in the decision space, where k is the number of all candidates, and h is the number of members in the selected team. This paper is our continuing work since 2018; here, we introduce the completed version of the Min Distance to the Boundary model (MDSB) that allows access to both the “deep” and “wide” aspects of the selected team. The compromise programming approach enables decision-makers to ignore the parameters in the decision-making process. Instead, they point to the one scenario they expect. The aim of model construction focuses on finding the solution that matched the most to the expectation. We develop two algorithms: one is the genetic algorithm and another based on the philosophy of DC programming (DC) and its algorithm (DCA) to find the optimal solution. We also compared the introduced algorithms with the MIQP-CPLEX search algorithm to show their effectiveness. Full article

Three-dimensional (3D) printing has great potential for establishing a ubiquitous service in the medical industry. However, the planning, optimization, and control of a ubiquitous 3D printing network have not been sufficiently discussed. Therefore, this study established a collaborative and ubiquitous system for making dental parts using 3D printing. The collaborative and ubiquitous system split an order for the 3D printing facilities to fulfill the order collaboratively and forms a delivery plan to pick up the 3D objects. To optimize the performance of the two tasks, a mixed-integer linear programming (MILP) model and a mixed-integer quadratic programming (MIQP) model are proposed, respectively. In addition, slack information is derived and provided to each 3D printing facility so that it can determine the feasibility of resuming the same 3D printing process locally from the beginning without violating the optimality of the original printing and delivery plan. Further, more slack is gained by considering the chain effect between two successive 3D printing facilities. The effectiveness of the collaborative and ubiquitous system was validated using a regional experiment in Taichung City, Taiwan. Compared with two existing methods, the collaborative and ubiquitous 3D printing network reduced the manufacturing lead time by 45% on average. Furthermore, with the slack information, a 3D printing facility could make an independent decision about the feasibility of resuming the same 3D printing process locally from the beginning. Full article