Search Results (56)

Covering problems constitute a central theme in facility location research. This study extends the classical Maximal Covering Location Problem (MCLP) and Partial Set Covering Location Problem (PSCLP) to their generalized variants, in which each demand point must be simultaneously served by multiple facilities. This generalization captures reliability requirements inherent in applications such as emergency response and robust communication networks. We first present integer programming formulations for both generalized problems, followed by equivalent reformulations that facilitate algorithmic development. Building on these, we design exact Benders decomposition algorithms that exploit structural properties of the problems to achieve enhanced scalability and computational efficiency. Computational experiments on large-scale synthetic instances with up to 200,000 demand points demonstrate that our method attains more than a threefold speedup over CPLEX. We further validate the effectiveness of the proposed approach through experiments on a real-world dataset. In addition, we compare our method with a tabu search heuristic, and the numerical results show that within a fixed time limit, our method is generally able to identify higher-quality feasible solutions. These results collectively demonstrate both the effectiveness and the practical applicability of our approach for large-scale generalized covering problems. Full article

As the electrification reform accelerates in ports worldwide, the application of electric tugboats is becoming more widely applied, posing a challenge in the balance between working arrangement and energy replenishment, especially when the shore energy replenishment facilities are limited. Aligning with the emerging trends of port electrification, unmanned operations, and intelligentization, this paper investigates unmanned electric tugboat scheduling considering battery-swapping operations that combine the assignment of tasks to the working periods of tugboats, the allocation of battery-swapping operations to the shore battery-swapping stations, and the sequencing of operations at each station. The problem is formulated into a mixed-integer linear programming to minimize the total completion time of the battery-swapping operations. A logic-based Benders decomposition method is proposed that decomposes the problem into a master problem and a subproblem. The master problem relaxes the sequencing constraints and solves the assignment of tasks to tugboats and the allocation of battery-swapping operations to stations. The SP, based on the solution to the master problem, determines the sequencing of battery-swapping operations at each station. Considering the interdependence of swapping operations of each tugboat that might be allocated to different stations, a dispatching heuristic is designed to efficiently obtain high-quality sequences for the stations. Numerical experiments are conducted based on 80 randomly-generated instances with up to 100 tasks, ten tugboats, and six battery-swapping stations. The results demonstrate that LBBD is capable of solving all 80 instances, whereas the commercial solver CPLEX fails to solve those with 80 or more tasks. Moreover, the average computational time of CPLEX on the instances it can solve is 241.32 s, nearly 32 times that of LBBD (7.57 s). This clearly indicates that LBBD significantly outperforms CPLEX in terms of both computational capacity and efficiency. Further analyses show that the increase in the number of tugboats will significantly shorten the makespan and make ETSBS easier to solve, while the increase in the number of battery-swapping stations makes the problem more challenging with longer computational time. Full article

In computer numeric controller (CNC) milling machining, air-cutting, where the tool moves without engaging the material, will reduce the machining efficiency. This study proposes a novel methodology to detect and minimize non-productive (air-cutting) time in real-time using spindle load monitoring, vibration signal analysis, and NC code tracking. A logic-based benders decomposition (LBBD) approach was used to optimize toolpath segments by analyzing air-cutting occurrences and dynamically modifying the NC code. Two optimization strategies were proposed: increasing the feedrate during short air-cutting segments and decomposing longer segments using G00 and G01 codes with positioning error compensation. A human–machine interface (HMI) developed in C# enables real-time monitoring, detection, and minimization of air-cutting. Experimental results demonstrate up to 73% reduction of air-cutting time and up to 42% savings in total machining time, validated across multiple scenarios with varying cutting parameters. The proposed methodology offers a practical and effective solution to enhance CNC milling productivity. Full article

The internet data center (IDC) has experienced rapid growth recently. Computing power tasks have the characteristic of flexible adjustment and can participate in demand-side response; thus, they are suitable for balancing stochastic wind and solar power. Existing studies lack research on joint optimization between the IDC and power grid. This paper proposes a joint optimization scheduling approach for IDC and power systems, focusing on the response of computing tasks. Based on the adjustment characteristics of computing tasks, tasks are categorized, and operational constraints for each category are defined. The bi-level optimization model for the IDC and power grid is established, taking into account the task constraints, as well as the operational limits of power generation units and the IDC. A novel elasticity coefficient matrix for time-of-use (TOU) electricity pricing is proposed, considering the load characteristics of IDC tasks. The IDC’s demand response volume is determined using the elasticity coefficient matrix. The enhanced Benders decomposition method is then employed, incorporating the IDC’s demand response capacity and the constraints of the bi-level optimization model, to solve the optimal planning problem. To achieve scenario reduction, the K-means algorithm is utilized to derive the typical daily load profiles of the IDC. The simulation results validate the effectiveness and accuracy of the proposed method and show that the approach effectively reduces the operational costs of the IDC power system and enhances the sustainable integration of renewable energy. Full article

The optimization of distillation processes is particularly challenging due to the presence of nonlinear equations and integer variables, resulting in complex mixed-integer nonlinear programming (MINLP) problems. This work introduces an enhanced optimization algorithm, the logic-based proximity principle Bender’s decomposition (LB-PBD), to address non-convex MINLP issues in simulator-based distillation optimization. The key innovation, the proximity principle, improves lower bound predictions by prioritizing information from the closest known integer solutions. Additionally, the integration of a multi-start points strategy and a delayed convergence strategy ensures the algorithm achieves global optimality while avoiding premature convergence. The effectiveness if the proposed LB-PBD is validated through three case studies. Numerical experiments demonstrate so-called proximity principle superior ability of original algorithm to navigate local optima, making LB-PBD more versatile than traditional deterministic algorithm (logic-based outer approximation algorithm) and stochastic algorithm (adaptive superstructure-differential evolution algorithm). In a single-column distillation case, LB-PBD achieves high accuracy. In an extractive distillation case, the algorithm successfully optimizes the separation of a near-azeotropic mixture, reducing energy consumption and improving product recovery compared to previous solutions. These results highlight LB-PBD as a robust and effective tool for solving non-convex MINLLP problems, particularly in simulator-based distillation process optimization. Full article

As wind penetration rates continue to increase, the main challenge faced by operators is how to schedule flexible resources, such as traditional generation and storage, in the future to ensure the safe and stable operation of power grids under multiple uncertainties. In this paper, a security-constrained multi-stage robust dynamic economic dispatch model with storage (SMRDEDS) is proposed to address multiple uncertainties of wind power outputs and N-1 contingencies. Compared to the traditional two-stage robust dynamic economic dispatch model, the proposed multi-stage dispatch model yields sequential operation decisions with uncertainties revealed gradually over time. What is more, a combined two-stage Benders’ decomposition and relaxed approximation–robust dual dynamic programming (RA-RDDP) is proposed to handle the computational issue of multi-stage problems due to large-scale post-contingency constraints and the convergence issue of the stochastic dual dynamic programming (SDDP) algorithm. First, a two-stage Benders’ decomposition algorithm is applied to relax the SMRDEDS model into a master problem and sub-problem. The master problem determines the generator output and storage charge and discharge, and the sub-problem determines the total generation and storage reserve capacity to cover all the generator N-1 contingencies. Second, a relaxed approximation–RDDP algorithm is proposed to solve the multi-stage framework problem. Compared to the traditional SDDP algorithm and RDDP algorithm, the proposed RA-RDDP algorithm uses the inner relaxed approximation and outer approximation methods to approximate the upper and lower bounds of the future cost-to-go function, which overcomes the convergence issue of the traditional SDDP algorithm and solution efficiency of the RDDP algorithm. We tested the proposed algorithm on the IEEE-3 bus, IEEE-118 bus, and the German power system. The simulation results verify the effectiveness of the proposed model and proposed algorithm. Full article

In this paper, we introduce a shipping logistics network optimization method for construction waste recycling. In our case, construction waste is transported by a relay mode integrating land transportation, shipping transportation, and land transportation. Under the influence of urban economic life, the quantity (demand) of construction waste is uncertain and stochastic. Considering the randomness of construction waste generation, a two-stage stochastic integer programming model for the design of a shipping logistics network for construction waste recycling is proposed, and an accurate algorithm based on Benders decomposition is presented. Based on an actual case in Shanghai, numerical experiments are carried out to evaluate the efficacy of the proposed model and algorithm. Based on an actual case study in Shanghai, numerical experiments demonstrate that the proposed model can help to reduce transportation costs of construction waste. Sensitivity analysis highlights that factors like the penalty for untransported waste and capacity constraints play a crucial role in network optimization decisions. The findings provide valuable theoretical support for developing more efficient and sustainable logistics networks for construction waste recycling. Full article

This article presents a novel methodology for analyzing the resilience of an active distribution system (ADS) integrated with an urban gas network (UGN). It demonstrates that the secure adoption of gas turbines with optimal capacity and allocation can enhance the resilience of the ADS during high-impact, low-probability (HILP) events. A two-level tri-layer resilience problem is formulated to minimize load shedding as the resilience index during post-event outages. The challenge of unpredictability is addressed by an adaptive distributionally robust optimization strategy based on multi-cut Benders decomposition. The uncertainties of HILP events are modeled by different moment-based probability distributions. In this regard, considering the nature of each uncertain variable, a different probabilistic method is utilized. For instance, to account for the influence of power generated from renewable energy sources on the decision-making process, a diurnal version of the long-term short-term memory network is developed to forecast day-ahead weather. In comparison with standard LSTM, the proposed approach reduces the mean absolute error and root mean squared error by approximately 47% and 71% for wind speed, as well as 76% and 77% for solar irradiance network. Finally, the optimal operating framework for improving power grid resilience is validated using the IEEE 33-bus ADS and 7-node UGN. Full article

In recent years, the intelligent reflecting surface (IRS) has attracted increasing attention for its capability to intelligently reconfigure the wireless propagation channel. However, most existing works ignore the dynamic power consumption of IRS related to the phase shift configuration. This relationship gets even more intractable for a multi-bit IRS because of its nonlinearity and implicit form. In this paper, we investigate the beamforming optimization for multi-bit IRS-aided systems with the practical phase shift-dependent power consumption (PS-DPC) model, aiming at minimizing the power consumption of the system. To solve the implicit and nonlinear relationship, we introduce a selection matrix to explicitly represent the power consumption and the phase shift matrix of the IRS, respectively. Then, we propose a generalized Benders decomposition-based beamforming optimization algorithm in the single-user scenario. Furthermore, in the multi-user scenario, we design a coordinate descent-based algorithm and a genetic algorithm for the beamforming optimization. The simulation results show that the proposed algorithms significantly decrease the power consumption of the multi-bit IRS-aided systems. Full article

Effective supply and demand matching for construction materials is a crucial challenge in large-scale railway projects, particularly in complex and hazardous environments. We propose a two-stage stochastic programing model that incorporates environmental uncertainties, such as natural disasters, into the supply chain optimization process. The first stage determines optimal locations and capacities for material supply points, while the second stage addresses material distribution under uncertain demand. We further enhance the model’s efficiency with Benders decomposition algorithm. The performance of our model is rigorously compared with existing optimization approaches, demonstrating its superior capability in handling environmental uncertainties and complex logistical scenarios. This study provides a novel framework for optimizing supply chains in challenging environments, offering significant improvements over traditional models in both adaptability and robustness. Full article

In this paper, the quadratic p-median optimization problem is discussed, where the goal is to connect users to a selected group of facilities (emergency services, telecommunications servers, healthcare facilities) at the lowest possible cost. The problem is aimed at minimizing the cost of connecting these selected facilities. The costs are symmetric, meaning connecting two different points is the same in both directions. This problem extends the traditional p-median problem, a combinatorial problem used in various fields like facility location, network design, transportation, supply chain networks, emergency services, healthcare, and education planning. Surprisingly, the quadratic version has not been thoroughly considered in the literature. The paper highlights the formulation of two mixed-integer quadratic programming models to find optimal solutions to this problem. One model is a classic formulation, and the other is based on set cover theory. Linear versions and Bender’s decomposition formulations for each model are also derived. A Bender’s decomposition is solved using an algorithm that adds constraints during each iteration to improve the solution. Lazy constraints in the Gurobi solver’s branch and cut algorithm are dynamically added whenever a mixed-integer programming solution is found. Additionally, an efficient local search meta-heuristic is proposed that usually finds optimal solutions for tested instances. Challenging instances with up to 60 facilities and 2000 users are successfully solved. Our results show that Bender’s models with lazy constraints are the most effective for Euclidean and random test cases, achieving optimal solutions in less CPU time. The meta-heuristic also finds near-optimal solutions rapidly for these cases. Full article

Digitalization plays a crucial role in improving the performance of chemical companies. In this context, different modeling, simulation, and optimization techniques such as MILP, discrete-event simulation (DES), and data-driven (DD) models are being used. Due to their heterogeneity, these techniques must be executed individually, and holistic optimization is manual and time-consuming. We propose Benders decomposition to combine these techniques into one rigorous optimization procedure. The main idea is that heterogeneous models can simultaneously be optimized as Benders subproblems. We illustrate this concept with the distributed permutation flow shop scheduling problem (DPFSP) and assume that a MILP, DES, and DD model exist for three flow shops. Our approach can compute bounds and report gap information on the optimal makespan for five medium-sized literature instances. The approach is promising because it enables the optimization of heterogeneous models and makes it possible to build optimization capabilities on an existing model and tool landscape in chemical companies. Full article

Collaborative designing of service networks using multiple logistics carriers can bring advantages in both economic and environmental terms, and these carriers have symmetry in their service areas. To enable such a collaborative service network and the corresponding benefits, this study proposes a problem of collaborative service network design (CSND) considering demand uncertainty. This problem is formulated as a two-stage robust optimization model using a budget uncertainty set to handle the uncertain demand. A column-and-constraint generation algorithm is developed to accurately solve the robust model. Numerical experiments show that the proposed algorithm outperforms the Benders decomposition algorithm in terms of solving efficiency and quality. Through comparative experiments, this research validates the advantages of collaborative designing and the robustness of model solutions. In addition, three allocation mechanisms are tested to investigate the importance of allocation in CSND. Full article

This paper presents a model for a “hub-and-spoke network design considering congestion and flow-based cost function”. The number of hubs and spokes is unknown, and the objective is to minimize the cost (including the transportation cost, lost demand, and facility setup cost). In the post-pandemic era, it is expected to have government-imposed restrictions on the congestion of airports, as a measure of health and safety. Unlike the current literature which considers a monetary penalty for congestion, we consider congestion as an externally imposed factor, which should be modeled as a constraint. We take a gravity-based modeling approach to obtain the desirability of a facility and calculate the demand matrix of the network. To solve the model, a Benders decomposition approach is proposed. Without the Benders decomposition approach, only instances with up to ten nodes were solved within a reasonable time, but with the Benders decomposition approach, instances with up to forty nodes were solved. A heuristic algorithm is developed to have a mechanism for dealing with larger instances. A set of experiments are conducted using data from the Turkish Network dataset to study various aspects of the proposed formulation and different parameters’ effects on the performance of the model. Full article

Aiming at the disrupted flight recovery problem, this paper established a mixed-integer programming model based on the resource assignment model to minimize the recovery cost. To deal with the large-scale examples, the Logic-Based Benders decomposition algorithm is designed to divide the problem into a master problem and sub-problems. The algorithm uses MIP in the master problem to determine flight cancellations and aircraft replacements. In the sub-problems, MIP or CP is used to determine the departure time of delayed flights. Later, incorporating sectional constraints into the main problem and iterating until an optimal solution is obtained. Furthermore, the added cutting plane constraint in the iterations of the Benders decomposition algorithm are strengthened to eliminate more inferior solutions. By comparing the results of CPLEX, the Logic-Based Benders decomposition algorithm, and the enhanced Benders decomposition algorithm, it is verified that the improved Benders decomposition algorithm can solve large-scale examples more efficiently with a faster time and fewer iterations. Full article