Search Results (765)

Maximizing the expected value of a concave and strictly increasing utility function defines a fundamental class of discrete optimization problems. Among them, coverage decision problems with diminishing marginal returns under uncertainty, typically modeled via a set-union operator, have been extensively studied. In the classical framework, an item becomes active once it is covered by at least one chosen meta-item. Motivated by increasing robustness requirements in applications such as automated systems, social networks, and emergency response planning, we extend this setting by introducing threshold-based activation. The resulting generalized problem can be formulated as a mixed-integer nonlinear programming problem, for which we further propose three exact algorithms. The first two methods linearize the utility function using submodular cuts (SC) and outer-approximation (OA) techniques, respectively, resulting in formulations that can be solved exactly by off-the-shelf mixed-integer linear programming solvers. The third method builds upon the OA framework and further employs Benders decomposition (BD) to project out the item-related variables, which enables superior performance on ultra-large-scale instances. Extensive computational experiments show that, compared with the SC and BD methods, the OA method exhibits a substantial speed advantage on instances with a size of around 40,000, which can be solved within 100 s. In contrast, for ultra-large-scale instances with more than 100,000 items, the BD method demonstrates superior computational efficiency. These results provide practical guidance for algorithmic strategy selection and further demonstrate the computational tractability of this broader class of utility maximization problems under threshold-based activation. Full article

This paper investigates the joint scheduling problem of battery electric bus fleets and plug-in charging infrastructure in an urban transit system. The operation of an electric bus network is inherently a multi-component system, where vehicle assignment, battery energy management, and charger capacity decisions interact and jointly determine system performance and cost efficiency. To capture these interdependencies, we propose a system-level integrated scheduling framework that simultaneously determines bus trip assignments, charging event timing and duration, and charger utilization plans. The problem is formulated as a continuous-time mixed-integer linear programming model that minimizes the total system cost, subject to operational feasibility, battery state-of-charge dynamics, and charger capacity constraints. To enhance computational tractability, a Lagrangian relaxation-based decomposition approach is developed, coupled with a linear programming-based diving heuristic. Computational experiments on benchmark instances demonstrate that the proposed framework produces high-quality system-level schedules with substantially reduced solution time compared with directly using a commercial solver. A real-world case study based on a large charging station in Beijing shows that the optimized joint schedules reduce the required fleet size from 22 to 13 buses and the number of chargers from five to two, leading to a 38.3% reduction in total system cost. These results highlight the effectiveness and practical value of the proposed approach for the planning and operation of urban electric bus transit systems. Full article

This paper presents a comprehensive power system transition-planning model positioned between conventional generation and transmission expansion planning (GTEP) formulations and broader macro-energy system (MES) tools. Existing planning models are typically unable to simultaneously represent detailed network constraints, adaptive long-term uncertainty, and a broad set of grid-enhancing transition technologies within a single tractable optimization framework; this work enables such integrated, scenario-based planning. The framework remains rooted in detailed electrical system modeling while expanding the decision space to include transition-relevant technologies: conventional and renewable generation, transmission, advanced flow-control devices, dynamic line rating, energy storage, and retrofit options, all within a long-term-planning model under uncertainty. The contribution is the integrated representation of these options and the modeling constructs required to capture their interactions, including expressions enabling concurrent investment decisions across FACTS, dynamic line rating, and transmission expansion; network-embedded modeling of series compensation devices; a battery degradation model that avoids exogenous degradation cost proxies; and a GIS-based zoning resolution methodology balancing spatial fidelity and computational tractability. The resulting formulation is a mixed-integer multi-stage stochastic program. Analytical value is demonstrated through a detailed small-scale example based on Alberta’s power system. To overcome the computationally prohibitive results encountered when scaling the formulation to a practical test case consistent with Alberta’s long-term power-system-planning practices, Stochastic Dual Dynamic Programming is employed in parallel. The resulting solution demonstrates the feasibility of a subclass of highly detailed, transition-oriented electrical system planning models that are otherwise intractable under monolithic workstation-based approaches. Full article

The electrification of long-haul freight transport introduces significant challenges in fleet planning, charging decisions, and reliability management under uncertainty. This study proposed a Stochastic Electric Freight Operations Planning Problem on Predefined Routes with Partial Recharging and Heterogeneous Fleets (SEFOP-PR-HF), to support corridor-based electric truck operations under uncertain demand. The model represents real-world interregional logistics, where vehicles operate on fixed long-haul routes and may perform partial recharging at fast-charging stations. Freight demand is modeled as a normally distributed random variable, and Chance-Constrained Programming (CCP) is employed to ensure probabilistic feasibility of vehicle capacity and battery constraints. The objective is to minimize total long-term system cost, including fleet acquisition and charging expenditures, while maintaining operational reliability. A Mixed-Integer Linear Programming (MILP) formulation is applied for multiple corridor instances using real heavy-duty electric truck data. Computational results show that incorporating demand uncertainty improves robustness but raises total cost by 6–33% compared to deterministic solutions. Sensitivity analyses further reveal how reliability levels and demand variability influence fleet allocation and charging strategies. Full article

Static honeypot deployment and one-shot attack-path analysis often become ineffective against adaptive adversaries because fixed decoy layouts are easy to fingerprint and risk estimates quickly go stale. This paper presents a unified, mathematically grounded TrapManager framework that couples graph representation learning with budget-constrained combinatorial optimization for dynamic cyber deception. We model attacker progression on vulnerability-based attack graphs and learn context-aware node embeddings using a Graph Attention Network (GAT) that fuses vulnerability-driven risk signals (e.g., CVSS-derived node scores) with structural features. The learned representations are used to estimate edge plausibility and rank candidate source–target routes at the path level. Given limited resources, we formulate pointTrap placement as a Mixed-Integer Programming (MIP) problem that maximizes the expected interception of high-risk paths while penalizing deployment cost under explicit budget constraints, including mandatory coverage of the top-ranked critical paths. To enable online adaptiveness, a pointTrap-triggered, event-driven feedback mechanism locally amplifies risk around alerted regions, updates path weights without retraining the GAT, and re-solves the MIP for rapid redeployment. Experiments on MulVAL-generated benchmark attack graphs and cross-domain transfer settings demonstrate fast convergence, strong discrimination between attack and non-attack edges, and early interception within a small number of hops even with minimal decoy budgets. Overall, the proposed framework provides a scalable and resource-efficient approach to closed-loop attack-path defense by integrating attention-based learning and integer optimization. Full article

Electric vehicles have strengthened the coupling between transportation systems and power distribution networks, giving rise to new challenges in the coordinated management of traffic flow and charging demand. Monetary incentives, such as tariffs and subsidies, have been widely adopted to influence drivers’ route and charging decisions and to improve system-level performance. This paper proposes a user-centric incentive framework in which a system operator allocates rewards to guide drivers’ behavior, thereby enabling coordinated operation of power–traffic networks. A reward scheme is developed to provide joint subscription-based and path-based incentives that account for drivers’ behavioral responses through a logit choice model for scheme adoption embedded within a traffic assignment model. The resulting interaction is formulated as a bilevel optimization problem, in which a coupled power–traffic system operator determines incentive schemes to achieve system optimality within a given budget constraint, while individual drivers respond by selecting routes and charging strategies to minimize their perceived travel costs. A single-level Karush–Kuhn–Tucker (KKT) reformulation is developed, and linearization techniques are employed to compute the resulting equilibrium, yielding a tractable mixed-integer second-order cone program (MISOCP). Numerical experiments demonstrate the effectiveness of the subscription-based and path-based reward schemes in improving network performance and budget saving. Full article

Renewable energy sources (RESs) play a key role in the global energy transition by reducing carbon emissions, enhancing energy security, and supporting sustainable development. This study presents a fairness-oriented energy management strategy for residential communities integrated with hydrogen-based technologies. The proposed system comprises photovoltaics (PV), a wind turbine (WT), an energy storage system (ESS), an electrolyzer (EL), a hydrogen tank, and bidirectional grid interaction. For the first time, four fairness indices are introduced to ensure the equitable utilization of renewable generation, stored hydrogen, and ESS among households. The problem was formulated as a mixed-integer linear programming (MILP) model to minimize operating costs. A case study conducted for a residential area in Lüleburgaz, Kırklareli assessed system performance in terms of cost, grid consumption, and carbon emissions. The results demonstrate that the proposed framework reduced grid consumption by 32.25% and carbon emissions by 31.82%. Moreover, increasing renewable capacity by 2.5 times reduced costs by 81,253.16 TL and yielded a profit of 70,107.39 TL, while a similar expansion of ESS capacity enabled 100% green energy accessibility for all households. Full article

Background: Agricultural logistics in arid, geographically dispersed areas require complex trade-offs among efficiency, equity, and robustness under uncertainty. Standard multi-objective vehicle routing problem (VRP) formulations, which primarily focus on cost or environmental parameters, do not explicitly account for social equity or transparency in decision-making. However, existing work seldom combines the objective of social equity as an endogenous optimization objective with robustness and interpretability within a unified mathematical framework. Methods: In this paper, we present a systems engineering decision-support framework informed by a multi-objective mixed-integer linear programming formulation for agricultural logistics planning. Economic, environmental, operational, and social equity goals are combined through ε-constraint to create trade-offs that can be interpreted at the policy level. We assess robustness against demand and travel-time uncertainty using the Bertsimas–Sim framework. A staged activation strategy separates conceptual model completeness from numerical implementation, and sensitivity analyses are conducted by perturbing vital operational parameters. Results: An illustrative situation in Northern Chile shows that this framework produces stable decision regimes and clear trade-offs in practice. The results show that meaningful improvements in workload balance and service equity can be achieved with negligible changes in operational efficiency. As we have learned in sensitivity experiments, assignment structures and qualitative trade-off patterns are robust under realistic parameter variations, and structural changes occur only beyond known threshold regimes. Conclusions: The major contribution of this work is the formulation of a systems engineering framework that extends traditional multi-objective VRP formulations and integrates social equity, robustness, and decision transparency as core design principles. Instead of focusing only on numerical optimization performance, the framework encourages auditable planning decisions in the face of uncertainty. The numerical analysis results are for a proof-of-concept scale only; however, the framework can be extended to larger agricultural networks using decomposition and/or hybrid solutions. Full article

This paper addresses the Pickup and Delivery Problem with Time Windows (PDPTW), an NP-hard combinatorial optimization problem with major practical relevance in logistics and transportation. The study focuses on a quadratic unconstrained binary optimization (QUBO) formulation for quantum annealing and benchmarks it against two classical optimization paradigms. A modular Python framework is developed that encodes PDPTW in three ways: a mixed-integer linear programming (MILP) model that serves as an exact reference, a genetic algorithm (GA) metaheuristic, and a QUBO model that is compatible with quantum annealers. The framework supports test scenarios with increasing structural complexity, with both feasible and intentionally infeasible instances. An additional contribution is the conceptual design and preliminary analysis of an automatic-penalty weight-tuning scheme for the QUBO model. Experimental results show that the proposed QUBO formulation can produce high-quality solutions for simpler PDPTW instances, but its performance strongly depends on the careful calibration of penalty weights. MILP provides optimal baselines on small instances but becomes intractable as problem size grows. The GA scales to the largest scenario and finds feasible solutions of reasonable quality, but they are not necessarily optimal. The evaluation also includes a large number of problem instances and runs on IBM Quantum hardware using the Quantum Approximate Optimization Algorithm (QAOA). Full article

This study proposes an integrated decision-support framework that combines robust multi-objective optimization and discrete-event simulation to enhance sustainability and resilience in automotive supply chain management. Automotive supply chains are highly complex and exposed to significant uncertainty arising from demand fluctuations, supply disruptions, and procurement constraints, particularly in emerging economies. To address these challenges, the proposed framework incorporates mixed-integer programming with a multi-objective formulation to balance production, supply, holding, and penalty costs. Additionally, robust optimization based on the Bertsimas–Sim approach is employed to hedge against demand uncertainty. Additionally, a discrete-event simulation model is developed to validate and refine the optimization results under stochastic operating conditions, and to assess the practical performance of the proposed strategies. The framework is applied to a real-world automotive case study, where flexible production policies, including fractional production and urgent procurement, are evaluated in terms of their economic and social sustainability impacts. The results demonstrate that integrating robust optimization with simulation improves supply chain resilience, reduces vulnerability to uncertainty, and supports more sustainable operational decision-making. The proposed approach provides valuable insights for managers seeking to design resilient and sustainable automotive supply chains under uncertain environments. Full article

Background: The rapid growth of e-commerce has intensified the need for last-mile delivery systems that can navigate urban congestion while minimizing environmental impact. Hybrid truck–drone networks offer a promising solution by combining heavy-duty ground transport with aerial flexibility; however, their deployment faces significant challenges in jointly managing operational risks, energy limits, and regulatory compliance. Methods: This study proposes a hybrid matheuristic framework to solve this multi-objective problem, simultaneously minimizing transportation cost, service time, energy consumption, and operational risk. A two-phase approach combines a metaheuristic for initial truck routing with a Mixed-Integer Linear Programming (MILP) formulation for optimal drone assignment and scheduling. This decomposition strikes a balance between exact optimization and computational scalability. Results: Experiments across various instance sizes (up to 100 customers) and fleet configurations demonstrate that integrating MILP enhances solution diversity and convergence compared to standalone strategies. Sensitivity analyses reveal significant impacts of drone speed and endurance on system efficiency. Conclusions: The proposed framework provides a practical decision-support tool for balancing complex trade-offs in time-sensitive, risk-constrained delivery environments, thereby contributing to more informed urban logistics planning. Full article

This paper presents an optimization-based method to support distribution system operators (DSOs) in planning large-scale photovoltaic (PV) integration at the medium-voltage (MV) level. The PV hosting capacity (PV-HC) problem is formulated as a mixed-integer quadratically constrained program (MIQCP) without linearizing approximations to determine PV sizes and locations while enforcing operating limits and planning constraints, including candidate PV locations, per-unit PV capacity limits, active power exchange with the upstream grid, and PV power factor. Our method defines two HC solution classes: (i) sparse solutions, which allocate the PV capacity to a limited subset of candidate nodes, and (ii) non-sparse solutions, which are derived from locational hosting capacity (LHC) computations at all candidate nodes, and are then aggregated into conservative zonal HC values. The approach is implemented in a Hosting Capacity–Distribution Planning Tool (HC-DPT) composed of a Python–AMPL optimization environment and a Python–OpenDSS probabilistic evaluation environment. The worst-case operating conditions are obtained from probabilistic models of demand and solar irradiance, and Monte Carlo simulations quantify the performance under uncertainty over a representative daily window. To support integrated assessment, the index $G_{\exp }$ is introduced to jointly evaluate exported energy and changes in local distribution losses, enabling a system-level interpretation beyond loss variations alone. A strategy was also proposed to derive worst-case scenarios from zonal HC solutions to bound performance metrics across multiple PV integration schemes. Results from a real MV case study show that PV location policies, export constraints, and zonal HC definitions drive differences in losses, exported energy, and solution quality while maintaining computation times compatible with DSO planning workflows. Full article

To promptly address the disruptions caused by various sudden weather events to the normal operations of the quay apron, this study focuses on the optimization of integrated berth and quay crane (QC) scheduling under the impact of adverse weather. It emphasizes two key influences of adverse weather: port closures and the uncertainty in vessel handling times induced by weather conditions. A decision mechanism is designed, and strategies such as vessel dispatch, cargo omission, and backhaul are incorporated. Meanwhile, constraints including the prohibition of QC crossover and the spatio-temporal limitations on vessel berthing are taken into account. With the optimization objective of minimizing the total scheduling cost, a mixed-integer programming (MIP) model is constructed. A variable neighborhood search (VNS) algorithm is developed for solving the model, which proposes multi-layer encoding and a corresponding hybrid initialization strategy. Finally, comparative experiments are conducted to verify the effectiveness of the model and the rationality of the algorithm. Sensitivity analysis is also performed on the duration of port closures and QC handling efficiency. The research results can provide decision support for ports in formulating response strategies against adverse weather. Full article

The exponential growth of the digital economy has transformed data centers into major energy consumers, yet their inflexible power consumption patterns and substantial waste heat generation pose significant challenges to grid stability and carbon neutrality targets. Existing energy management strategies often overlook the deep coupling potential between computing workload flexibility, thermal dynamics, and carbon trading mechanisms, leading to suboptimal resource utilization. To address these issues, this study proposes a collaborative low-carbon economic scheduling strategy for data center microgrids. A multiple-dimensional coupling framework is established, integrating a queuing theory-based model for delay-tolerant workload shifting and a heat-determined computing mechanism for active waste heat recovery (WHR). Furthermore, a mixed-integer linear programming (MILP) model is formulated, incorporating a linearized tiered carbon trading mechanism to facilitate source–load coordination. Simulation results demonstrate that the proposed strategy achieves a dual optimization of economic and environmental benefits, reducing total operating costs by 11.7% while minimizing carbon emissions to 6879 kg compared to baseline scenarios. Additionally, by leveraging temperature aware load migration, the daily weighted power usage effectiveness (PUE) is optimized to 1.2607. These findings quantify the marginal benefits of load flexibility under tiered pricing, providing insights for operators to balance service timeliness and energy efficiency in next generation green computing infrastructure. Full article

The growing demand for sustainable energy alternatives highlights the need for decision support tools in biodiesel supply chains. This study proposes a mixed-integer programming (MIP) model for tactical planning in the palm oil biodiesel supply chain, focusing on refining, blending, and distribution. The model incorporates economies of scale, inventory, and transport constraints and is enhanced with valid inequalities (VI) and a warm-start heuristic procedure (WS) to improve computational efficiency. Computational experiments on simulated instances with up to 6273 variables and 47 million iterations demonstrated robust performance, achieving solutions within 15 min. The model also reduced time-to-first-feasible (TTFF) solutions by 60–75% and CPU times by 17–21% compared to the baseline, confirming its applicability in realistic contexts. The proposed model provides actionable insights for managers by supporting decisions on facility scaling, product allocation, and profitability under supply–demand constraints. Beyond palm oil biodiesel, the formulation and its VI + WS enhancement provide a transferable blueprint for tactical planning in other process industry and renewable energy supply chains, where (i) multi-echelon flow conservation holds and (ii) discrete operating scales couple throughput with fixed/variable cost structures, enabling fast scenario analyses under changing prices, demand, and capacities. Full article