Convex hull pricing (CHP) is a pivotal approach to enhance market transparency by minimizing uplift costs. This pa per revisits the mathematical foundation of CHP and provides an explicit formulation of the Lagrangian dual formulation for network-constrained unit commitment (NCUC), further defining the CHP. Here, a convex hull model for single-unit commitment (1UC) problems is established with ramping constraints and minimum on/off time, making this explicit formulation implementable and further delivering the optimal Lagrangian dual solution via two linear programming (LP) models. The first LP reformulates the NCUC by replacing mixed-integer constraints with convex hull relaxations, while the second, obtained by fixing the inner variables in the Lagrangian dual problem of the NCUC to their optimal val ues from the first LP, generates the optimal Lagrangian dual solution. Numerical experiments on the IEEE-118 and Polish-2383 sys tems validate the superiority of CHP in reducing uplift costs and of this proposed pricing method in computational efficiency.

Inverse of the Gomory corner relaxation of integer programs

Spatial optimization of the sustainable aviation fuel supply chains from forest residues via fast pyrolysis/hydrotreatment considering feedstock ash content variability

This paper proposes a customer-focused resilience enhancement planning framework in power distribution systems considering a leader-follower approach under appropriate regulatory mechanisms. The regulator, distribution system operator (DSO), and customers are the key players in this framework, implemented through a three-step process. Firstly, the regulator establishes a penalty-reward model (PRM). Subsequently, the revenue-cap regulation is applied, and finally, customers' participation is incorporated through a leader-follower approach, modeled using a bi-level optimization problem. This approach considers the individual objectives of the DSO (as the leader) and interested customers to invest in self-generation (as followers), reflecting the accuracy, realism, and practicality of this framework since each entity looks for optimizing its own objective. Furthermore, the incentives provided by the DSO for customers' participation are directly modeled into the objectives of both the leader and followers. The proposed stochastic bi-level optimization problem, which takes the form of a mixed-integer linear programming (MILP) model, is solved using a reformulation and decomposition technique based on the column-and-constraint generation. Deploying the IEEE 33-bus test system exposed to a hurricane, the capability of the proposed framework is validated in enhancing the energy supply resilience under the regulatory objectives while achieving economic benefits for all involved entities.

High self-adaptive task offloading framework in vehicular fog networks: A hybrid approach leveraging case-based reasoning and integer linear programming

Efficiently allocating resources to enable flights to land and take-off at an airport is a heavily constrained problem. Airlines request to use slots , where permission is granted to use airport infrastructure, which are allocated within the limits of the capacity of an airport. As demand for slots often significantly exceeds supply, this can lead to airlines being allocated undesirable slots that do not align with their intended operations. This issue is exacerbated when schedules are created independently at different airports across a network, as undesirable allocations may result in infeasible airline operations. This paper introduces a novel integer linear program (ILP) formulation for the network slot allocation problem, incorporating rejected requests, flight time flexibility and seasonality. We investigate solving the network-level slot allocation problem simultaneously across a network, compared to allocating slots at each airport independently. Our results show that scheduling over the network simultaneously ensures the feasibility of operational constraints that are not met when each airport is scheduled independently. Additionally, a matheuristic destroy-and-repair approach is developed to schedule flights over a network of ten of the largest airports across Europe. The flight request data used is derived from the real-world operations at each airport. The proposed matheuristic approach leads to comparable solutions to an exact solver within significantly shorter run times, contributing new tools that can be deployed by schedulers for real-world scenarios within a reasonable computational time.

Optimizing interoperable hydrogen supply chain design: A case study in Auvergne-Rhône-Alpes

An iterative MILP-based model for optimal V2G scheduling considering battery degradation and thermal dynamics

Coordinated vehicle platooning on tree networks: Efficient time discretization and strengthened formulation

Given a connected graph G , a set of vertices X ⊂ V ( G ) is a weak k -resolving set of G if for each two vertices y , z ∈ V ( G ) , the sum of the values | d G ( y , x ) − d G ( z , x ) | over all x ∈ X is at least k , where d G ( u , v ) stands for the length of a shortest path between u and v . The cardinality of a smallest weak k -resolving set of G is the weak k -metric dimension of G , and is denoted by wdim k ( G ) . In this paper, wdim k ( K n □ K n ) is determined for every n ≥ 3 and every 2 ≤ k ≤ 2 n . An improvement of a known integer linear programming formulation for this problem is developed and implemented for the graphs K n □ K m . Conjectures regarding these general situations are posed.

Genomic fingerprint of polyethylene-degrading bacteria.

Reinforcement learning for residential energy storage management at the neighborhood scale: A multi-benchmark evaluation

Flexibility providers play a crucial role in balancing the rapidly changing supply and demand in power systems. However, coordinating these heterogeneous providers necessitates a thorough understanding of their diverse response delays, which complicates effective scheduling. To address these challenges, we propose a multi-period adaptive robust framework designed to optimize the scheduling of flexibility providers while accounting for their varied response times. Our framework incorporates updated demand information, allowing for timely adjustments to scheduling decisions and aiming to maximize the total revenue of the system operator. We employ a mixed- integer linear programming (MILP) approach, where decision variables represent different types of flexibility providers, categorized as either continuous or discrete. To balance computational efficiency, optimality, and scalability, we utilize a partition-and-bound method that iteratively refines partitions of the uncertain demand sets. Numerical studies validate the effectiveness of our algorithm and underscore the importance of characterizing heterogeneous response delays in adaptive scheduling.

• We proposed a novel NFV model that balances cost, workload, and resource use. • We modeled server reliability to guide VNF placement and reduce congestion. • We linearized the non-convex MINLP using dynamic programming for scalability. • We developed a cutting-plane heuristic to accelerate convergence. • We validated our approach on real topologies, outperforming baseline solutions. This paper introduces a novel optimization framework for Network Functions Virtualization (NFV) that addresses the efficient implementation of end-to-end service requests in physical networks. Our approach characterizes each server node by a reliability function reflecting its computational load, which aids in balancing workloads and mitigating congestion. By optimizing the reliability metric along the route, our approach ensures robust end-to-end service quality. We formulate the NFV deployment problem as a non-convex mixed-integer non-linear programming (MINLP) model aimed at minimizing both deployment and operational costs while maximizing resource utilization, addressing also per-node installation conflicts and inter-VNF incompatibilies. Given the NP-hard nature of the problem, we develop efficient linearization techniques and bounding schemes, using also dynamic programming, to convert the formulation into a tractable mixed-integer linear programming (MILP) model. Additionally, a cutting-plane-based heuristic with a warm-start strategy is proposed to further accelerate convergence. Experimental evaluations on real-world network topologies demonstrate that our framework offers scalable and cost-effective solutions compared to existing approaches.

Unmanned Aerial Vehicles (UAVs) are widely used in modern military missions, primarily for surveillance, reconnaissance, search and detection, and air-to-ground strikes. The widespread use of UAVs in recent conflicts, such as the Russia-Ukraine war, once again highlighted their growing strategic importance. The complexity of military missions carried out by UAVs, coupled with the need for autonomous and coordinated fleet operations, requires analytical approaches to optimize deployment planning and improve operational efficiency. In this study, we address a UAV deployment planning problem for search and detection missions, in which a homogeneous fleet of UAVs is tasked with searching for hostile assets across a network of disjoint regions. Each region is characterized by an a priori probability of target presence, a search difficulty factor which affects the probability of detection, and known inter-region distances. For this purpose, we first develop a mixed-integer nonlinear programming formulation which determines the base locations of UAVs, allocates the limited search time across regions, and sequences the visits to maximize the total time-weighted detection probability mass to achieve the highest probability as much and as early as possible during the operation. Next, we apply a tangent line approximation technique to reformulate the model as a mixed-integer linear programming problem, which we solve using commercial off-the-shelf solvers. We then propose a hybrid heuristic approach based on the ant colony optimization method to generate high-quality solutions. Our computational experiments reveal that the proposed heuristic significantly reduces solution time while maintaining superior performance compared to the linear approximation model.

Emerging Internet of Things (IoT)-enabled cyber-physical applications, such as autonomous critical infrastructure inspection, demand low-latency, energy-efficient, and reliable execution across resource-constrained edge devices with heterogeneous multicore processors and diverse sensing and actuating capabilities, in collaboration with a hub device and a cloud server. These workflow-based applications comprise interdependent tasks that must be executed under stringent deadline, reliability, capability, memory, storage, and energy constraints. Given their critical nature, exact optimization is necessary to obtain optimal schedules that ensure dependable operation. Existing scheduling approaches, both exact and heuristic, fail to jointly address all these objectives and constraints. To this end, we propose an exact multi-objective and multi-constrained workflow scheduling approach for edge-hub-cloud cyber-physical systems, based on continuous-time mixed integer linear programming. The proposed formulation jointly optimizes latency, energy, and reliability, while holistically addressing timing and resource constraints. To enhance reliability while avoiding the overhead of unnecessary task replicas, it selectively employs task duplication. We evaluate our approach against a widely used heuristic, which we extend to ensure a fair and meaningful comparison, using a real-world IoT workflow and synthetic task graphs of varying sizes, across different system configurations and objective trade-offs. The proposed method consistently outperforms the heuristic, achieving up to 29.83%, 33.96%, and 28.49% average improvements in latency, energy, and reliability, respectively, while attaining practical runtimes. Overall, the experimental results demonstrate the effectiveness of our approach under various system configurations and objective trade-offs, and show its practical scalability to task graphs of sizes relevant to the targeted applications and system architecture.

Precast component (PC) production is a critical stage within the prefabricated construction supply chain. Motivated by a practical challenge observed in PC manufacturing, this study investigates an integrated PC production scheduling problem that concurrently addresses outsourcing decisions and multiskilled workforce constraints from the manufacturer’s perspective. This integration presents significant complexity, requiring the joint optimization of two interdependent subproblems: (1) determining the quantity of PC orders to outsource, and (2) scheduling self-produced orders across production lines while sequencing tasks under multiskilled workforce constraints. To address this challenge, a novel model is established to describe the decision-making problem and is then linearized as an integer linear programming (ILP), which is solvable by the off-the-shelf commercial optimizer for small-scale instances. For computationally intensive large-scale problems, an efficient Deep Q-network (DQN) algorithm is designed. The proposed methods are validated through extensive computational experiments based on a real-world PC production case, including comparative analysis against alternative methods and sensitivity analysis of key factors. Compared with the prevalent empirical approach, the proposed methods yield average monthly cost savings exceeding 31,000 Chinese yuan (CNY) across both shoulder and peak seasons. Furthermore, primary findings and managerial insights are derived from experimental results to assist managers in making decisions concerning outsourcing, self-production scheduling, and the flexible allocation of multiskilled employees.

• Introduces a unified MILP framework coupling electrical and thermal energy optimization. • Demonstrates synergy of bioenergy and battery storage in hybrid renewable systems. • Identifies key economic and policy levers for accelerating residential decarbonization. • Offers actionable insights for achieving resilient, low-carbon home energy transitions. • Enhances grid resilience and reduces reliance on unstable conventional energy networks. Residential energy analyses often optimize electricity and heat separately, masking their tight operational coupling and the cascading effects of technology choices across both domains. This study addresses that gap with a unified mixed-integer linear programming (MILP) framework that co-optimizes capacity sizing and hourly operation across photovoltaic panels and wind turbines (electric generation), geothermal and biogas systems (thermal generation), an air-source heat pump that couples power-to-heat conversion, and lithium-ion battery storage for a four-person dwelling. The model evaluates three policy scenarios designed to assess progressive decarbonization pathways: business-as-usual (BAU) to establish baseline performance, a 50% natural-gas capacity constraint aligned with European Union emission targets, and dual 70% constraints on gas capacity and CO 2 emissions addressing Iran’s energy challenges and ambitious net-zero commitments. Sensitivity analyses examine electricity price and carbon tax thresholds that drive technology transitions. Under BAU, gas-based technologies dominate, yielding 11.66 kg CO 2 daily emissions. Imposing a 50 % gas constraint electrifies heat via the heat pump, reduces emissions by 54 % to 5.4 kg CO 2 , and increases renewable penetration to 47 %. With dual 70 % constraints, renewables supply 95 % of total energy, grid imports decline by 73 %, and daily emissions fall to 0.93 kg CO 2 as battery cycling intensifies eight-fold. Battery storage mitigates short-term power variability, manages peak grid interactions, and enables load-shifting to periods of higher renewable availability, collectively enabling deeper decarbonization under stringent policy constraints. Economic sensitivity analyses reveal critical thresholds: renewables reach cost parity at €0.18 kWh −1 grid electricity prices, and 57 % renewable penetration occurs at €120 tCO 2 −1 carbon taxation. By optimizing electricity, heat, and storage within a single framework, this study identifies practical policy levers—moderate pricing reforms coupled with storage incentives—for economically viable, net-zero-ready residential energy systems.

This paper addresses the two-stage fixed-charge transportation problem with distribution-center (DC) opening costs.We propose adaptive random-key particle swarm optimization with DC-closure local search (ARK-PSO-CLS), a random-key particle swarm optimization (PSO) method with adaptive coefficient scheduling, stagnationtriggered partial restart, and a DC-closure local search, combined with a feasibility-preserving decoder.Experiments are conducted on 149 public benchmark instances from Mendeley Data (50 small, 50 medium, 49 large).For small instances, exact optima are obtained by mixed-integer linear programming (MILP) solved with HiGHS, enabling true optimality gaps; for medium and large instances, gaps are computed relative to the best value found within the compared set.Using swarm size N = 10 and T = 10 iterations, results show statistically significant improvements over greedy construction, random-key PSO (RK-PSO), and random-key genetic algorithm (RK-GA) baselines, while accounting for the additional evaluation cost of local search.Average ranks (lower is better) are 1.75 for ARK-PSO-CLS, 2.28 for RK-PSO, 2.78 for Greedy, and 3.19 for RK-GA.

Optimizing smart home energy management: a mixed integer linear programming model with digital twin and blockchain integration