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

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.

Genomic fingerprint of polyethylene-degrading bacteria.

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

To elucidate the geographical distribution patterns and hotspots of medicinal gymnosperms in China, providing a scientific basis for formulating conservation strategies for this group, we compiled 17,999 occurrence records for 148 medicinal gymnosperm species native to China. Species were categorized into all, endemic, threatened, and nationally key protected medicinal gymnosperms groups. Distributions were analyzed across 943,100 × 100 km grid cells. Priority conservation areas were identified using an optimal algorithm based on an integer linear programming set-cover formulation, which minimizes grids required to represent all species at least once, and compared with the Dobson algorithm. Conservation gaps were assessed by overlaying priority grids with national nature reserves and national parks. Medicinal gymnosperms showed a "more in the south, less in the north" distribution pattern, concentrated in mountainous areas and provincial borders. The distribution hotspots for all and endemic medicinal gymnosperms were in the Hengduan Mountains, while that for threatened and nationally key protected medicinal gymnosperms was in areas such as northern Guangxi. The optimal algorithm identified 41 priority conservation grids, mainly in areas like the border between Guizhou and Guangxi, outperforming the Dobson algorithm (which required 14% more grids on average). Overlay analysis revealed eight conservation gap grids, including high-priority areas in the Hengduan Mountains. Current national reserves inadequately protect medicinal gymnosperms. Targeted conservation measures are needed based on identified gaps in this study. The optimal algorithm provides a resource-efficient conservation tool. However, several limitations should be acknowledged. The use of 100 km grid cells, derived largely from county-level records, may overestimate species' distribution areas and mask fine-scale patterns. Uneven collection may also introduce spatial sampling biases. In addition, our analysis only considered national reserves, potentially overlooking local initiatives. Future work should incorporate higher-resolution distribution data and sub-national conservation designations to refine priority assessments.

ABSTRACT In this paper, the index of a family of critical points of the systole function on Teichmüller space is calculated. The members of this family are interesting in that their existence implies the existence of strata in the Thurston spine for which the systoles do not determine a basis for the homology of the surface. Previously, index calculations of critical points with this pathological feature were impossible, because the only known examples were in surfaces with huge genus. A related concept is that of a “minimal filling subset” of the systoles at the critical point. Such minimal filling sets are studied, as they relate to the dimension of the Thurston spine near the critical point. We find an example of a minimal filling set of simple closed geodesics in genus 5 with cardinality 8, that are presumably realized as systoles. More generally, we determine the smallest and largest cardinality of a minimal filling set related to a tessellation of a hyperbolic surface by regular, right-angled m -gons for m ∈ { 5 , 6 , 7 } . For this, we use integer linear programming together with a hand-tailored symmetry breaking technique.

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.

Mapping cells to spatial locations is crucial for understanding biological processes, disease mechanisms, and therapeutic strategies. However, dropout events in both spatial transcriptomics and scRNA-seq data, along with intercellular interactions and spatial dependencies among spots, challenge the accuracy of spatial mapping. This study proposes a novel method termed Spatial Mapping of single cells via Correlation and Importance between cells and spots (SM-CI). We introduce dropout handling strategies specifically designed for both spatial transcriptomics and scRNA-seq data. Imputation index sets and dropout imputation functions tailored to each data type are developed: the first effectively utilizes spatial location and gene expression information, while the second leverages data from neighboring cell types. Furthermore, we establish criteria for assessing the importance of spots (or cells) in relation to others and construct a linear programming model that integrates these criteria with correlation measures to enhance spatial mapping accuracy. Benchmarking on simulated datasets shows that SM-CI consistently outperforms existing methods across four metrics, while applications to real datasets demonstrate its effectiveness in reconstructing spatial distributions of diverse cell types across tissues. Additionally, ablation experiments validate the effectiveness of the dropout handling strategies and importance assessment criteria.

As global shipping expands, Automated Container Terminals (ACTs) are vital for port competitiveness. However, modern three-stage yard layouts often suffer from spatio-temporal conflicts between dual yard cranes during relay operations, while uncoordinated container placement causes localized overloads and safety hazards. To address these issues, this study proposes a multi-objective mixed-integer linear programming (MILP) model integrating three-stage operations with spatio-temporal mutual exclusion constraints. The model minimizes makespan, external truck waiting time, and inventory disparities across landside bays. To solve this NP-hard problem, an Improved Octopus Optimization Algorithm (IOOA) is developed, featuring discrete space mapping, Euclidean-based state determination, integer flight steps, and local fine-tuning. Numerical experiments demonstrate that this approach significantly reduces the total makespan and truck waiting times while ensuring a highly uniform container distribution across bays. Ultimately, this study mitigates safety risks associated with space overloads and isolated stack collapses, providing a robust decision-making framework to enhance the efficiency and safety of next-generation ACTs.

Wireless sensor networks (WSNs) are the backbone of IoT-enabled smart manufacturing, environmental monitoring, and industrial automation. However, their broadcast nature makes communication links vulnerable to eavesdropping, routing manipulation, and denial-of-service attacks. Strategically placing monitor nodes to check each link is an effective approach to protect against attacks, but energy, connectivity, and capacity constraints should be considered while picking monitor nodes. In this paper, we tackle the Minimum-Weighted Connected Capacitated Vertex Cover (MWCCVC) problem, which minimizes monitoring costs, ensures backbone connectivity, and adheres to per-node capacity constraints. Unlike prior works that consider weighted vertex cover, connectivity constraints, or capacitated variants separately, the proposed MWCCVC model jointly integrates all three dimensions within a single vertex cover-based monitoring framework. We first provide a Branch-and-Bound (B&B) solver with linear programming relaxation bounds and constraint-based pruning strategies that produces optimum solutions. Three constructive greedy heuristics (GD, GR, GW) and two hybrid genetic algorithms (HGA, HGA-v2) that combine parameterized greedy decoders with evolutionary search are proposed; all methods guarantee full edge coverage, induced-subgraph connectivity, and max-flow-validated capacity feasibility. Tests on 130 small, 160 medium, and 19 large benchmark instances show that HGA matches B&B optima on every small instance, beats the time-limited B&B by 6.6% on medium instances, where the percentage is computed based on the relative difference in average total weight with respect to B&B, and stays the best on large graphs with up to 1000 nodes. The HGA-v2 tries to balance the quality and speed, with only a 3.1% difference at faster execution.

Subject to the risk of disruptions in high-speed rail (HSR) logistics networks caused by natural disasters or equipment failures, this study proposes an emergency scheduling optimization framework based on truck transshipment. By establishing a Mixed-Integer Linear Programming (MILP) model that integrates vehicle deployment point selection, route planning, and timeliness constraints, it achieves, for the first time, multi-level collaborative decision-making covering "vehicle deployment point selection - truck scheduling - goods transshipment" following an HSR logistics disruption. An Adaptive Large Neighborhood Search (ALNS) algorithm is designed, incorporating a dynamic strategy combining destroy operators (random/worst/Shaw/depot consolidation removal) and repair operators (greedy/regret-2/regret-3 insertion) to generate high-quality scheduling schemes. Using both the Zhengzhou-Qingdao Express Rail Line disruption case and multi-scale random instances, the model's effectiveness is validated: ALNS achieves solution quality comparable to CPLEX with a maximum gap of only 0.037% while substantially reducing computation time, and significantly outperforms GA in both solution quality and efficiency.

NashOpt is an open-source Python library for computing and designing generalized Nash equilibria (GNEs) in noncooperative games with shared constraints and real-valued decision variables. The library exploits the joint Karush–Kuhn–Tucker (KKT) conditions of all players to handle both general nonlinear GNEs and linear-quadratic games, including their variational versions. Nonlinear games are solved via nonlinear least-squares formulations, relying on JAX for automatic differentiation. Linear-quadratic GNEs are reformulated as mixed-integer linear programs, enabling efficient computation of multiple equilibria. The framework also supports inverse-game and Stackelberg game-design problems. The capabilities of NashOpt are demonstrated through several examples, including noncooperative game-theoretic control problems of linear quadratic regulation and model predictive control. The library is available at https://github.com/bemporad/nashopt.

Increasing load demand and localized constraints are driving the need for cost-effective alternatives to traditional network reinforcement. However, existing Non-Wires Alternative (NWA) planning approaches often rely on simplified assumptions or computationally intensive full-year optimization, limiting their practical applicability. This study proposes a planning-oriented method integrating 8760-h Direct Load Flow (DLF)-based assessment, worst-case screening, and Mixed-Integer Linear Programming (MILP)-based resource sizing for the coordinated deployment of Energy Storage Systems (ESSs), Demand Response (DR), and Photovoltaic (PV) resources, along with building-scale microgrid candidates. The proposed microgrid candidates are modeled as grid-connected, building-scale configurations in which PV, ESSs, and DR are co-located at a single node, representing integrated resource units within the distribution system. The results show that voltage constraints are the dominant limiting factor and that NWAs primarily function as an investment deferral strategy rather than a full replacement for traditional reinforcement, delaying constraint violations by approximately 2 to 14 years. An ESS provides the most direct contribution to constraint mitigation, while DR and PV offer complementary support. The results also highlight the importance of locational deployment. In particular, a co-located microgrid configuration (MG_111) is selected as the optimal portfolio under moderate load growth conditions (Case B, 2%), demonstrating the practical feasibility of integrated DER deployment at a single node. Economic feasibility is found to be highly sensitive to incentive design, with profitability achieved only under favorable compensation conditions. These results demonstrate that coordinated DER portfolios can effectively extend deferral periods and provide practical insights into cost-effective NWA planning under realistic operating conditions.

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

Wireless mesh networks (WMNs) have emerged as a promising solution for resilient, scalable, cost-effective broadband connectivity in scenarios such as disaster recovery, smart cities and rural deployments. However, inherent characteristics like dynamic topology, interference, limited spectrum availability, and heterogeneous Quality of Service (QoS) demands create design challenges with tradeoffs between conflicting performance goals. These interdependencies make Multi-objective Optimization (MOO) a critical approach in WMN research, enabling simultaneous consideration of multiple objectives, including maximizing throughput, minimizing latency, reducing energy consumption and improving fairness. The objective of this survey is to systematically review, classify and analyze MOO techniques for WMNs, identify research trends and underexplored areas and highlight potential directions for future work. We categorize existing approaches into Integer Linear Programming (ILP), heuristic, metaheuristic, evolutionary, learning-based, and hybrid algorithms. Our analysis of sixteen design aspects shows heuristic methods are most applied (32%), followed by metaheuristic (26%), hybrid (21%), evolutionary (11%), learning-based (8%) and ILP (2%). Throughput-centric optimization dominates (44%), while security, mobility, and power control remain underexplored (<5%). We also identify gaps in multi-objective interdependencies, with previous studies covering only 24.22% of potential relationships studied. Our findings advocate integrated optimization of mobility-aware routing and cross-layer security to enhance scalability and robustness of next-generation WMNs.

The current pattern of food production and consumption in the world has put great pressure on the environment, so a shift towards sustainable diets seems more urgent than ever. Within this context, organizations such as hospitals offer valuable opportunities to promote sustainable eating practices. The aim of the present study is to design a menu that minimizes environmental impact and cost, while simultaneously maximizing nutrient-rich food (NRF). A two-phase linear optimization was conducted at Imam Reza Hospital, Mashhad, Iran, combining linear and goal programming to optimize the quantities of each food. In this regard, data on recipes, quantities, and prices were collected over a 461-day period in the hospital canteen. For each meal, NRF, water footprint, carbon footprint, and cost were calculated. Four different scenarios were developed, and the best scenario was used to design one-year meal plans that meet macronutrient targets for protein, fat, and carbohydrates, and maintain dietary variety. The optimized menu attained a 36% reduction in carbon footprint and a 42% reduction in water footprint, while enhancing NRF by 10% and reducing cost by 42% in comparison with the prevailing menu. The mean percentage change in fat and carbohydrates from the obtained menu was -7.5% and 6%, respectively, which ensured the mean percentage change in all macronutrient levels aligns with recommended guidelines. The results of this study showed that healthier menus can be designed with a smaller environmental footprint, while maintaining or even significantly reducing costs.

ABSTRACT Cost optimization in manufacturing has become a critical management imperative, particularly in the rapidly evolving Electric Vehicle (EV) sector. Rising operational costs, supply chain volatility, and intense market competition necessitate systematic, data-driven approaches to resource allocation and production planning. This study applies Linear Programming (LP) techniques to develop a comprehensive cost optimization model for Vaagn Auto Pvt. Ltd., a Chengalpattu-based EV manufacturer specializing in electric three-wheelers. The model incorporates key cost components raw materials, labour, machine utilization, and component costs—and is solved using LINGO optimization software. Multiple LP formulations are developed to address profit maximization, total production cost minimization, labour cost reduction, machine cost efficiency, and overall production cost optimization. Results demonstrate that the TITAN CARGO OPEN (X₇) with a unit cost of ₹218,000 dominates cost- minimization strategies, while BEAST LX CLOSED (X₄) leads profit-maximization scenarios with ₹45,000 profit per unit. The findings confirm that LP is a reliable, practical tool for production planning and cost control in EV manufacturing environments, with the potential to significantly reduce wastage, improve resource utilization, and enhance organizational profitability. Keywords: Cost Optimization, Linear Programming, Electric Vehicles, Resource Allocation, Production Planning, LINGO, EV Manufacturing

Flood disasters often disrupt road networks and severely reduce ground accessibility, hindering the timely delivery of emergency supplies. To address this challenge, this study investigates a collaborative routing problem involving multiple vehicles and multiple UAVs under road disruptions and formulates a mixed-integer linear programming model that jointly minimizes mission makespan and priority-weighted response time for critical nodes. The model explicitly captures road feasibility, vehicle speeds affected by flood depth, multi-point UAV sorties, payload-dependent energy consumption, and vehicle–UAV spatiotemporal synchronization. To balance solution quality and scalability, a dual-track solution framework is developed: exact optimization is used for small instances, while a adaptive large neighborhood search algorithm with embedded dynamic programming is designed for larger instances. A case study based on the 2024 Guangdong flood with 135 demand points shows that the heuristic can obtain high-quality solutions efficiently and outperforms time-limited MILP solutions on large instances. Comparative experiments further demonstrate that multi-point sorties, integrated coordination, and embedded sortie refinement are all crucial to performance improvement. Sensitivity analysis indicates that setting the trade-off coefficient α within 0.2–0.8 provides a robust balance between overall mission efficiency and timely response to critical nodes.

The routing-and-driving problem for plug-in hybrid electric vehicles (PHEVs) is an extension of the vehicle routing problem with time windows, where routing involves determining optimal routes and recharging decisions for a fleet of PHEVs, whereas driving involves choosing the speed and operating mode on each road segment traveled by a vehicle. Specifically, four driving modes are considered: fuel only, electricity only, a combination of fuel and electricity, and energy recuperation, which returns energy to the battery. We consider two variants of the problem where the speed variables are either continuous, which results in a nonlinear model, or discrete, which represents the case when speeds are chosen from a predetermined set. To solve these two models, we propose a set of valid inequalities to strengthen the continuous linear programming relaxation, and we use a tailored branch-and-cut algorithm. Extensive computational experiments demonstrate the efficiency of the proposed solution methods, which can optimally solve instances with a realistic number of customers and recharging stations. In addition, we show that incorporating speed optimization can significantly reduce the energy consumption costs of a PHEV fleet compared with using fixed speeds. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by the GuangDong Basic and Applied Basic Research Foundation [Grant 2026A1515030009]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.1016 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.1016 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Post-optimality analysis in linear programming is done through either the stability of the optimal solution (discrete decision variables) or the stability of a given optimal basis with respect to perturbations of the input data (continuous decision variables). Both approaches have been well studied in the literature. In this article, a post-optimality analysis technique is presented that is more general than the tolerance approach and less computationally expensive. Namely, this article extends the notion of local quasi-stability radii in order to allow perturbations into the input data. The present result is applied to ore production problems. As the input data might be of different magnitude, the advantage of this extension is to incorporate information provided by the decision maker into the computation of the local quasi-stability radii. Then, better individual tolerances of the input data of linear multi-objective optimization problems are obtained. The extension is based on the introduction of weighted norms in the formulation of the post-optimality analysis. The weighted norms account for the information provided by the decision maker.