How Hybrid Ant Colony Optimization Can Revolutionize Smart Waste Collection Routing

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Municipal solid waste management has become one of the most pressing operational challenges for rapidly growing cities. Among the various stages of waste management, collection and transportation account for the largest share of operational expenditure, often exceeding two-thirds of the total system cost. As urban populations expand and waste generation continues to increase, traditional route planning methods are becoming less capable of handling dynamic operational conditions, fluctuating waste volumes, and vehicle capacity constraints. These limitations create unnecessary travel, excessive fuel consumption, higher operational costs, and avoidable environmental impacts.

Optimization algorithms have therefore emerged as powerful decision-support tools for designing more efficient waste collection systems. Vehicle Routing Problems (VRP) have been widely studied for decades, yet real-world waste collection introduces additional complexities, including dynamic vehicle capacity, variable travel conditions, and route feasibility. This study proposes an improved hybrid optimization framework that combines Ant Colony Optimization with sequential neighborhood search strategies to address these practical challenges. The research offers valuable insights for engineers, operations researchers, municipal authorities, smart city planners, and logistics professionals seeking more intelligent approaches to sustainable waste collection.

Bibliographic Information

Item Information
Article Title A comparative study utilizing hybridized ant colony optimization algorithms for solving dynamic capacity of vehicle routing problems in waste collection system
Authors Thaeer Mueen Sahib, Rosmiwati Mohd-Mokhtar, and Azleena Mohd-Kassim
Journal Teknomekanik
Volume & Issue Volume 7, Issue 1
Publication Year 2024
Pages 38–61
DOI https://doi.org/10.24036/teknomekanik.v7i1.28872
Publisher Universitas Negeri Padang
License Creative Commons Attribution 4.0 International (CC BY 4.0)

1. Research Background

  • Municipal solid waste collection is the most expensive stage of waste management. Previous studies cited by the authors indicate that waste collection and transportation account for approximately 70% of the total municipal solid waste management cost. Consequently, even small improvements in routing efficiency can produce substantial economic savings while reducing fuel consumption and operational time.
  • Global waste generation continues to increase rapidly. Rapid urbanization, population growth, and changing consumption patterns have significantly increased municipal solid waste production worldwide. This trend places growing pressure on municipalities to operate collection systems more efficiently without proportionally increasing operational resources.
  • Traditional waste collection practices remain inefficient in many regions. Numerous municipalities, particularly in developing countries, continue to rely on manually planned collection routes or conventional routing strategies that cannot adequately respond to dynamic operational conditions. Such approaches often result in longer travel distances, unnecessary vehicle usage, higher transportation costs, and lower service efficiency.
  • Vehicle Routing Problems (VRP) provide an important optimization framework. Over the past several decades, Vehicle Routing Problems have become one of the most extensively studied optimization problems in operations research. Various extensions—including Capacitated Vehicle Routing Problem (CVRP), Arc Routing Problem (CARP), and Vehicle Routing Problem with Time Windows (VRPTW)—have been developed to model increasingly realistic transportation scenarios.
  • Dynamic vehicle capacity introduces additional complexity. Unlike conventional routing problems that assume fixed vehicle capacities, real waste collection operations continuously change vehicle loading conditions as collection progresses. These dynamic capacity changes directly influence route feasibility, travel cost, scheduling decisions, and fleet utilization, making optimization considerably more challenging.
  • Metaheuristic algorithms have shown strong potential. Nature-inspired optimization techniques such as Ant Colony Optimization (ACO) have demonstrated promising performance in solving complex combinatorial optimization problems. Their ability to explore large search spaces makes them attractive for routing applications where exact mathematical solutions become computationally expensive.
  • Conventional ACO still exhibits several weaknesses. Although Ant Colony Optimization is capable of generating competitive routing solutions, previous research has identified limitations related to slow convergence, premature convergence toward local optima, and limited exploitation capability. These shortcomings motivate the development of hybrid optimization strategies capable of improving solution quality while maintaining computational efficiency.
  • The literature reveals an important research gap. The comparative review conducted by the authors shows that previous waste collection studies rarely integrate dynamic vehicle capacity, route elimination strategies, adaptive neighborhood search, and hybridized Ant Colony Optimization within a single optimization framework. Existing approaches often focus on only one or two routing constraints, leaving opportunities for more comprehensive optimization methods.
  • This study proposes a hybrid optimization framework. To address the identified gap, the researchers develop a Hybridized Ant Colony Optimization (HACO) algorithm that combines conventional ACO with Sequential Variable Neighborhood Search Change Step (SVNSCS) and Sequential Variable Neighborhood Descent (SVND). The proposed framework aims to strengthen both exploration and exploitation capabilities while simultaneously reducing redundant routes and improving vehicle utilization under dynamic capacity constraints.

2. Research Objectives

  • To develop a systematic Hybridized Ant Colony Optimization (HACO) framework that improves the exploration and exploitation performance of conventional Ant Colony Optimization for dynamic waste collection routing.
  • To design a route optimization strategy capable of eliminating unnecessary sub-tours, thereby reducing the total number of collection routes and improving fleet utilization.
  • To incorporate dynamic vehicle capacity into the vehicle routing model by introducing a capacity threshold that better reflects practical waste collection operations.
  • To determine vehicle arrival times by considering average vehicle speed within the proposed optimization framework.
  • To formulate mathematical objective functions that simultaneously minimize travel distance, transportation cost, and travel time while maximizing waste collection efficiency.
  • To compare the optimization performance of the proposed HACO algorithm against the conventional Ant Colony Optimization algorithm using multiple benchmark datasets.
  • To evaluate the robustness and sensitivity of the proposed optimization framework under dynamic vehicle capacity conditions.

3. Why This Research Matters

  • Supports smarter municipal waste management. More efficient route planning can substantially reduce transportation costs, vehicle operating hours, and fuel consumption, enabling municipalities to deliver higher-quality public services with existing resources.
  • Advances intelligent transportation systems. The proposed hybrid optimization framework contributes to the growing field of intelligent logistics by demonstrating how multiple metaheuristic techniques can be integrated to solve complex routing problems more effectively.
  • Improves engineering decision-making. Engineers responsible for fleet planning and operational logistics can utilize hybrid optimization methods to generate routing solutions that better balance travel distance, vehicle utilization, and operational efficiency.
  • Promotes environmental sustainability. Shorter travel distances and fewer redundant collection routes reduce fuel consumption and greenhouse gas emissions, contributing to cleaner and more sustainable urban waste management systems.
  • Strengthens Smart City initiatives. Dynamic route optimization aligns closely with smart city concepts that integrate computational intelligence into public infrastructure, transportation management, and urban services.
  • Provides practical value beyond waste collection. Although developed for municipal solid waste management, the proposed hybrid optimization strategy has potential applications in other engineering domains involving capacitated routing, including parcel delivery, warehouse logistics, maintenance scheduling, healthcare transportation, and emergency response operations.
  • Encourages further research on hybrid metaheuristics. The study demonstrates that combining complementary optimization techniques can overcome weaknesses associated with individual algorithms, offering valuable guidance for future research in computational intelligence and engineering optimization.

4. Research Methodology

  • Research Type

    This study employed quantitative engineering research focusing on combinatorial optimization and computational intelligence. Rather than conducting laboratory experiments or field surveys, the researchers developed a mathematical optimization framework designed to improve municipal solid waste collection by solving a Dynamic Capacity Vehicle Routing Problem (DCVRP). The research combines mathematical modeling, metaheuristic optimization, and computational performance evaluation within a unified decision-support framework.

  • Optimization Problem

    The investigated problem belongs to the Dynamic Capacity Vehicle Routing Problem (DCVRP), an extension of the classical Capacitated Vehicle Routing Problem (CVRP). Unlike conventional routing models that assume fixed vehicle capacity, the proposed model considers dynamic changes in vehicle loading during waste collection. The optimization simultaneously considers travel distance, vehicle capacity thresholds, travel time, fleet utilization, and route feasibility throughout the collection process.

  • Mathematical Formulation

    The waste collection system was formulated as a graph optimization problem consisting of collection points, depot locations, connecting edges, travel distances, vehicle capacities, and waste quantities. Three binary decision variables were introduced to represent vehicle movements, vehicle availability, and collection assignments. Two objective functions were simultaneously formulated:

    • Minimize total travel distance, transportation cost, and travel time.
    • Maximize the quantity of waste collected while satisfying vehicle capacity constraints.

    A comprehensive set of routing constraints was incorporated to ensure feasible solutions, including depot departure and return, capacity limitations, vehicle availability, container servicing requirements, travel symmetry, and route continuity.

  • Hybrid Optimization Algorithm

    The core contribution of the study is the development of a Hybridized Ant Colony Optimization (HACO) algorithm. Instead of relying solely on the standard Ant Colony Optimization (ACO), the researchers integrated two sequential neighborhood improvement procedures:

    • Sequential Variable Neighborhood Search Change Step (SVNSCS)
    • Sequential Variable Neighborhood Descent (SVND)

    The hybridization was designed to improve both exploration and exploitation capabilities. While ACO effectively explores promising search regions, the sequential neighborhood search procedures refine intermediate solutions by escaping local optima and improving route quality.

  • Framework Architecture

    The proposed optimization framework consists of four interconnected stages:

    • Construction of the initial routing solution using Ant Colony Optimization.
    • Detection and elimination of redundant sub-tour routes.
    • Demployment and reconstruction of candidate solutions through sequential neighborhood search procedures.
    • Selection of the global best solution through iterative pheromone updating and solution evaluation.

    This iterative framework allows routing solutions to evolve progressively until convergence criteria are satisfied.

  • Initial Solution Construction

    Candidate routes were initially generated using the probabilistic search mechanism of Ant Colony Optimization. Vehicle movement decisions were guided by pheromone intensity and heuristic information derived from inter-container distances. A Tabu Search mechanism was incorporated during initialization to prevent repeated visits to identical collection points while improving route diversity.

  • Sub-tour Elimination Strategy

    One of the study's methodological innovations is a dedicated strategy for eliminating unnecessary sub-tours. Instead of accepting all generated routes, the algorithm identifies routes containing relatively small waste quantities and attempts to merge them with neighboring routes whenever vehicle capacity allows. This strategy reduces the total number of required vehicles while simultaneously improving fleet utilization.

  • Neighborhood Improvement Procedures

    Following initial solution construction, Sequential Variable Neighborhood Search Change Step (SVNSCS) explores neighboring routing configurations by systematically exchanging collection sequences among routes. Each candidate solution is evaluated against the mathematical objective functions before Sequential Variable Neighborhood Descent (SVND) performs further local refinement to identify higher-quality routing solutions.

  • Performance Evaluation

    The proposed HACO algorithm was evaluated using four internationally recognized benchmark datasets representing different waste collection scenarios. Performance was compared directly against the conventional Ant Colony Optimization algorithm by measuring solution quality, convergence behavior, routing efficiency, travel distance, and computational performance.

  • Validation Strategy

    Validation focused on comparative algorithm performance rather than statistical hypothesis testing. The proposed algorithm was compared with both the original ACO implementation and published Best Known Solutions (BKS). Additional sensitivity analyses investigated the influence of dynamic vehicle capacity thresholds on routing performance, enabling a comprehensive assessment of algorithm robustness under varying operational conditions.

5. Key Findings

Hybridized Ant Colony Optimization Consistently Outperformed Conventional ACO

The most significant outcome of this study is the superior performance of the proposed Hybridized Ant Colony Optimization (HACO) algorithm compared with the conventional Ant Colony Optimization algorithm. Across four benchmark datasets, HACO consistently generated routing solutions that were closer to the Best Known Solutions while requiring fewer unnecessary route explorations.

The comparative experiments demonstrated improvement rates of approximately 100%, 91%, 100%, and 87% across the evaluated benchmark instances. These results indicate that integrating sequential neighborhood search procedures substantially enhances the search capability of conventional ACO by balancing global exploration with effective local optimization.

Hybridization Accelerated Algorithm Convergence

Besides improving solution quality, the proposed hybrid framework exhibited noticeably faster convergence during iterative optimization. Conventional Ant Colony Optimization frequently required additional iterations before approaching stable routing solutions because pheromone accumulation alone may guide the search toward local optima.

By introducing Sequential Variable Neighborhood Search Change Step (SVNSCS) and Sequential Variable Neighborhood Descent (SVND), candidate solutions were continuously refined throughout the optimization process. The convergence plots presented in the study show that HACO reached high-quality solutions more rapidly than the conventional algorithm, reducing unnecessary computational effort while maintaining solution stability.

Sub-tour Elimination Improved Fleet Utilization

One of the practical innovations introduced in this research is the explicit elimination of redundant sub-tours. Instead of treating every generated route as an independent solution, the proposed algorithm evaluates whether lightly loaded routes can be merged into neighboring routes without violating vehicle capacity thresholds.

This strategy enables better utilization of available vehicle capacity while simultaneously reducing the total number of collection routes. Fewer routes translate directly into fewer vehicle deployments, lower transportation costs, reduced driver working hours, and improved operational efficiency for municipal waste collection services.

Dynamic Capacity Modeling Better Represents Real Waste Collection Operations

Unlike many earlier Vehicle Routing Problem studies that assume constant vehicle capacities throughout route execution, this research incorporates dynamic capacity thresholds reflecting actual waste accumulation during collection activities.

By monitoring vehicle loading throughout each route, the optimization model produces routing plans that better resemble real operational conditions. This enhancement improves route feasibility while reducing the likelihood of overloaded vehicles, unnecessary depot returns, and inefficient collection schedules.

Sequential Neighborhood Search Strengthened Local Optimization

The integration of Sequential Variable Neighborhood Search procedures proved essential for improving routing quality. These neighborhood operators systematically reconstruct candidate solutions after each iteration, allowing the algorithm to escape poor local optima that commonly limit conventional Ant Colony Optimization.

Rather than relying exclusively on pheromone updates, the hybrid framework actively explores alternative neighborhood structures, producing more balanced routing configurations and shorter travel distances. This demonstrates that hybrid metaheuristics can significantly outperform individual optimization algorithms when solving highly constrained engineering problems.

The Proposed Framework Demonstrates Strong Practical Potential

Beyond numerical improvements, the study illustrates how advanced computational intelligence can address practical engineering challenges encountered by municipal waste management agencies. The proposed framework simultaneously considers routing efficiency, travel cost, vehicle utilization, dynamic loading, and operational feasibility within a single optimization model.

The overall findings suggest that the proposed methodology could serve as a practical decision-support tool for smart waste management systems, particularly in urban environments where increasing waste generation requires more intelligent logistics planning. The framework also demonstrates considerable potential for adaptation to other transportation and logistics optimization problems involving dynamic operational constraints.

6. Scientific Contribution

  • Introduces a novel Hybridized Ant Colony Optimization (HACO) framework that combines conventional Ant Colony Optimization with Sequential Variable Neighborhood Search Change Step (SVNSCS) and Sequential Variable Neighborhood Descent (SVND).
  • Extends Dynamic Capacity Vehicle Routing Problem (DCVRP) research by incorporating dynamic vehicle capacity thresholds into the routing optimization process instead of relying solely on fixed-capacity assumptions.
  • Develops a dedicated sub-tour elimination mechanism capable of reducing redundant routes while improving overall vehicle utilization and operational efficiency.
  • Integrates exploration and exploitation strategies within a single optimization framework, overcoming common weaknesses associated with conventional Ant Colony Optimization.
  • Provides comprehensive benchmark validation through comparison with internationally recognized benchmark datasets and Best Known Solutions.
  • Demonstrates the effectiveness of hybrid metaheuristics for solving complex engineering optimization problems characterized by multiple operational constraints.

7. Industrial Implications

  • Reduces municipal operational expenditure. Improved routing efficiency can substantially decrease transportation costs, fuel consumption, and fleet operating expenses.
  • Supports Smart City implementation. The optimization framework aligns with intelligent urban infrastructure initiatives by enabling data-driven waste collection scheduling and route planning.
  • Improves fleet management. Better vehicle utilization allows municipalities to maximize existing transportation resources before investing in additional collection vehicles.
  • Enhances logistics planning. The proposed methodology can support engineering decision-making in transportation systems that involve capacity-constrained routing problems.
  • Promotes sustainable waste management. Reduced travel distances contribute directly to lower greenhouse gas emissions, decreased fuel usage, and improved environmental performance.
  • Supports Industry 4.0 and Digital Engineering. The integration of computational intelligence, mathematical optimization, and intelligent routing algorithms reflects the growing adoption of digital technologies in infrastructure management.
  • Provides transferable optimization strategies. Although developed for municipal waste collection, the proposed hybrid optimization framework may also be adapted for parcel delivery, healthcare logistics, warehouse distribution, emergency response routing, utility maintenance scheduling, and other transportation engineering applications.

8. Research Limitations

  • The proposed optimization framework was evaluated using benchmark datasets rather than operational data collected from a live municipal waste management system. Although benchmark instances provide standardized comparisons, real-world implementation may involve additional operational uncertainties such as unexpected traffic congestion, road closures, weather conditions, and vehicle breakdowns.
  • The study focuses on homogeneous vehicle fleets. Many municipalities operate heterogeneous fleets with different vehicle capacities, loading mechanisms, fuel consumption rates, and operational costs, which may require additional optimization strategies.
  • The optimization assumes predefined waste quantities at collection points. In practical applications, waste generation may fluctuate throughout the day and may require real-time monitoring through smart sensors or Internet of Things (IoT) technologies.
  • Although travel time is incorporated into the objective function, traffic conditions are represented using average vehicle speed rather than dynamic traffic information. Consequently, routing decisions may differ under highly congested urban environments.
  • The proposed Hybridized Ant Colony Optimization framework was compared primarily with the conventional Ant Colony Optimization algorithm. Additional comparisons with other state-of-the-art metaheuristic algorithms could further strengthen performance benchmarking.
  • The research emphasizes routing optimization and transportation efficiency. Other operational aspects of municipal solid waste management, including waste segregation, recycling logistics, transfer station scheduling, and environmental impact assessment, were beyond the scope of the present study.

9. Future Research Opportunities

  • Investigate the performance of the proposed HACO framework using real-time waste collection data obtained from smart bins equipped with IoT sensors.
  • Extend the optimization model to heterogeneous vehicle fleets with different capacities, operational costs, and energy consumption characteristics.
  • Integrate dynamic traffic information, GPS navigation, and intelligent transportation systems to enable real-time route adaptation.
  • Develop multi-objective optimization models that simultaneously minimize operational cost, greenhouse gas emissions, energy consumption, and service delays.
  • Evaluate the proposed framework within large-scale smart city environments involving thousands of collection points and multiple transfer stations.
  • Combine Hybridized Ant Colony Optimization with emerging artificial intelligence techniques such as reinforcement learning, graph neural networks, or deep learning to improve adaptive routing decisions.
  • Investigate uncertainty-aware optimization models capable of handling stochastic waste generation, variable customer demand, and unexpected operational disruptions.
  • Compare the proposed HACO framework with additional state-of-the-art metaheuristic algorithms such as Genetic Algorithms, Particle Swarm Optimization, Artificial Bee Colony, Grey Wolf Optimizer, and Adaptive Large Neighborhood Search.
  • Develop cloud-based decision support systems that integrate the proposed optimization algorithm into municipal fleet management platforms.
  • Assess the economic, environmental, and social impacts of deploying hybrid routing optimization within sustainable municipal waste management policies.

10. Potential for Public Policy Citation (Overton)

This study demonstrates meaningful potential for citation within public policy documents because municipal solid waste collection represents a core public service directly managed by local governments. The proposed optimization framework addresses practical challenges related to operational efficiency, transportation cost reduction, and sustainable urban service delivery. These issues are highly relevant to municipalities seeking evidence-based approaches for improving waste collection performance while controlling public expenditure.

The research could contribute to government technical reports, smart city implementation strategies, municipal solid waste management guidelines, digital transformation roadmaps, and urban sustainability initiatives. Its emphasis on computational optimization aligns with current efforts to modernize public infrastructure through digital engineering and intelligent transportation systems.

Nevertheless, the study is unlikely to directly influence technical standards or regulatory documents because its primary contribution concerns algorithm development rather than policy evaluation or regulatory compliance. Broader policy adoption would benefit from future studies demonstrating successful implementation in operational municipal waste collection systems under real-world conditions.

11. Who Should Read This Paper?

  • Researchers in operations research and combinatorial optimization.
  • Transportation engineers.
  • Municipal solid waste management researchers.
  • Industrial engineers.
  • Logistics and supply chain professionals.
  • Artificial intelligence and computational intelligence researchers.
  • Graduate students studying optimization algorithms.
  • Smart city planners.
  • Environmental engineers.
  • Municipal government agencies responsible for waste management.
  • Urban infrastructure consultants.
  • Decision-makers responsible for fleet management and public service optimization.

12. Final Thoughts

This study presents a well-designed contribution to the growing body of research on intelligent vehicle routing for municipal solid waste collection. Rather than introducing an entirely new optimization paradigm, the authors demonstrate how carefully integrating complementary metaheuristic techniques can substantially improve the practical performance of an established optimization algorithm. The proposed Hybridized Ant Colony Optimization framework successfully addresses several limitations commonly associated with conventional Ant Colony Optimization, particularly slow convergence, local optimum stagnation, and inefficient route utilization.

One of the study's principal strengths lies in its comprehensive optimization framework, which combines mathematical modeling, dynamic vehicle capacity, neighborhood search procedures, and sub-tour elimination within a coherent algorithmic architecture. The comparative evaluation using benchmark datasets further strengthens confidence in the reported improvements while demonstrating the practical value of hybrid metaheuristic design.

From an engineering perspective, the proposed methodology has significance beyond municipal waste collection. Similar routing challenges exist across logistics, healthcare transportation, warehouse distribution, infrastructure maintenance, emergency response, and last-mile delivery systems. Consequently, the concepts introduced in this research have broad applicability throughout modern transportation engineering and intelligent logistics.

Overall, this article represents a valuable contribution to computational optimization and sustainable urban infrastructure. It provides both theoretical advancement and practical engineering insight while establishing a solid foundation for future research integrating artificial intelligence, smart city technologies, and next-generation transportation optimization.

Suggested Citation

Teknomekanik (UNP) Style

Sahib, T. M., Mohd-Mokhtar, R., & Mohd-Kassim, A. (2024). A comparative study utilizing hybridized ant colony optimization algorithms for solving dynamic capacity of vehicle routing problems in waste collection system. Teknomekanik, 7(1), 38–61. https://doi.org/10.24036/teknomekanik.v7i1.28872

APA (7th Edition)

Sahib, T. M., Mohd-Mokhtar, R., & Mohd-Kassim, A. (2024). A comparative study utilizing hybridized ant colony optimization algorithms for solving dynamic capacity of vehicle routing problems in waste collection system. Teknomekanik, 7(1), 38–61. https://doi.org/10.24036/teknomekanik.v7i1.28872

IEEE Style

T. M. Sahib, R. Mohd-Mokhtar, and A. Mohd-Kassim, "A comparative study utilizing hybridized ant colony optimization algorithms for solving dynamic capacity of vehicle routing problems in waste collection system," Teknomekanik, vol. 7, no. 1, pp. 38–61, 2024, doi:10.24036/teknomekanik.v7i1.28872.

Harvard Style

Sahib, T.M., Mohd-Mokhtar, R. & Mohd-Kassim, A., 2024. A comparative study utilizing hybridized ant colony optimization algorithms for solving dynamic capacity of vehicle routing problems in waste collection system. Teknomekanik, 7(1), pp.38–61. Available at: https://doi.org/10.24036/teknomekanik.v7i1.28872.

Vancouver Style

Sahib TM, Mohd-Mokhtar R, Mohd-Kassim A. A comparative study utilizing hybridized ant colony optimization algorithms for solving dynamic capacity of vehicle routing problems in waste collection system. Teknomekanik. 2024;7(1):38-61. doi:10.24036/teknomekanik.v7i1.28872.

Chicago (Author–Date)

Sahib, Thaeer Mueen, Rosmiwati Mohd-Mokhtar, and Azleena Mohd-Kassim. 2024. "A Comparative Study Utilizing Hybridized Ant Colony Optimization Algorithms for Solving Dynamic Capacity of Vehicle Routing Problems in Waste Collection System." Teknomekanik 7 (1): 38–61. https://doi.org/10.24036/teknomekanik.v7i1.28872.

MLA (9th Edition)

Sahib, Thaeer Mueen, et al. "A Comparative Study Utilizing Hybridized Ant Colony Optimization Algorithms for Solving Dynamic Capacity of Vehicle Routing Problems in Waste Collection System." Teknomekanik, vol. 7, no. 1, 2024, pp. 38–61. Crossref, https://doi.org/10.24036/teknomekanik.v7i1.28872.

Editorial Note

Editorial Note: This blog post is an independent scholarly review intended for educational and scientific communication purposes. It summarizes and discusses the published article in the author's own words while providing full attribution to the original publication, consistent with the principles of the CC BY 4.0 license.

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