# Hexaly Documentation

> The world's fastest optimization solver for Routing, Scheduling, Packing, and more . Formerly known as LocalSolver until November 2023, when it rebranded to better reflect its evolution from a local search-based solver to a global optimization platform.

Hexaly serves a fast-growing community of 1,000 developers who have leveraged the Hexaly platform - Optimizer, Modeler, Cloud, Studio - to build 400 optimization apps for 20,000 users. Hexaly is a global optimization solver with a unique modeling API that combines multiple optimization techniques for solving complex routing, scheduling, and packing problems.

## Installation & licensing

[Installation on Windows](https://www.hexaly.com/docs/last/installation/installationonwindows.html#installation-on-windows): Complete guide for setting up Hexaly Optimizer on Windows systems, covering system requirements, installation procedures, and licensing options including Free Trial, Academic, Desktop, and Server licenses with alternative license locations and uninstallation instructions.
[Installation on Linux](https://www.hexaly.com/docs/last/installation/installationonlinux.html#installation-on-linux): Comprehensive installation guide for Linux environments, detailing system requirements, installation steps, and licensing configuration for Free Trial, Academic, Desktop, and Server licenses with testing procedures and removal instructions.
[Installation on macOS](https://www.hexaly.com/docs/last/installation/installationonmacosx.html#installation-on-macos): Step-by-step installation instructions for macOS platforms, including system compatibility requirements, installation process, and licensing setup for Free Trial, Academic, Desktop, and Server licenses with alternative license paths and uninstallation guidance.
[Python setup (optional)](https://www.hexaly.com/docs/last/installation/pythonsetup.html#python-setup-optional): Optional configuration guide for integrating Hexaly SDK with Python environments, enabling Python-based optimization modeling and development.

## Quick start guide

[What is Hexaly Optimizer?](https://www.hexaly.com/docs/last/quickstart/hexalyoptimizerintroduction.html#what-is-hexaly-optimizer): Comprehensive introduction to Hexaly Optimizer providing foundational guidance on creating your first optimization model and applying it to solve real business problems with practical examples.
[Quick tour of Hexaly Modeler](https://www.hexaly.com/docs/last/quickstart/quickstarthxm/quicktourofhexalymodeler.html#quick-tour-of-hexaly-modeler): Essential overview of Hexaly Modeler covering HXM file structure, loop constructs and iterated assignments, the core "model" function, solution value retrieval, and command line argument handling for flexible model execution.
[Solving your first model with Hexaly Modeler](https://www.hexaly.com/docs/last/quickstart/quickstarthxm/solvingyourfirstmodelinhxm.html#solving-your-first-model-with-hexaly-modeler): Hands-on tutorial demonstrating the complete process of writing and launching your first optimization model using the Hexaly Modeler language and environment.
[Solving your first business problem with Hexaly Modeler](https://www.hexaly.com/docs/last/quickstart/quickstarthxm/solvingyourfirstbusinessprobleminhxm.html#solving-your-first-business-problem-with-hexaly-modeler): End-to-end guide for tackling real business optimization challenges using Hexaly Modeler, covering data input processing, problem modeling techniques, optimizer configuration, and solution output generation.
[Solving your first model in Python](https://www.hexaly.com/docs/last/quickstart/quickstartpython/solvingyourfirstmodelinpython.html#solving-your-first-model-in-python): Step-by-step Python tutorial for creating optimization models using the Hexaly Python SDK, including model implementation, program execution, and running Hexaly Optimizer in environments without pip installation.
[Solving your first business problem in Python](https://www.hexaly.com/docs/last/quickstart/quickstartpython/solvingyourfirstbusinessprobleminpython.html#solving-your-first-business-problem-in-python): Complete Python-based workflow for solving business optimization problems, demonstrating input data handling, problem modeling with Python syntax, optimizer parameter configuration, and solution file generation.
[Solving your first model in C++](https://www.hexaly.com/docs/last/quickstart/quickstartcpp/solvingyourfirstmodelincpp.html#solving-your-first-model-in-c): Practical C++ implementation guide covering optimization model development, compilation procedures, and program execution using the Hexaly C++ SDK for high-performance applications.
[Solving your first business problem in C++](https://www.hexaly.com/docs/last/quickstart/quickstartcpp/solvingyourfirstbusinessproblemincpp.html#solving-your-first-business-problem-in-c): Comprehensive C++ tutorial for business problem solving using Hexaly, including data input processing, problem modeling with C++ constructs, optimizer parameterization, and solution output handling.
[Solving your first model in C#](https://www.hexaly.com/docs/last/quickstart/quickstartcsharp/solvingyourfirstmodelincsharp.html#solving-your-first-model-in-c): Complete C# development guide for optimization modeling, covering model implementation, compilation and execution procedures for both .NET and .NET Framework environments, with detailed output analysis.
[Solving your first business problem in C#](https://www.hexaly.com/docs/last/quickstart/quickstartcsharp/solvingyourfirstbusinessproblemincsharp.html#solving-your-first-business-problem-in-c): End-to-end C# workflow for business optimization, demonstrating data input handling, problem modeling using C# language features, optimizer configuration, and comprehensive solution file generation.
[Solving your first model in Java](https://www.hexaly.com/docs/last/quickstart/quickstartjava/solvingyourfirstmodelinjava.html#solving-your-first-model-in-java): Introductory Java tutorial for optimization model development using the Hexaly Java SDK, including model implementation and Java program compilation and execution procedures.
[Solving your first business problem in Java](https://www.hexaly.com/docs/last/quickstart/quickstartjava/solvingyourfirstbusinessprobleminjava.html#solving-your-first-business-problem-in-java): Complete Java-based approach to business problem solving with Hexaly, covering data input processing, object-oriented problem modeling, optimizer parameter setup, and solution output management.

## Modeling Features

[Mathematical modeling features](https://www.hexaly.com/docs/last/modelingfeatures/mathematicalmodelingfeatures.html#mathematical-modeling-features): Comprehensive reference covering the fundamental building blocks of optimization models including decision variables, constraints, objectives, and available mathematical operators.
[Multiobjective resolution](https://www.hexaly.com/docs/last/modelingfeatures/multiobjectiveresolution.html#multiobjective-resolution): Advanced optimization techniques for handling multiple conflicting objectives using lexicographic ordering approaches and phased optimization strategies to find Pareto-optimal solutions.
[At operator](https://www.hexaly.com/docs/last/modelingfeatures/atoperator.html#at-operator): Detailed guide to array indexing and element access using the at operator, covering both 1-dimensional and multi-dimensional array operations, jagged array handling, and common modeling pitfalls to avoid.
[Piecewise operator](https://www.hexaly.com/docs/last/modelingfeatures/piecewiseoperator.html#piecewise-operator): Complete explanation of the piecewise linear function operator, demonstrating how to model non-linear relationships through piecewise linear approximations and practical implementation techniques.
[List and set variables](https://www.hexaly.com/docs/last/modelingfeatures/collectionvariables.html#list-and-set-variables): Comprehensive guide to collection data types including creation, manipulation, and practical modeling approaches.
[Lambda expressions](https://www.hexaly.com/docs/last/modelingfeatures/delegates.html#lambda-expressions): Advanced functional programming concepts covering range definitions, lambda function creation and usage, and techniques for applying lambda functions to iterable collections for concise model expression.
[External functions](https://www.hexaly.com/docs/last/modelingfeatures/externalfunctions.html#external-functions): Integration guide for incorporating external computational functions into optimization models, covering fundamental principles, practical implementation examples, common pitfalls, and surrogate modeling techniques for expensive function evaluations.
[Modeling guide for routing problems](https://www.hexaly.com/docs/last/modelingfeatures/routing.html#modeling-guide-for-routing-problems): Comprehensive routing problem modeling reference covering classic variants including TSP, CVRP, CVRPTW, and specialized routing problems.

## Technical features

[Retrieving solution status and values](https://www.hexaly.com/docs/last/technicalfeatures/solution.html#retrieving-solution-status-and-values): Comprehensive guide to accessing optimization results including solution status and value extraction for different variable types.
[Export your Hexaly model](https://www.hexaly.com/docs/last/technicalfeatures/export.html#export-your-hexaly-model): Complete instructions for exporting Hexaly optimization models to various formats for analysis, sharing, or integration with other systems and tools.
[Setting an initial solution](https://www.hexaly.com/docs/last/technicalfeatures/initialsolution.html#setting-an-initial-solution): Detailed procedures for providing initial feasible solutions to the optimizer to improve convergence speed and solution quality through warm-start techniques.
[Infeasibility and inconsistency](https://www.hexaly.com/docs/last/technicalfeatures/inconsistency.html#infeasibility-and-inconsistency): Diagnostic techniques and analytical methods for identifying and resolving model infeasibilities and constraint inconsistencies during optimization problem formulation.
[Callbacks and events](https://www.hexaly.com/docs/last/technicalfeatures/callbacks.html#callbacks-and-events): Advanced programming interface for implementing callback functions and event handlers to monitor, control, and customize the behavior of the Hexaly Optimizer during execution.
[Hexaly Cloud](https://www.hexaly.com/docs/last/technicalfeatures/cloud.html#hexaly-cloud): Cloud deployment guide covering getting started with Hexaly Cloud services, understanding the architecture and security framework, and implementing advanced configuration options for scalable optimization.
[Hexaly Modeler API](https://www.hexaly.com/docs/last/technicalfeatures/modeler.html#hexaly-modeler-api): Programming interface documentation for interacting with the Hexaly Modeler programmatically, including API usage patterns and complete implementation examples for automated model generation and execution.

## Guidelines

[Modeling principles](https://www.hexaly.com/docs/last/guidelines/modelingprinciples.html#modeling-principles): Essential best practices for effective optimization modeling including strategies to distinguish between decision variables and intermediate variables, techniques for separating hard constraints from first-priority objectives, and methods for properly defining objective functions for optimal solver performance.
[Debugging a model](https://www.hexaly.com/docs/last/guidelines/debuggingamodel.html#debugging-a-model): Systematic debugging methodology for optimization models featuring incremental constraint and objective introduction techniques, strategies for injecting feasible solutions as initial starting points, and protocols for interpreting and addressing solver warnings effectively.
[How to migrate from MIP to Hexaly Optimizer?](https://www.hexaly.com/docs/last/guidelines/howtomigratefrommiptohexaly.html#how-to-migrate-from-mip-to-hexaly-optimizer): Comprehensive migration guide for transitioning from Mixed Integer Programming (MIP) solvers to Hexaly Optimizer, covering the transformation of decision variables and intermediate expressions, leveraging non-linear operators instead of traditional linearizations, and identifying and removing unnecessary constraints for improved model efficiency.

## Code Templates

[Toy Problem](https://www.hexaly.com/templates/toy): **Packing** - A simple knapsack problem with 8 items having specified weights and values. This combinatorial optimization problem demonstrates basic modeling with boolean decision variables, constraints, and objectives. The goal is to maximize value while staying within weight capacity of 102. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Knapsack Problem](https://www.hexaly.com/templates/knapsack) **Packing** - Classic knapsack combinatorial optimization problem where items with weights and values must be selected to maximize value while respecting weight constraints. Shows how to create generic models using data from files and write solutions to output files. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Curve Fitting Problem](https://www.hexaly.com/templates/curve-fitting-problem) **Nonlinear** - Parameter optimization for mathematical functions to best fit observed data points. This continuous optimization problem uses float decision variables and non-linear expressions with sin, cos, and power operators to minimize sum of square errors between predicted and observed outputs. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Facility Location (FLP)](https://www.hexaly.com/templates/facility-location-problem) **Location** - The p-median combinatorial optimization problem where optimal facility locations are selected to minimize transportation costs. Given N locations and transportation costs between pairs, select p facilities to minimize total distance from each location to its closest facility. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Smallest Circle Problem](https://www.hexaly.com/templates/smallest-circle) **Location** - Geometric continuous optimization to find the circle with minimal radius that contains all given points in a plane. Uses float decision variables for circle center coordinates and non-linear expressions with sqrt and pow operators. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Branin Function](https://www.hexaly.com/templates/branin) **Nonlinear** - Mathematical function continuous optimization using the Branin function f(x) = a(x2 - b*x1² + c*x1 - r)² + s(1-t)cos(x1) + s. Demonstrates highly non-linear optimization with trigonometric and polynomial expressions using float decision variables. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Max Cut Problem](https://www.hexaly.com/templates/max-cut) **Nonlinear** - Graph partitioning combinatorial optimization problem where vertices are divided into two subsets to maximize the total weight of edges crossing between subsets. Uses boolean decision variables and comparison operators to model the bipartition constraint. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Hosaki Function](https://www.hexaly.com/templates/hosaki) **Simulation** - Box-constrained continuous optimization of the Hosaki function using external functions and surrogate modeling. Demonstrates how to handle computationally expensive objective functions with evaluation limits and surrogate modeling features for simulation-based optimization. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Order Picking Problem](https://www.hexaly.com/templates/order-picking) **Routing** - Warehouse routing optimization to find the optimal picking sequence that minimizes distance traveled. This combinatorial optimization problem uses list decision variables, at operators for accessing elements, and Manhattan distance calculations for rectangular warehouse layouts. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Car Sequencing Problem](https://www.hexaly.com/templates/car-sequencing) **Scheduling** - Production line sequencing optimization where cars with different options must be sequenced to respect station capacity constraints. This combinatorial optimization problem uses list variables for permutations and violation expressions to handle capacity constraints on assembly line stations. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Car Sequencing Problem with Colors](https://www.hexaly.com/templates/car-sequencing-problem-with-color) **Scheduling** - Extended car sequencing combinatorial optimization problem with additional color constraints for paint shop operations. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Social Golfer Problem](https://www.hexaly.com/templates/social-golfer) **Scheduling** - Scheduling combinatorial optimization problem where golfers are grouped weekly to maximize social interaction while minimizing repeated meetings. Demonstrates combinatorial constraint satisfaction with boolean decision variables and n-ary operators. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Steel Mill Slab Design Problem](https://www.hexaly.com/templates/steel-mill) **Packing** - Industrial combinatorial optimization where steel orders are assigned to slabs to minimize waste while respecting capacity and color constraints. Shows advanced modeling with set variables and non-linear waste calculation using precomputed arrays. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Bin Packing Problem (BPP)](https://www.hexaly.com/templates/bin-packing-problem) **Packing** - Classic NP-hard combinatorial optimization problem where items with known weights must be assigned to bins with uniform capacity to minimize the number of bins used. Uses set decision variables and partition constraints with lambda expressions for weight calculations. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Bin Packing Problem with Conflicts (BPPC)](https://www.hexaly.com/templates/bin-packing-problem-with-conflicts) **Packing** - Extended bin packing combinatorial optimization with conflict constraints between items that cannot be placed in the same bin. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Capacitated Facility Location (CFLP)](https://www.hexaly.com/templates/capacitated-facility-location-problem-cflp) **Location** - Facility location combinatorial optimization problem with capacity constraints on facilities. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Optimal Bucket Problem](https://www.hexaly.com/templates/optimal-bucket) **Nonlinear** - Geometric continuous optimization for bucket shape design. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Portfolio Selection Optimization Problem](https://www.hexaly.com/templates/portfolio-selection-optimization-problem) **Nonlinear** - Financial continuous optimization for portfolio management with risk and return constraints. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[K-Means Clustering Problem (MSSC)](https://www.hexaly.com/templates/k-means) **Location** - Unsupervised machine learning clustering continuous optimization algorithm implementation for partitioning data points into k clusters. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Quadratic Assignment Problem(QAP)](https://www.hexaly.com/templates/quadratic-assignment) **Location** - Fundamental combinatorial optimization problem for assigning facilities to locations to minimize distance-flow product costs. Uses list variables for permutations and demonstrates non-linear optimization without requiring linearization. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Simple Assembly Line Balancing Problem (SALBP)](https://www.hexaly.com/templates/simple-assembly-line-balancing-problem-salbp) **Scheduling** - Manufacturing combinatorial optimization to balance workload across assembly line stations. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Flow Shop Problem](https://www.hexaly.com/templates/flow-shop-problem) **Scheduling** - Scheduling combinatorial optimization problem where jobs must be processed in the same sequence on all machines. Uses list variables for job sequencing and recursive arrays to define start/end times. Minimizes makespan with precedence constraints. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Job Shop Scheduling Problem (JSSP)](https://www.hexaly.com/templates/job-shop) **Scheduling** - Complex scheduling combinatorial optimization where jobs have different machine processing orders. Uses interval decision variables for time ranges and list variables for job ordering on machines. Demonstrates disjunctive resource constraints and makespan minimization. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Job Shop Scheduling Problem with Intensity](https://www.hexaly.com/templates/job-shop-scheduling-problem-with-intensity) **Scheduling** - Advanced job shop scheduling combinatorial optimization incorporating variable processing intensities and resource consumption rates. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Flexible Resource Constrained Project Scheduling Problem](https://www.hexaly.com/templates/flexible-resource-constrained-project-scheduling-problem) **Scheduling** - Project scheduling combinatorial optimization with flexible resource allocation and skill-based task assignments. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Flexible Job Shop Problem (FJSP)](https://www.hexaly.com/templates/flexible-job-shop) **Scheduling** - Job shop variant combinatorial optimization where operations can be processed on alternative machines with different processing times and capabilities. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Flexible Job Shop Problem with Setup Times (FJSP-SDST)](https://www.hexaly.com/templates/flexible-job-shop-problem-with-setup-times-fjsp-sdst) **Scheduling** - Enhanced FJSP combinatorial optimization incorporating setup times that depend on the sequence of operations on machines. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Flexible Job Shop Problem with Machine Changeover Times](https://www.hexaly.com/templates/flexible-job-shop-problem-with-machine-changeover-times) **Scheduling** - FJSP variant combinatorial optimization with machine-specific changeover times between different operation types. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Open Shop Scheduling Problem](https://www.hexaly.com/templates/open-shop-scheduling-problem) **Scheduling** - Scheduling combinatorial optimization where jobs can be processed in any order on machines, offering maximum flexibility in operation sequencing. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Stochastic Packing Problem](https://www.hexaly.com/templates/stochastic-packing) **Packing** - Packing combinatorial optimization under uncertainty with probabilistic item sizes or container capacities. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Stochastic Job Shop Scheduling Problem](https://www.hexaly.com/templates/stochastic-job-shop-scheduling-problem) **Scheduling** - Job shop scheduling combinatorial optimization under uncertainty with random processing times or machine breakdowns. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Resource Constrained Project Scheduling Problem (RCPSP)](https://www.hexaly.com/templates/resource-constrained-project-scheduling-problem-rcpsp) **Scheduling** - Project scheduling combinatorial optimization with limited renewable and non-renewable resources, precedence constraints, and activity durations. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Preemptive Resource Constrained Project Scheduling Problem](https://www.hexaly.com/templates/preemptive-resource-constrained-project-scheduling-problem-prcpsp) **Scheduling** - RCPSP variant combinatorial optimization allowing activities to be interrupted and resumed later when resources become available. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Batch Scheduling Problem](https://www.hexaly.com/templates/preemptive-resource-constrained-project-scheduling-problem-prcpsp) **Scheduling** - Scheduling combinatorial optimization of batch operations in manufacturing environments with batch size constraints and setup considerations. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Project Scheduling Problem with Production and Consumption of Resources](https://www.hexaly.com/templates/project-scheduling-with-production-and-consumption-of-resources) **Scheduling** - Advanced project scheduling combinatorial optimization where activities both consume and produce resources during execution. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Traveling Salesman  Problem (TSP)](https://www.hexaly.com/templates/traveling-salesman-problem) **Routing** - Classic combinatorial optimization problem finding the shortest route visiting all cities exactly once and returning to the starting point. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Capacitated Vehicle Routing Problem (CVRP)](https://www.hexaly.com/templates/capacitated-vehicle-routing-problem-cvrp) **Routing** - Fleet combinatorial optimization where vehicles with uniform capacity service customers with known demands. Uses multiple list decision variables for route sequences, partition constraints to ensure all customers are served, and lambda expressions for capacity and distance calculations. Minimizes fleet size and total distance. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Vehicle Routing Problem with Time Windows (CVRPTW)](https://www.hexaly.com/templates/vehicle-routing-problem-with-time-windows-cvrptw) **Routing** - Extension of CVRP combinatorial optimization with customer time windows for service appointments. Uses recursive arrays to handle temporal constraints, calculating arrival times, waiting periods, and lateness penalties. Demonstrates multi-objective optimization with lexicographic ordering. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Pickup and Delivery Problem with Time Windows (PDPTW)](https://www.hexaly.com/templates/pickup-and-delivery-problem-with-time-windows-pdptw) **Routing** - Vehicle routing combinatorial optimization where each request involves pickup and delivery locations with time window constraints for both operations. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Dial-A-Ride Problem (DARP)](https://www.hexaly.com/templates/dial-a-ride-problem-darp) **Routing** - On-demand transportation combinatorial optimization for passenger pickup and delivery with quality of service constraints. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Clustered Vehicle Routing (cluVRP)](https://www.hexaly.com/templates/clustered-vehicle-routing) **Routing** - VRP variant combinatorial optimization where customers are grouped into clusters and entire clusters must be served by single vehicles. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Inventory Routing Problem (IRP)](https://www.hexaly.com/templates/inventory-routing-problem-irp) **Routing** - Integrated combinatorial optimization combining inventory management decisions with vehicle routing for supply chain efficiency. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Split Delivery Vehicle Routing Problem (SDVRP)](https://www.hexaly.com/templates/split-delivery-vehicle-routing-sdvrp) **Routing** - VRP combinatorial optimization allowing customer demands to be split across multiple vehicles and deliveries. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Time Dependent Problem with Time Windows (TDCVRPTW)](https://www.hexaly.com/templates/time-dependent-routing-problem-with-time-windows-tdcvrptw) **Routing** - CVRPTW combinatorial optimization with time-dependent travel times reflecting traffic conditions and congestion patterns. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Capacitated Arc Routing Problem (CARP)](https://www.hexaly.com/templates/capacitated-arc-routing-problem-carp) **Routing** - Routing combinatorial optimization where service is required on edges (arcs) rather than nodes, common in waste collection and street maintenance. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Multi-Trip Capacitated Vehicle Routing Problem (MTCVRP)](https://www.hexaly.com/templates/multi-trip-capacitated-vehicle-routing-problem-mtcvrp) **Routing** - VRP combinatorial optimization allowing vehicles to make multiple trips from the depot during their working period. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Multi Depot Vehicle Routing Problem (MDVRP)](https://www.hexaly.com/templates/multi-depot-vehicle-routing-problem-mdvrp) **Routing** - VRP combinatorial optimization with multiple depots where vehicles can start and end at different depot locations. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Location Routing Problem (LRP)](https://www.hexaly.com/templates/location-routing-problem-lrp) **Routing** - Combined combinatorial optimization of facility location decisions and vehicle routing from selected facilities. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Vehicle Routing Problem with Transshipment Facilities (VRPTF)](https://www.hexaly.com/templates/vehicle-routing-problem-with-transshipment-facilities-vrptf) **Routing** - VRP combinatorial optimization incorporating intermediate transhipment facilities for cargo consolidation and transfer. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Prize-Collecting Vehicle Routing (PCVRP)](https://www.hexaly.com/templates/prize-collecting-vehicle-routing-problem) **Routing** - VRP combinatorial optimization where not all customers need to be visited, balancing travel costs against prizes collected from served customers. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Aircraft Landing Problem](https://www.hexaly.com/templates/aircraft-landing-problem-2) **Scheduling** - Airport operations combinatorial optimization for scheduling aircraft landings with runway capacity and time window constraints. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Movie Shoot Scheduling](https://www.hexaly.com/templates/movie-shoot-scheduling) **Scheduling** - Entertainment industry scheduling combinatorial optimization optimizing actor availability, location access, and scene requirements. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Revenue Management](https://www.hexaly.com/templates/revenue-management) **Nonlinear** - Pricing and capacity allocation continuous optimization to maximize revenue in service industries. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Pooling](https://www.hexaly.com/templates/pooling) **Nonlinear** - Blending continuous optimization problem where different input streams are mixed to meet output quality specifications. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Vehicle Routing Problem with Backhauls (VRPB)](https://www.hexaly.com/templates/vehicle-routing-with-backhauls-vrpb) **Routing** - VRP combinatorial optimization combining delivery and pickup operations where vehicles collect items after making deliveries. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Cantilevered Beam Problem](https://www.hexaly.com/templates/cantilevered-beam-problem) **Nonlinear** - Structural engineering continuous optimization for beam design balancing weight, strength, and manufacturing constraints. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Surgery Scheduling Problem](https://www.hexaly.com/templates/surgery-scheduling-problem) **Scheduling** - Healthcare operations combinatorial optimization for operating room scheduling with surgeon availability, equipment requirements, and patient constraints. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Constrained Pit Limit Problem (CPIT)](https://www.hexaly.com/templates/constrained-pit-limit-cpit): **Packing/Scheduling** - Mining operations combinatorial optimization for extracting blocks from a pit across multiple time periods with resource constraints and precedence dependencies. Uses set decision variables for period-based extraction planning, with blocks having time-dependent profit values. Resource consumption is limited per period and blocks must be extracted after their predecessors. Demonstrates lambda functions for resource calculation and profit maximization with discounted rewards. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Workforce Scheduling Problem](https://www.hexaly.com/templates/workforce-scheduling-problem): **Scheduling** - Employee scheduling combinatorial optimization for assigning agents to tasks throughout the week with individual availability constraints and skill requirements. Uses boolean decision variables for task assignment timing and pre-computed availability indicators to reduce model complexity. Features multi-objective lexicographic optimization minimizing understaffing, overstaffing, and working day length. Includes working time bounds and task duration constraints to ensure realistic professional scheduling. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Workforce Shift Scheduling Problem](https://www.hexaly.com/templates/workforce-shift-scheduling-problem): **Scheduling** - Shift-based workforce scheduling combinatorial optimization where agents are assigned to discretized time shifts for activities with specific durations and time windows. Uses boolean decision variables for shift assignments with no-overlap constraints and mandatory break times between shifts. Features multi-objective lexicographic optimization prioritizing understaffing minimization over workload balancing. Includes agent availability windows and exactly two shifts per day requirements. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Multi-Mode Resource-Constrained Project Scheduling (MRCPSP)](https://www.hexaly.com/templates/multi-mode-resource-constrained-project-scheduling-mrcpsp): **Scheduling** - Project scheduling combinatorial optimization where tasks can be executed in multiple modes with different durations and resource consumption patterns. Uses optional interval decision variables with presence operators to model mode selection and hull operators for task management. Features renewable and non-renewable resource constraints with precedence dependencies between tasks. Minimizes makespan while respecting resource capacities and task execution requirements. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.
[Shelf Packing Problem](https://www.hexaly.com/templates/shelf-packing-problem) - **Packing** - Hierarchical packing combinatorial optimization extending bin packing where items are assigned to bins placed on shelves with capacity constraints at both levels. Uses set decision variables with union operators to model shelf contents from bin assignments. Features category-based item limits per shelf and multi-objective optimization minimizing shelf count first, then bin count. Demonstrates JSON data handling and intersection operations for category constraint enforcement. Example available in Hexaly Modeler, Python, C++, C#, and Java SDKs.

## Hexaly Modeler

[Quick tour of Hexaly Modeler](https://www.hexaly.com/docs/last/modelerreference/quicktourmodeler.html#quick-tour-of-hexaly-modeler): Essential introduction to the Hexaly Modeler language providing foundational concepts and practical examples for optimization modeling.
[Programming style](https://www.hexaly.com/docs/last/modelerreference/programmingstyle.html#programming-style): Comprehensive guide to Hexaly Modeler programming conventions covering data types, control structures, and function definitions.
[Built-in variables and functions](https://www.hexaly.com/docs/last/modelerreference/builtinvariablesandfunctions.html#built-in-variables-and-functions): Reference documentation for the core built-in functionality including system parameters and essential programming functions available in the Hexaly Modeler environment.
[Syntax and lexical analysis](https://www.hexaly.com/docs/last/modelerreference/syntaxlexical.html#syntax-and-lexical-analysis): Detailed specification of the Hexaly Modeler language syntax covering file structure, encoding, comments, identifiers, and keywords.
[Values and types](https://www.hexaly.com/docs/last/modelerreference/valuestypes.html#values-and-types): Complete type system documentation covering standard and commonly used data types as well as specialized types available in the Hexaly Modeler language.
[Variables](https://www.hexaly.com/docs/last/modelerreference/variables.html#variables): Variable declaration and management guide covering global variable scope, local variable usage, and memory management principles in Hexaly Modeler programs.
[Expressions](https://www.hexaly.com/docs/last/modelerreference/expressions.html#expressions): Comprehensive expression reference covering arithmetic, logical, and relational operations with operator precedence and syntax rules.
[Statements](https://www.hexaly.com/docs/last/modelerreference/statements.html#statements): Complete statement syntax guide covering assignments, control flow, exception handling, and optimization declarations.
[Functions](https://www.hexaly.com/docs/last/modelerreference/functions.html#functions): Function programming guide covering function definition, calls, variadic functions, and lambda expressions.
[Modules](https://www.hexaly.com/docs/last/modelerreference/modules.html#modules): Module system documentation covering module creation, import mechanisms, and lookup path configuration.
[Classes](https://www.hexaly.com/docs/last/modelerreference/classes.html#classes): Object-oriented programming guide covering class declaration, instantiation, methods, constructors, fields, and inheritance.
[Command line](https://www.hexaly.com/docs/last/modelerreference/commandline.html#command-line): Command-line interface documentation for executing Hexaly Modeler programs and configuring runtime options.
[Main mode](https://www.hexaly.com/docs/last/modelerreference/mainmode.html#main-mode): Main mode programming guide covering activation procedures and integrated modeling workflows.
[Builtin functions and variables](https://www.hexaly.com/docs/last/modelerreference/standardlibrary/builtinfunctions.html#builtin-functions-and-variables): Core function library reference covering essential functions, mathematical operators, and global variables available in the Hexaly Modeler standard library.
[Charset module](https://www.hexaly.com/docs/last/modelerreference/standardlibrary/charsetmodule.html#hxmmodule-charset): Character encoding module providing comprehensive support for text encoding and decoding operations.
[CSV module](https://www.hexaly.com/docs/last/modelerreference/standardlibrary/csvmodule.html#hxmmodule-csv): Comma-separated values processing module offering functions for reading and writing CSV files with format configuration options.
[Date/time module](https://www.hexaly.com/docs/last/modelerreference/standardlibrary/datetimemodule.html#hxmmodule-datetime): Date and time manipulation module providing functions for temporal calculations and date formatting.
[Geodata module](https://www.hexaly.com/docs/last/modelerreference/standardlibrary/geodatamodule.html#hxmmodule-geodata): Geographic data processing module offering functions for spatial calculations and geospatial operations.
[Hexaly module](https://www.hexaly.com/docs/last/modelerreference/standardlibrary/hexalymodule/index.html#hexaly-module): Core Hexaly integration module providing essential functions for interfacing with the Hexaly optimization engine and accessing solver capabilities.
[HTTP module](https://www.hexaly.com/docs/last/modelerreference/standardlibrary/httpmodule.html#hxmmodule-http): HTTP communication module offering functions for web requests and HTTP handling with configuration options.
[I/O module](https://www.hexaly.com/docs/last/modelerreference/standardlibrary/iomodule.html#hxmmodule-io): Input/output operations module providing functions for file handling and stream management.
[JSON module](https://www.hexaly.com/docs/last/modelerreference/standardlibrary/jsonmodule.html#hxmmodule-json): JSON data processing module offering functions for parsing and serialization with detailed parser and writer behavior.
[Map module](https://www.hexaly.com/docs/last/modelerreference/standardlibrary/mapmodule.html#hxmmodule-map): Map data structure module providing advanced mapping functionality and associative container operations.
[Math module](https://www.hexaly.com/docs/last/modelerreference/standardlibrary/mathmodule.html#hxmmodule-math): Mathematical operations module offering essential constants and mathematical functions including trigonometric and hyperbolic operations.
[Random module](https://www.hexaly.com/docs/last/modelerreference/standardlibrary/randommodule.html#hxmmodule-random): Random number generation module providing functions for probabilistic operations and random distributions.
[String module](https://www.hexaly.com/docs/last/modelerreference/standardlibrary/stringmodule.html#hxmmodule-string): String manipulation module offering comprehensive text processing functions and utilities for string operations.
[XLSX module](https://www.hexaly.com/docs/last/modelerreference/standardlibrary/xlsxmodule.html#hxmmodule-xlsx): This module implements the XLSX (Microsoft Excel) format, allowing you to read and write Excel spreadsheets.

## Python API Reference

### Hexaly Optimizer

[HexalyOptimizer Class](https://www.hexaly.com/docs/last/pythonapi/optimizer/hexalyoptimizer.html#hexalyoptimizer-class): Main Hexaly Optimizer environment class for building models, solving optimization problems, and retrieving solutions and statistics.
[HxArray Class](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxarray.html#hxarray-class): Value type for array expressions containing mixed data types with methods for element access and type checking.
[HxCollection Class](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxcollection.html#hxcollection-class): Value type for collection expressions representing lists or sets with methods for element manipulation and Python-like collection behavior.
[HxEvaluationPoint Class](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxevaluationpoint.html#hxevaluationpoint-class): Evaluation point for external functions with surrogate modeling, allowing specification of known input-output pairs to improve optimization performance.
[HxExpression Class](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxexpression.html#hxexpression-class): Mathematical modeling expression class for building optimization models as directed acyclic graphs, with comprehensive operator overloading and expression management capabilities.
[HxExternalArgumentValues Class](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxexternalargumentvalues.html#hxexternalargumentvalues-class): Argument values container for external functions providing type checking and value retrieval methods for function arguments.
[HxExternalContext Class](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxexternalcontext.html#hxexternalcontext-class): External function context management class for configuring external function properties including bounds, NaN handling, and surrogate modeling.
[HxInconsistency Class](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxinconsistency.html#hxinconsistency-class): Inconsistency core analysis class representing an irreducible inconsistent subproblem for debugging infeasible optimization models.
[HxInterval Class](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxinterval.html#hxinterval-class): Value type for interval expressions representing continuous time or resource intervals with methods for property queries and containment testing.
[HxModel Class](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxmodel.html#hxmodel-class): Mathematical optimization model builder for creating expressions, decision variables, constraints, and objectives with comprehensive modeling operators and lifecycle management.
[HxParam Class](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxparam.html#hxparam-class): Solving parameters configuration class for controlling optimization behavior including computational resources, time limits, output settings, and advanced tuning options.
[HxPhase Class](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxphase.html#hxphase-class): Optimization phase configuration for lexicographic multiobjective optimization with phase duration control and objective targeting.
[HxSolution Class](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxsolution.html#hxsolution-class): Solution container carrying values for all expressions in the optimization model with methods for value retrieval, constraint checking, and solution quality assessment.
[HxStatistics Class](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxstatistics.html#hxstatistics-class): Search statistics class providing runtime performance metrics including execution time and iteration count.
[HxSurrogateParameters Class](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxsurrogateparameters.html#hxsurrogateparameters-class): Parameters for surrogate modeling feature with evaluation budget management and evaluation point collections for external functions.
[HxVersion Class](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxversion.html#hxversion-class): Version, license and copyright information class providing version details, copyright information, and license management functionality.
[HxError Class](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxerror.html#hxerror-class): Hexaly Optimizer exception class containing debugging information with attributes for error details and formatted exception messages.
[HxCallbackType Enumeration](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxcallbacktype.html#hxcallbacktype-enumeration): Enumeration of callback event types for monitoring optimization phases and progress.
[HxErrorCode Enumeration](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxerrorcode.html#hxerrorcode-enumeration): Enumeration of error codes for HxError exceptions covering API, file, model, callback, license, solver, and internal errors.
[HxObjectiveDirection Enumeration](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxobjectivedirection.html#hxobjectivedirection-enumeration): Enumeration defining optimization directions with values MINIMIZE (for minimization objectives) and MAXIMIZE (for maximization objectives).
[HxOperator Enumeration](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxoperator.html#hxoperator-enumeration): Comprehensive enumeration of mathematical operators available for modeling optimization problems.
[HxSolutionStatus Enumeration](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxsolutionstatus.html#hxsolutionstatus-enumeration): Enumeration indicating solution quality from inconsistent to optimal status.
[HxState Enumeration](https://www.hexaly.com/docs/last/pythonapi/optimizer/hxstate.html#hxstate-enumeration): Enumeration representing the state of the Hexaly Optimizer environment from modeling to solving phases.

### Hexaly Modeler

[HexalyModeler Class](https://www.hexaly.com/docs/last/pythonapi/modeler/hexalymodeler.html#hexalymodeler-class): Main modeler environment class for creating and manipulating virtual machines that execute Hexaly modeling language programs.
[HxmClass Class](https://www.hexaly.com/docs/last/pythonapi/modeler/hxmclass.html#hxmclass-class): Class introspection and instantiation class representing loaded classes in modules with methods for property queries and member management.
[HxmField Class](https://www.hexaly.com/docs/last/pythonapi/modeler/hxmfield.html#hxmfield-class): Class field representation for object fields declared in Hexaly Modeler classes.
[HxmFunction Class](https://www.hexaly.com/docs/last/pythonapi/modeler/hxmfunction.html#hxmfunction-class): Function representation class for both external Python functions and Hexaly Modeler language functions.
[HxmMap Class](https://www.hexaly.com/docs/last/pythonapi/modeler/hxmmap.html#hxmmap-class): Data structure mapping keys to values that functions as both associative table and array with Python-like dictionary behavior.
[HxmModule Class](https://www.hexaly.com/docs/last/pythonapi/modeler/hxmmodule.html#hxmmodule-class): Module representing a collection of global variables from HXM files with methods to execute modules (run, run_main) and special operators for variable management (__getitem__, __setitem__, __delitem__, __contains__).
[HxmProperty Class](https://www.hexaly.com/docs/last/pythonapi/modeler/hxmproperty.html#hxmproperty-class): Class property representation for getter/setter properties declared in Hexaly Modeler classes.
[HxmReferenceScope Class](https://www.hexaly.com/docs/last/pythonapi/modeler/hxmreferencescope.html#hxmreferencescope-class): Reference scope management class for controlling object lifetime and automatic resource cleanup in the modeler environment.
[HxmValue Class](https://www.hexaly.com/docs/last/pythonapi/modeler/hxmvalue.html#hxmvalue-class): Generic value wrapper class representing any value type in the Hexaly Modeler environment including objects, primitives, and other modeler-specific types.

## C++ API Reference

### Hexaly Optimizer

[HexalyOptimizer Class](https://www.hexaly.com/docs/last/cppapi/optimizer/hexalyoptimizer.html#hexalyoptimizer-class): The main class for the Hexaly Optimizer C++ library, providing a complete optimization environment with model building, solving, and solution retrieval capabilities.
[HxArray Class](https://www.hexaly.com/docs/last/cppapi/optimizer/hxarray.html#hxarray-class): A value type for array expressions containing mixed data types like integers, doubles, intervals, or nested arrays, with methods for element access and type checking.
[HxCollection Class](https://www.hexaly.com/docs/last/cppapi/optimizer/hxcollection.html#hxcollection-class): A value type for collection expressions representing ordered lists or unordered sets of integers, with methods for adding, removing, and querying elements.
[HxEvaluationPoint Class](https://www.hexaly.com/docs/last/cppapi/optimizer/hxevaluationpoint.html#hxevaluationpoint-class): A class for defining known evaluation points for external functions in surrogate modeling, allowing specification of argument and return values to warm-start optimization.
[HxExpression Class](https://www.hexaly.com/docs/last/cppapi/optimizer/hxexpression.html#hxexpression-class): The core mathematical modeling expression class for building optimization models, supporting various operators, operands, and providing overloaded operators for expression construction.
[HxExternalArgumentValues Class](https://www.hexaly.com/docs/last/cppapi/optimizer/hxexternalargumentvalues.html#hxexternalargumentvalues-class): A class for querying argument values passed to external functions, providing type checking and value retrieval methods for various data types.
[HxExternalContext Class](https://www.hexaly.com/docs/last/cppapi/optimizer/hxexternalcontext.html#hxexternalcontext-class): A context class for external functions that allows setting bounds, NaN handling properties, and enabling surrogate modeling for computationally expensive functions.
[HxInconsistency Class](https://www.hexaly.com/docs/last/cppapi/optimizer/hxinconsistency.html#hxinconsistency-class): A class representing the inconsistency core of optimization models, identifying the minimal set of expressions responsible for infeasibility.
[HxInterval Class](https://www.hexaly.com/docs/last/cppapi/optimizer/hxinterval.html#hxinterval-class): A value type for interval expressions representing time intervals with start and end bounds, supporting operations like containment checking and element counting.
[HxModel Class](https://www.hexaly.com/docs/last/cppapi/optimizer/hxmodel.html#hxmodel-class): The mathematical optimization model class for creating expressions, decision variables, constraints, and objectives, with extensive methods for model building and management.
[HxParam Class](https://www.hexaly.com/docs/last/cppapi/optimizer/hxparam.html#hxparam-class): A solving parameters class for configuring optimization settings including time limits, thread counts, verbosity, objective thresholds, and advanced tuning options.
[HxPhase Class](https://www.hexaly.com/docs/last/cppapi/optimizer/hxphase.html#hxphase-class): An optimization phase class for lexicographic multiobjective optimization, allowing configuration of time limits, iteration limits, and objective prioritization for each phase.
[HxSolution Class](https://www.hexaly.com/docs/last/cppapi/optimizer/hxsolution.html#hxsolution-class): A solution class for retrieving and setting values of expressions in optimization models, with methods for accessing different data types and checking solution status.
[HxStatistics Class](https://www.hexaly.com/docs/last/cppapi/optimizer/hxstatistics.html#hxstatistics-class): A statistics class providing information about the optimization search process, including running time and iteration counts.
[HxSurrogateParameters Class](https://www.hexaly.com/docs/last/cppapi/optimizer/hxsurrogateparameters.html#hxsurrogateparameters-class): A parameters class for configuring surrogate modeling of computationally expensive external functions, with evaluation limits and pre-defined evaluation points.
[HxVersion Class](https://www.hexaly.com/docs/last/cppapi/optimizer/hxversion.html#hxversion-class): A utility class providing static methods for accessing Hexaly Optimizer version information, license management, and copyright details.
[HxException Class](https://www.hexaly.com/docs/last/cppapi/optimizer/hxexception.html#hxexception-class): An exception class for handling Hexaly Optimizer errors, providing detailed debugging information including file names, line numbers, and error codes.
[HxArrayExternalFunction Interface](https://www.hexaly.com/docs/last/cppapi/optimizer/hxarrayexternalfunction.html#hxarrayexternalfunction-interface): An interface for implementing custom external functions that return arrays, with support for both integer and double array types.
[HxCallback Interface](https://www.hexaly.com/docs/last/cppapi/optimizer/hxcallback.html#hxcallback-interface): An interface for implementing custom callback functions that respond to optimization events, allowing user-defined actions during the search process.
[HxExternalFunction Interface](https://www.hexaly.com/docs/last/cppapi/optimizer/hxexternalfunction.html#hxexternalfunction-interface): An interface for implementing custom external functions that return scalar values, supporting both C++ functors and lambda functions.
[HxCallbackType Enumeration](https://www.hexaly.com/docs/last/cppapi/optimizer/hxcallbacktype.html#hxcallbacktype-enumeration): Enumeration of callback event types for monitoring optimization phases and progress.
[HxErrorCode Enumeration](https://www.hexaly.com/docs/last/cppapi/optimizer/hxerrorcode.html#hxerrorcode-enumeration): Enumeration of error codes for HxException covering API, file, model, callback, license, solver, and internal errors.
[HxObjectiveDirection Enumeration](https://www.hexaly.com/docs/last/cppapi/optimizer/hxobjectivedirection.html#hxobjectivedirection-enumeration): Enumeration defining optimization directions with values OD_Minimize (for minimization objectives) and OD_Maximize (for maximization objectives).
[HxOperator Enumeration](https://www.hexaly.com/docs/last/cppapi/optimizer/hxoperator.html#hxoperator-enumeration): Comprehensive enumeration of mathematical operators available for modeling optimization problems.
[HxSolutionStatus Enumeration](https://www.hexaly.com/docs/last/cppapi/optimizer/hxsolutionstatus.html#hxsolutionstatus-enumeration): Enumeration indicating solution quality from inconsistent to optimal status.
[HxState Enumeration](https://www.hexaly.com/docs/last/cppapi/optimizer/hxstate.html#hxstate-enumeration): Enumeration representing the state of the Hexaly Optimizer environment from modeling to solving phases.

### Hexaly Modeler

[HexalyModeler Class](https://www.hexaly.com/docs/last/cppapi/modeler/hexalymodeler.html#hexalymodeler-class): Main modeler environment class for creating and manipulating virtual machines that execute Hexaly modeling language programs.
[HxmClass Class](https://www.hexaly.com/docs/last/cppapi/modeler/hxmclass.html#hxmclass-class): Class introspection and instantiation class representing loaded classes in modules with property queries and member management.
[HxmField Class](https://www.hexaly.com/docs/last/cppapi/modeler/hxmfield.html#hxmfield-class): Class field representation for object fields declared in Hexaly Modeler classes.
[HxmFunction Class](https://www.hexaly.com/docs/last/cppapi/modeler/hxmfunction.html#hxmfunction-class): Function representation class for both external C++ functions and Hexaly Modeler language functions.
[HxmMap Class](https://www.hexaly.com/docs/last/cppapi/modeler/hxmmap.html#hxmmap-class): Data structure mapping keys to values that functions as both associative table and array with C++-style container behavior.
[HxmMapIterator Class](https://www.hexaly.com/docs/last/cppapi/modeler/hxmmapiterator.html#hxmmapiterator-class): Iterator class for traversing HxmMap data structures providing standard iterator functionality for C++ container operations.
[HxmModule Class](https://www.hexaly.com/docs/last/cppapi/modeler/hxmmodule.html#hxmmodule-class): Module representing a collection of global variables from HXM files with execution and variable management capabilities.
[HxmProperty Class](https://www.hexaly.com/docs/last/cppapi/modeler/hxmproperty.html#hxmproperty-class): Class property representation for getter/setter properties declared in Hexaly Modeler classes.
[HxmValue Class](https://www.hexaly.com/docs/last/cppapi/modeler/hxmvalue.html#hxmvalue-class): Generic value wrapper class representing any value type in the Hexaly Modeler environment including objects, primitives, and other modeler-specific types.
[HxmFunctor Interface](https://www.hexaly.com/docs/last/cppapi/modeler/hxmfunctor.html#hxmfunctor-interface): Interface for implementing custom external functions in C++ that can be called from Hexaly Modeler programs.
[HxmMemberType Enumeration](https://www.hexaly.com/docs/last/cppapi/modeler/hxmmembertype.html#hxmmembertype-enumeration): Enumeration defining types of class members including fields, methods, and properties in Hexaly Modeler classes.
[HxmType Enumeration](https://www.hexaly.com/docs/last/cppapi/modeler/hxmtype.html#hxmtype-enumeration): Enumeration of data types available in the Hexaly Modeler environment including primitives, objects, and special types.

## C# API Reference

### Hexaly Optimizer

[HexalyOptimizer Class](https://www.hexaly.com/docs/last/csharpapi/optimizer/hexalyoptimizer.html#hexalyoptimizer-class): The main class for the Hexaly Optimizer C# library providing a complete optimization environment with model building and solving capabilities.
[HxArray Class](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxarray.html#hxarray-class): A value type for array expressions containing mixed data types like integers, doubles, intervals, or nested arrays, with methods for element access and type checking.
[HxCollection Class](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxcollection.html#hxcollection-class): A value type for collection expressions representing ordered lists or unordered sets of integers, with methods for adding, removing, and querying elements plus C# indexer support.
[HxEvaluationPoint Class](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxevaluationpoint.html#hxevaluationpoint-class): A class for defining known evaluation points for external functions in surrogate modeling, allowing specification of argument and return values to warm-start optimization.
[HxException Class](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxexception.html#hxexception-class): An exception class for handling Hexaly Optimizer errors, providing detailed debugging information including file names, line numbers, and error codes.
[HxExpression Class](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxexpression.html#hxexpression-class): The core mathematical modeling expression class for building optimization models, supporting various operators, operands, and providing C# operator overloading for expression construction.
[HxExternalArgumentValues Class](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxexternalargumentvalues.html#hxexternalargumentvalues-class): A class for querying argument values passed to external functions, providing type checking and value retrieval methods for various data types.
[HxExternalContext Class](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxexternalcontext.html#hxexternalcontext-class): A context class for external functions that allows setting bounds, NaN handling properties, and enabling surrogate modeling for computationally expensive functions.
[HxInconsistency Class](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxinconsistency.html#hxinconsistency-class): A class representing the inconsistency core of optimization models, identifying the minimal set of expressions responsible for infeasibility.
[HxInterval Class](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxinterval.html#hxinterval-class): A value type for interval expressions representing time intervals with start and end bounds, supporting operations like containment checking and element counting.
[HxModel Class](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxmodel.html#hxmodel-class): The mathematical optimization model class for creating expressions, decision variables, constraints, and objectives with C# convenience methods.
[HxParam Class](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxparam.html#hxparam-class): A solving parameters class for configuring optimization settings including time limits, thread counts, verbosity, objective thresholds, and advanced tuning options.
[HxPhase Class](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxphase.html#hxphase-class): An optimization phase class for lexicographic multiobjective optimization, allowing configuration of time limits, iteration limits, and objective prioritization for each phase.
[HxSolution Class](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxsolution.html#hxsolution-class): A solution class for retrieving and setting values of expressions in optimization models, with methods for accessing different data types and checking solution status.
[HxStatistics Class](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxstatistics.html#hxstatistics-class): A statistics class providing information about the optimization search process, including running time and iteration counts.
[HxSurrogateParameters Class](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxsurrogateparameters.html#hxsurrogateparameters-class): A parameters class for configuring surrogate modeling of computationally expensive external functions, with evaluation limits and pre-defined evaluation points.
[HxVersion Class](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxversion.html#hxversion-class): A utility class providing static methods for accessing Hexaly Optimizer version information, license management, and copyright details.
[HxCallback Delegate](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxcallback.html#hxcallback-delegate): Delegate type for implementing custom callback functions that respond to optimization events, accepting HexalyOptimizer and HxCallbackType parameters.
[HxLambdaFunction Delegate](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxfunction.html#hxlambdafunction-delegate): Delegate type for implementing lambda functions used in model expressions, supporting various argument counts and returning HxExpression values.
[HxExternalFunction Delegate](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxexternalfunction.html#hxexternalfunction-delegate): Delegate type for implementing custom external functions that return scalar or array values, supporting integer and double data types.
[HxCallbackType Enumeration](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxcallbacktype.html#hxcallbacktype-enumeration): Enumeration of callback event types for monitoring optimization phases and progress.
[HxErrorCode Enumeration](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxerrorcode.html#hxerrorcode-enumeration): Enumeration of error codes for HxException covering API, file, model, callback, license, solver, and internal errors.
[HxObjectiveDirection Enumeration](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxobjectivedirection.html#hxobjectivedirection-enumeration): Enumeration defining optimization directions with values Minimize (for minimization objectives) and Maximize (for maximization objectives).
[HxOperator Enumeration](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxoperator.html#hxoperator-enumeration): Comprehensive enumeration of mathematical operators available for modeling optimization problems.
[HxSolutionStatus Enumeration](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxsolutionstatus.html#hxsolutionstatus-enumeration): Enumeration indicating solution quality from inconsistent to optimal status.
[HxState Enumeration](https://www.hexaly.com/docs/last/csharpapi/optimizer/hxstate.html#hxstate-enumeration): Enumeration representing the state of the Hexaly Optimizer environment from modeling to solving phases.

### Hexaly Modeler

[HexalyModeler Class](https://www.hexaly.com/docs/last/csharpapi/modeler/hexalymodeler.html#hexalymodeler-class): Main modeler environment class for creating and manipulating virtual machines that execute Hexaly modeling language programs.
[HxmClass Class](https://www.hexaly.com/docs/last/csharpapi/modeler/hxmclass.html#hxmclass-class): Class introspection and instantiation class representing loaded classes in modules with methods to query class properties, inspect members, manage static members, and create instances.
[HxmField Class](https://www.hexaly.com/docs/last/csharpapi/modeler/hxmfield.html#hxmfield-class): Class field representation for object fields declared in Hexaly Modeler classes.
[HxmFunction Class](https://www.hexaly.com/docs/last/csharpapi/modeler/hxmfunction.html#hxmfunction-class): Function representation class for both external C# functions and Hexaly Modeler language functions.
[HxmMap Class](https://www.hexaly.com/docs/last/csharpapi/modeler/hxmmap.html#hxmmap-class): Data structure mapping keys to values that functions as both associative table and array with C# indexer support.
[HxmModule Class](https://www.hexaly.com/docs/last/csharpapi/modeler/hxmmodule.html#hxmmodule-class): Module representing a collection of global variables from HXM files with execution and variable management capabilities.
[HxmProperty Class](https://www.hexaly.com/docs/last/csharpapi/modeler/hxmproperty.html#hxmproperty-class): Class property representation for getter/setter properties declared in Hexaly Modeler classes.
[HxmReferenceScope Class](https://www.hexaly.com/docs/last/csharpapi/modeler/hxmreferencescope.html#hxmreferencescope-class): Reference scope management class for controlling object lifetime and automatic resource cleanup in the modeler environment.
[HxmValue Class](https://www.hexaly.com/docs/last/csharpapi/modeler/hxmvalue.html#hxmvalue-class): Generic value wrapper class representing any value type in the Hexaly Modeler environment including objects, primitives, and other modeler-specific types.
[HxmFunctor Delegate](https://www.hexaly.com/docs/last/csharpapi/modeler/hxmfunctor.html#hxmfunctor-delegate): Delegate type for implementing custom external functions in C# that can be called from Hexaly Modeler programs.
[HxmMemberType Enumeration](https://www.hexaly.com/docs/last/csharpapi/modeler/hxmmembertype.html#hxmmembertype-enumeration): Enumeration defining types of class members including fields, methods, and properties in Hexaly Modeler classes.
[HxmType Enumeration](https://www.hexaly.com/docs/last/csharpapi/modeler/hxmtype.html#hxmtype-enumeration): Enumeration of data types available in the Hexaly Modeler environment including primitives, objects, and special types.