Meet the Hexaly team at EURO 2024

Hexaly Optimizer is a new kind of global optimization solver. Its modeling interface is nonlinear and set-oriented. It also supports user-coded functions, thus enabling black-box optimization and, more particularly, simulation optimization. In a sense, Hexaly APIs unify modeling concepts from mixed-linear programming, nonlinear programming, and constraint programming. Under the hood, Hexaly combines various exact and heuristic optimization methods: spatial branch-and-bound, simplex methods, interior-point methods, augmented Lagrangian methods, automatic Dantzig-Wolfe reformulation, column and row generation, propagation methods, local search, direct search, population-based methods, and surrogate modeling techniques for black-box optimization.

Regarding performance benchmarks, Hexaly distinguishes itself against the leading solvers in the market, like Gurobi, IBM Cplex, and Google OR Tools, by delivering fast and scalable solutions to problems in the spaces of Supply Chain and Workforce Management like Routing, Scheduling, Packing, Clustering, and Location. For example, on notoriously hard problems like the Pickup and Delivery Problem with Time Windows or Flexible Job Shop Scheduling with Setup Times, Hexaly delivers solutions with a gap to the best solutions known in the literature smaller than 1% in a few minutes of running times on a basic computer.

In addition to the Optimizer, we provide an innovative development platform called Hexaly Studio to model and solve rich Vehicle Routing and Job Shop Scheduling problems in a no-code fashion. The user can define its problem and data, run the Optimizer, visualize the solutions and key metrics through dashboards, and deploy the resulting app in the cloud – without coding. This web-based platform is particularly interesting for educational purposes; it is free for faculty and students.

Hexaly Optimizer is a new kind of global optimization solver. Its modeling interface is nonlinear and set-oriented. It also supports user-coded functions, thus enabling black-box optimization and, more particularly, simulation optimization. In a sense, Hexaly APIs unify modeling concepts from mixed-linear programming, nonlinear programming, and constraint programming.

Regarding performance benchmarks, Hexaly distinguishes itself against the leading solvers in the market, like Gurobi, IBM Cplex, and Google OR Tools, by delivering fast and scalable solutions to problems in the spaces of Supply Chain and Workforce Management like Routing, Scheduling, Packing, Clustering, and Location. For example, on notoriously hard problems like the Pickup and Delivery Problem with Time Windows or Flexible Job Shop Scheduling with Setup Times, Hexaly delivers solutions with a gap to the best solutions known in the literature smaller than 1% in a few minutes of running times on a basic computer.

In addition to the Optimizer, we provide an innovative development platform called Hexaly Studio to model and solve rich Vehicle Routing and Job Shop Scheduling problems in a no-code fashion. The user can define its problem and data, run the Optimizer, visualize the solutions and key metrics through dashboards, and deploy the resulting app in the cloud – without coding. This web-based platform is particularly interesting for educational purposes; it is free for faculty and students. 

Hexaly Studio is a no-code SaaS platform for mathematical optimization. Hexaly No-Code Modeler allows users to create a mathematical optimization model based on a business description of its characteristics. The verticals currently handled by Hexaly No-Code Modeler are Vehicle Routing and Production Scheduling. Consequently, using Hexaly Studio, software developers and data scientists can build rich Vehicle Routing or Production Scheduling apps without writing a line of code. This no-code approach is particularly powerful for fast prototyping.

For each vertical, the user can describe the business problem – decisions, constraints, objectives – by selecting the appropriate business features along a straightforward workflow. Then, the Hexaly No-Code Modeler builds a Hexaly model, together with sample data inputs and a dashboard with appropriate widgets to visualize the solutions provided by Hexaly Optimizer. The widgets can be texts, tables, maps, (Gantt) charts, etc. Having explored the solution using sample data, the user can feed the Hexaly model with real-world data and adjust the model constraints and objectives in no-code, or directly by customizing the Hexaly model.

Hexaly Optimizer, formerly known as LocalSolver, is a model and run solver that integrates heuristics and exact methods. A set-based modeling formalism was introduced to simplify the modeling of certain combinatorial problems like routing or packing problems. For instance, in a routing problem, list variables can be used to model the sequence of visits made by each truck. These decision variables are well suited for a heuristic search but are much more difficult to integrate in a mathematical programming approach to compute lower bounds. A direct reformulation in a MILP model introduces a quadratic number of binary decisions with several big M constraints leading to poor scalability and bounds. Hexaly 13.0 automatically detects such structures in a user model and reformulates them in an extended MILP model to compute lower bounds. This model is solved efficiently using state of the art branch-cut-and-price technics from the literature. This talk will present the general approach and the algorithms used for the resolution and some benchmarks on the CVRP library.

Medical transport is increasingly important in ensuring access to care for patients unable to travel independently. The patient transport business comprises many aspects in which optimization needs can arise. For example, it could benefit from optimized vehicle routes, improved and more reliable access to patient care, and improved working conditions for ambulance drivers thanks to more predictable schedules.

This presentation will detail an industrial application developed by Hexaly for a leading French healthcare company. This tool optimizes the operational planning of non-emergency patient transport carried out the following day.

The problem consists in assigning vehicles to employees and creating mission rounds for each employee. The underlying optimization problem is related to the Dial-A-Ride Problem. Indeed, one of the key features of non-emergency patient transport is the possibility of transporting several people in the same vehicle at the same time. Employees’ schedules are also subject to numerous contractual and regulatory constraints such as breaks.

A typical dataset of the problem corresponds to a daily volume of 500 missions to be planned, with around 50 employees and vehicles available.

The optimization tool based on Hexaly Optimizer brought significant gains when it moved into production. The quality of the employee schedules and vehicle tours has improved, with gains of around 10% in terms of revenue per hour, percentage of shared rides and distance traveled.

Hexaly Optimizer, formerly known as LocalSolver, is a “model and run” mathematical optimization solver based on various exact and heuristic methods. The presentation will introduce the different components of Hexaly Optimizer’s local search through disjunctive scheduling problems.

We will first show how its modeling formalism can be used to express various academic and industrial scheduling problems using interval and list decision variables. These models are very compact, which enables the solver to handle even large-scale problems.

Detecting non-overlap constraints in the model provides the solver with valuable information, which can be exploited through various scheduling-specific movements implemented in Hexaly Optimizer’s local search. However, due to the tightness of precedence and non-overlap constraints in good solutions to disjunctive scheduling problems (Job Shop Scheduling Problem, for example), such a small-neighborhood search alone struggles to obtain good performance.

Hexaly Optimizer overcomes this issue by reinforcing its local search component with a solution repair algorithm based on constraint propagation. When a move renders the solution infeasible, it is gradually repaired, one constraint at a time, by heuristically shifting the variables just enough to repair. To extend the local transformation rather than cancel it, and to ensure the procedure is fast, we impose never to backtrack on a previous decision to increase or decrease a variable’s value.