Hexaly Optimizer 15.0

Announcements

Julien Head of Science July 21, 2026

We are pleased to announce the release of Hexaly Optimizer 15.0, which continues to deliver improved performance on routing, scheduling, packing, and many other problems (see the benchmarks).

Regarding performance improvement, two types of gaps are mentioned below. When simply written as “gap”, it means the gap to the state of the art (SOTA): the relative gap in % between the solutions computed by Hexaly on a standard server (AMD Ryzen 7 7700 processor, 8 cores, 3.8 GHz, 32MB cache, 32GB RAM) and the best known solutions available by the research, computed using dedicated algorithms within days of running times on much more powerful hardware. When referred to as “optimality gap”, it means the gap to optimality: the relative gap in % between the best feasible solution and the best dual bound found by the solver.

Routing

Hexaly 15.0 brings significant performance improvements for different types of vehicle routing problems:

Capacitated Vehicle Routing Problem: average gap of 0.5% in 1 minute of runtime across the X instances from the CVRPLib with up to 1,000 customers. In addition, Hexaly delivers improved lower bounds with an average optimality gap reduced to 4.5% after 10 minutes of runtime.
Prize Collecting Vehicle Routing Problem with Time Windows: average gap of 1.7% in 1 minute of runtime on internal benchmark with 1,000 customers.
Pickup and Delivery Problem: average gap of 3.9% in 1 minute of runtime on Li & Lim instances with up to 1,000 customers.

These specific gains also lead to broader performance improvements in solving real-world Vehicle Routing applications.

Scheduling

Hexaly 15.0 combines no-good search and column elimination to compute lower bounds for scheduling problems. This allows Hexaly to report an average optimality gap of 2.9% in 1 minute of runtime on the standard Flexible Jobshop benchmark and a more general improvement in the computation of lower bounds regarding scheduling problems with various objectives (makespan, sum of completion times, sum of resource completion times, etc.)

Other performance improvements have been made on real-world Disjunctive Scheduling applications with complex transitions and real-world Production Scheduling applications.

Packing

Hexaly 15.0 improves its performance on the primal and dual sides for huge packing problems with precedence constraints, such as the Ultimate Pit Limit and the Constrained Pit Limit. On the standard instances coming from the Minelib and containing up to 112,000 items and 3M precedences, Hexaly 15.0 obtains the following results:

Ultimate PIT limit: proven optimal solutions delivered for all instances in less than 10 seconds of runtime.
Constrained PIT Limit: optimality gap below 4.8% within 10 minutes of runtime.

Nonlinear

Hexaly 15.0 comes with an improved interior-point method, enabling significant performance gains for Optimal Power Flow (OPF) models. Hexaly finds solutions within 1% of the best-known solution for 231 out of 390 instances from Power Grid Lib in less than 1 minute of runtime.

Hexaly 15.0 extends the external operator to return gradient information when available. This information will be used by Hexaly’s internal algorithms rather than automatic differentiation. A typical use case is optimizing a neural network’s output.

function value(args) {
    return pow(args[0],2);
}

function gradient(args) {
    return { 2 * args[0] };
}

function model() {
    x <- float(-10, 10);
    f <- doubleExternalFunction(value, gradient);
    obj <- call(f, x);
    minimize obj;
}