Hexaly Optimizer 14.0

Announcements

Julien Head of Science July 18, 2025

We are pleased to announce the release of Hexaly 14.0, which continues to improve its performance on routing, scheduling, packing, and many other categories of problems (see our benchmarks). In addition, Hexaly 14.0 offers several new modeling features.

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 14.0 brings significant performance improvements for Vehicle Routing Problems (VRP) with various types of constraints and objectives:

Split Delivery Vehicle Routing Problem (SDVRP): average gap of 1.4% in 1 minute on the instances from the 2021 DIMACS challenge with up to 280 clients.
Inventory Routing Problem (IRP): average gap of 0.7% in 1 minute on the Archetti instances with up to 50 clients and 3 days.

The lower bounds delivered by Hexaly 14.0 are significantly improved for Vehicle Routing problems using a combination of Branch-Price-Cut techniques and column elimination techniques:

Capacitated Vehicle Routing (CVRP): average optimality gap below 6% after 10 minutes for all X instances of the CVRP library with up to 1,000 clients.
Capacitated Vehicle Routing with Time Windows (CVRPTW): average optimality gap below 2% after 10 minutes for all Solomon instances with 100 clients. On a subset of Homberger & Gehring instances with up to 1,000 clients, the reported optimality gap is below 10%.
Pickup and Delivery with Time Windows (PDPTW): average optimality gap below 9% after 10 minutes for all Li & Lim instances with 100 clients.

Scheduling

Hexaly 14.0 brings significant performance improvements for multi-mode scheduling problems thanks to the introduction of optional intervals and a better handling of cumulative constraints:

Multi-Mode RCPSP: average gap of 1.6% in 1 minute on MMLIB100 instances with 100 tasks, 3 modes, and 4 resources.
Resource Availability Cost Problem RACP: average gap of 1.8% in 1 minute on an internal benchmark consisting of 300 tasks and 4 resources.

Hexaly 14.0 includes improvements to scheduling problems involving task states, for example, two tasks can now run in parallel on the same machine if they share the same state:

    constraint and(0...nT, i => and(i+1...nT, j => {
        local sameStates <- s[i] == s[j];
        local iBeforej <- end(x[i]) + M[s[i]][s[j]] <= start(x[j]);
        local jBeforei <- end(x[j]) + M[s[j]][s[i]] <= start(x[i]);
        return sameStates || iBeforej || jBeforei;
    }));

Hexaly 14.0 also includes enhancements for project scheduling problems in which task completion times decrease as more resources are allocated to individual tasks:

    // Number of resources affected to the task
    nbResourcesForTask[i in 0...nbTasks] <- int(minResourcesForTask[i], maxResourcesForTask[i]);

    resourcesTasks[k in 0...nbResources][i in 0...nbTasks] <- contains(jobsOrder[k],i);
    for [i in 0...nbTasks] {
        constraint nbResourcesForTask[i] == sum[k in 0...nbResources](resourcesTasks[k][i]);
    }

    // Task duration
    for[i in 0...nbTasks] {
        constraint length(task[i]) == taskDuration[i][nbResourcesForTask[i]];
    }

Packing

Hexaly 14.0 introduces performance improvements for several packing problems:

Bin Packing Problem: average gap of 0.1% in 1 minute on the Irnisch instances with up to 5,500 items.
Bin Packing Problem with Conflicts: average gap of 0.3% in 1 minute on the Muritiba instances with up to 1,000 items.
Constrained Pit Limit: average gap below 6% in 10 minutes on a subset of the MineLib instances with up to 30,000 items and 1.2M precedence constraints.

The lower bounds delivered by Hexaly 14.0 have been significantly improved for packing problems thanks to column elimination techniques.

Bin Packing Problem: average optimality gap of 0.2% in 1 minute on a subset of the Irnisch instances with up to 5,500 items.
Bin Packing Problem with Conflicts: average optimality gap of 1.5% in 1 minute on the Muritiba instances with up to 1,000 items.
Vector Packing Problem: average optimality gap of 0.2% in 1 minute on the Spieksma, Caprara & Toth instances with up to 200 items and 20 dimensions.

Nonlinear

Hexaly 14.0 introduces a new, faster and more robust Interior Point algorithm for convex and nonconvex problems, allowing the Optimizer to find 55 locally optimal solutions in 1 minute on our internal Optimal Power Flow benchmark with 64 instances, including up to 3,000 variables and 15,000 constraints.

Modeler & APIs

Hexaly 14.0 introduces an optional interval decision variable and its related presence operator to easily model multi-mode scheduling problems such as Multi-Mode RCPSP. Several operators have been extended to accept new types of operands; please look at the complete changelog.

Adding several values in a collection with one HXM instruction or a call to collection.addAll() is now possible to speed up solution initialization:

function param() {
    lvalue[i in 0...N] = i;
    l.value = lvalue;
}

An Excel parser has been added to the Hexaly Modeler standard library:

use xlsx;

function main() {
    xlsxDocument = xlsx.open("my_excel_file.xlsx");
    sheet = xlsxDocument.getSheet(0);
    table = sheet.readTable("B2", 46, 34935);
}

New parameters have been added to the Optimizer:

hxWarningLevel: controls the warning computation effort.
hxNbDisplayedObjectives: controls the number of displayed objectives during the search.
hxNbDisplayedViolatedConstraints: controls the number of unsatisfied constraints reported for infeasible solutions.