Nineteen years, three hundred tasks, a better schedule

For one project in a public research benchmark, 634 was a remarkably stubborn number. It was the shortest known completion time for a schedule involving 300 activities, competing demands on shared resources and a web of dependencies. The result dated from 2007. As algorithms improved and computers grew more powerful, the number remained.

In 2026, 4colors found a schedule that finished at 630.

Four units might appear to be a small improvement. But 630 was already the published mathematical lower bound: a limit showing that no valid schedule could finish earlier. The new schedule reached it exactly. A problem that had remained open for nineteen years was closed.

This was not an isolated result. Across a benchmark of 480 projects, 4colors' schedules were best-known on 113 instances in the results comparison of October 29, 2026. Eleven matched published lower bounds. The work offers a window into one of optimization's enduring questions: how much better can a solution become when we change the way we search for it?

The mathematics of getting things done

A project schedule looks like a list of activities placed on a timeline. Its mathematics is much richer.

Some activities cannot start until others finish. Many depend on the same crews, machines or equipment. A resource used in one place is temporarily unavailable elsewhere. Bringing one task forward can free an important path through the project, or delay several other tasks that need the same capacity.

The research field calls this the resource-constrained project scheduling problem. Its objective is to find the shortest possible project duration while respecting both the order of activities and the limits on shared resources.

The benchmark's RG300 benchmark gives that challenge a particularly demanding form. It contains 480 carefully constructed projects, each with 300 activities and four types of renewable resources. The projects vary systematically in the density of their dependencies, how heavily resources are used and how scarce those resources are. This is a deliberate experimental design, not a collection of conveniently chosen examples.

Even a valid schedule is hard to find in some forms of the problem. Finding an excellent one means navigating an immense collection of alternatives, many of which differ in only a handful of decisions. A single change near the beginning can ripple through hundreds of subsequent start times.

A record from another era

In 2007, Dieter Debels and Mario Vanhoucke published an influential decomposition-based genetic algorithm for project scheduling. The method produced many of the leading results on RG300, establishing a reference point for subsequent research.

The field did not stand still. Researchers explored exact methods, constraint programming, mathematical bounds and new search strategies. Hardware improved. More computational effort was devoted to familiar benchmark instances. Yet numerous best-known schedules survived from the original 2007 work.

The rules of the problem stayed the same. What changed was the search.

In 2026, 4colors began replacing some of those long-standing results. As our algorithms developed, they also improved schedules produced earlier in the same research effort. What matters is the latest answer for each distinct problem, rather than the number of successive improvements along the way.

By October 29, 4colors' schedules were best-known on 113 of RG300's 480 instances. Some of those values are shared with other methods; others improved records that had stood since 2007. Among those advances, 49 were the first reported improvements to the original best-known schedules.

These results are publicly checkable schedules, not predictions of how an algorithm might perform. Each is a proposed set of activity start times that can be tested against the benchmark's resource and precedence rules. The benchmark's maintainers publish submitted results. The rules of the problem stayed the same. What changed was the search.

When a record meets a mathematical limit

To appreciate the significance of that four-unit improvement, it helps to distinguish two kinds of answer.

A best-known schedule tells us how short a project has been made so far. It is an achievement, but it leaves open the possibility that a still better schedule exists. A lower bound provides the opposite kind of information: a mathematically established limit below which no valid schedule can go.

A best-known schedule tells us how well we have done. A lower bound tells us how well we could possibly do. When the two numbers meet, the search is complete for that particular instance.

For RG300_70, the best-known completion time had remained at 634 since 2007. Other researchers later established a lower bound of 630. The four missing units were a narrow but genuine gap between what had been achieved and what mathematics said was possible.

The schedule found by 4colors closes that gap. The same thing happened on ten other RG300 instances, where our schedules also matched published lower bounds. Those bounds come from independent mathematical research; the contribution here is finding valid schedules that reach them.

For most of RG300, the two sides have not yet met. The best-known schedules may still improve, and stronger mathematical bounds may further narrow the space between possibility and proof.

The surprising difficulty of having choices

One of the more intriguing patterns in the results concerns the nature of the problems being improved.

It is tempting to assume that the hardest project is always the one with the fewest resources. Scarcity certainly creates difficult decisions. But RG300 also contains projects where resources are relatively plentiful, allowing many activities to run in parallel and leaving a great deal of freedom about their order.

A best-known schedule tells us how well we have done. A lower bound tells us how well we could possibly do.

That freedom can make the search harder in a different way. A tightly constrained project may rule out most possible sequences almost immediately. A more flexible one admits many plausible schedules, with small differences in timing that may determine which finishes first. There is more room to maneuver, and more room for an algorithm to overlook a better arrangement.

Many of 4colors' new results came from this relatively unconstrained part of the benchmark. It is a useful reminder that the difficulty of optimization is not measured by the number of constraints alone. Sometimes the challenge lies in the abundance of choices that remain.

Better schedules begin with better algorithms

An algorithm for scheduling needs more than a way to produce a valid timetable. It must decide which possibilities deserve attention, which decisions can be revised and how to use the time available for computation.

That makes algorithm design itself an optimization challenge. At 4colors, we combine mathematical reasoning, computational experimentation and automated exploration of algorithmic ideas. Promising methods are tested on demanding problems, refined and tested again. The RG300 work is part of that continuing search for more effective ways to navigate complex decisions.

Benchmarks make progress visible. They hold the problem definition steady while new approaches compete to improve the result. They also expose limits: a method that excels on one family of projects may behave differently when dependencies tighten, resources become scarce or the scheduling rules change.

The achievement is not simply a shorter timetable. It is evidence that a different search can reveal answers that years of earlier work left undiscovered.

Beyond the benchmark

RG300 uses abstract units of time and deliberately constructed projects. Four units in one of its schedules are not four days saved in a factory or four hours recovered on a construction site. The benchmark measures algorithmic progress under controlled conditions; the value of that progress in an operation depends on the operation itself.

The underlying decisions, however, are familiar. Manufacturing plans depend on machine capacity and the sequence of operations. Engineering programs need to coordinate tasks and specialist teams. Large projects must balance deadlines, dependencies and resources that cannot be in two places at once.

In each setting, there is value in finding a better feasible plan, exploring alternatives and responding when conditions change. Stronger scheduling algorithms expand what planners and developers can investigate with the time and resources they have.

Nineteen years after RG300's early records were set, the benchmark is still yielding better schedules. Some gaps have closed. Many remain. That is what makes the result both satisfying and promising: in a problem studied for nearly two decades, there were still better answers waiting to be found.

Explore 4colors Optimizer for Scheduling · Explore project scheduling

Research reference: RG300, developed by Debels and Vanhoucke (2007). Numerical results reflect the 4colors comparison dated October 29, 2026. The best-known values are subject to ongoing updates as new schedules are submitted.