The problem the researchers address is known formally as the container relocation problem, a combinatorial optimisation challenge that has occupied operations researchers for decades. In its classic, static form, the setup is a yard bay represented as a grid of stacks and tiers, where a given set of containers sits waiting to be retrieved in a known order. Because the retrieval sequence is fixed and fully known in advance, algorithms can plan the entire sequence of relocations from beginning to end. That assumption, however, is precisely where the static model breaks down in practice. Real container terminals are living systems: new containers arrive continuously while others are being loaded onto vessels, and the exact arrival times of future containers are rarely known with certainty when decisions about the current retrieval must be made.

This messier, more realistic setting is called the dynamic container relocation problem, and it is the focus of the new study. In the dynamic variant, containers enter the bay over time and are retrieved as their departure moments arrive, meaning that a decision about where to place a container today affects how easily it can be retrieved tomorrow, in circumstances that cannot be fully predicted. Traditional optimisation methods, which typically require complete information about the problem instance before they can compute a solution, struggle in this environment. Exact methods and metaheuristics can produce excellent plans when the whole picture is visible, but when information about container arrivals is not known in advance, recomputing an optimised plan after every new arrival becomes computationally prohibitive in the fast-paced setting of a working terminal.

The practical alternative, and the starting point for this research, is a family of fast decision-making procedures known as relocation rules. A relocation rule is a constructive heuristic: rather than planning the entire operation in advance, it makes a good decision on the spot each time the crane needs to move a container. When a blocking container must be relocated, the rule evaluates the available empty slots in the bay and selects one according to some criterion, typically based on properties of the containers themselves, such as their retrieval priorities or expected departure times. Because each decision is made in a fraction of a second, relocation rules can respond immediately to new arrivals and changing conditions, which makes them well suited to the dynamic setting where plans cannot be fixed in advance.

There is a catch, however, and it is the reason the authors turned to automated methods. Relocation rules are highly domain specific. A rule that performs brilliantly on one configuration of stacks, one pattern of arrivals, or one distribution of container priorities may perform poorly on another. Human experts have designed many such rules by hand over the years, each encoding a particular intuition, for example about whether it is better to place a container on top of a box that will leave sooner or later. But designing effective rules manually is difficult and laborious, and there is no guarantee that human intuition captures the subtle statistical structure of the problem. The space of possible rules is vast, and the best-performing rules may combine problem features in ways no designer would think to try.

The study’s answer to this difficulty is genetic programming, an evolutionary computation technique that automatically breeds computer programs toward a desired behaviour. In genetic programming, candidate solutions are represented as tree-structured expressions that combine elementary functions and problem-specific variables, in this case the measurable properties of containers and stacks that a relocation decision can consider. A population of randomly generated rules is evaluated on a set of problem scenarios, the rules that achieve lower relocation counts are selected as parents, and new rules are created by mixing and mutating the expressions of successful individuals. Over many generations, this Darwinian process sculpts decision logic that no human wrote by hand, tailored precisely to the objective of minimising the number of relocations needed to clear the retrieval demands of the bay.

What makes this application particularly compelling is that the evolved rules are not black-box neural networks requiring specialised hardware. A genetic programming rule is a symbolic expression, readable in principle and executable in microseconds, which means it can be embedded directly into terminal operating software and consulted every time a crane must choose a slot for a relocated container. The rule effectively becomes a piece of distilled expertise, discovered by the evolutionary process rather than by a human analyst, and expressed in the same mathematical vocabulary that human-designed heuristics use. This transparency matters in industrial settings, where operators and software engineers need to understand and trust the logic that guides million-dollar equipment.

To find out whether machine-bred rules genuinely beat human craftsmanship, the researchers put their automatically generated relocation rules through a demanding trial. The evolved rules were compared against several manually designed relocation rules drawn from the literature, across a wide range of dynamic problem scenarios covering different bay sizes, stack configurations, and patterns of container arrivals and retrievals. The evaluation was therefore not a single head-to-head contest but a broad stress test designed to reveal whether the advantage of automated design holds generally or only under favourable conditions. The outcome was unambiguous: the automatically generated rules significantly outperformed their manually designed counterparts across the tested scenarios, demonstrating that the evolutionary approach consistently discovers decision logic superior to the accumulated intuition of human heuristic designers.

The significance of this result extends beyond the container yard. The dynamic container relocation problem is a representative example of a broad class of real-time scheduling and routing challenges in which decisions must be made under uncertainty, from vehicle dispatching to machine scheduling on factory floors. The study’s central lesson is that when the problem environment is too dynamic for full optimisation and too intricate for hand-crafted heuristics, automated heuristic design offers a third path: algorithms that manufacture fast, effective decision rules on demand, matched to the statistical texture of the specific operational environment. As global trade volumes continue to grow and terminals face relentless pressure to turn vessels around faster, the ability to automatically generate and refresh such rules could become a standard tool in the logistics engineer’s kit.

The work, published open access on 28 August 2026 and supported by funding from the Croatian Science Foundation, the European Union’s NextGenerationEU framework, the Spanish Government, and the Principality of Asturias, also highlights a quiet shift in how optimisation research is done. Rather than asking researchers to design better heuristics one at a time, the field is increasingly asking machines to explore the design space themselves, with humans defining the objective and the ingredients. In the case of the dynamic container relocation problem, that shift has already paid off with rules that move fewer containers, waste less crane time, and adapt gracefully to a world in which the next arrival is never certain. For an industry that moves the physical backbone of the global economy, even small percentage improvements in yard efficiency translate into enormous savings, and this study shows that evolution, simulated in software, can out-design the experts who built the field.

Subject of Research: Automated design of relocation rules using genetic programming for the dynamic container relocation problem

Article Title: Automated design of relocation rules for the dynamic container relocation problem

Article References: Automated design of relocation rules for the dynamic container relocation problem. (n.d.). https://doi.org/10.1007/s40747-026-02467-1

Image Credits: AI Generated

DOI: 10.1007/s40747-026-02467-1

Keywords: genetic programming, container relocation problem, dynamic container relocation problem, relocation rules, combinatorial optimisation, heuristics, container terminals, evolutionary computation, port logistics, automated heuristic design, operations research, artificial intelligence