The research, led by Rui Hu, Xuan He, and Hongtao Hu of Shanghai Maritime University, together with Jiangang Jin of Shanghai Jiao Tong University and Yan Liang of Shanghai Zhenhua Heavy Industries, addresses a deceptively tangled decision problem at the heart of port logistics. In a container yard, rubber-tired or rail-mounted gantry cranes pick up and drop off containers while yard vehicles wait at designated parking positions alongside the container blocks. Where a vehicle parks determines how far the crane must travel to reach it. The crane’s sequence of jobs, in turn, determines when each vehicle is needed and where it should wait. Because these two decisions feed back into each other, they cannot be optimized sensibly in isolation, and the combined problem grows combinatorially explosive as the number of containers, vehicles, and cranes increases.

What sets this work apart from earlier scheduling studies is its explicit treatment of gantry startup energy. Each time a crane begins a new gantry movement, accelerating its massive frame from rest, it consumes a discrete burst of power that is disproportionately large compared with steady-state travel. The authors formulate a mixed-integer linear programming model that captures three distinct sources of energy use: the startup events themselves, the crane’s empty travel between jobs, and its loaded travel while carrying a container. By encoding these components directly into the mathematical model, the framework can reason about trade-offs that cruder models miss entirely, such as accepting a slightly longer empty move to avoid triggering an additional startup.

The optimization pursues two objectives at once: minimizing the makespan, meaning the total time to complete all assigned container handling jobs, and minimizing total gantry energy consumption. These goals genuinely conflict. A schedule that rushes through every job in the shortest possible time may force the crane into many extra repositioning moves and repeated startups, inflating energy use. An energy-thrifty schedule that clusters jobs to minimize crane movement may leave vehicles idling and stretch the overall completion time. Rather than collapsing the two objectives into a single weighted score, which would hide the shape of the trade-off, the researchers treat the problem as bi-objective and seek a set of Pareto-optimal solutions representing the best achievable compromises.

Solving such a problem exactly is impractical at realistic scale, so the team developed an improved version of the non-dominated sorting genetic algorithm II, or NSGA-II, a widely used evolutionary method for multi-objective optimization originally introduced by Deb and colleagues in 2002. Genetic algorithms maintain a population of candidate schedules and iteratively breed, mutate, and select them, with non-dominated sorting ensuring that the population spreads across the full trade-off frontier rather than converging on a single point. But a generic implementation struggles with the specific structure of crane-and-vehicle scheduling, so the authors embedded several problem-aware strategies into the algorithm’s machinery.

The first strategy concerns how the population is initialized. Instead of generating random schedules, the improved algorithm employs a parking-slot allocation heuristic that constructs high-quality starting solutions by assigning vehicles to parking positions in a way that anticipates the crane’s workload. Good initialization matters enormously in evolutionary computation: a population that already respects the problem’s constraints and near-optimal structure gives the search a running start and prevents generations from being wasted on obviously poor schedules. The heuristic effectively seeds the algorithm with solutions that a human dispatcher might spend hours crafting by trial and error.

Second, the researchers designed neighborhood search operators tailored to the physics of crane operation. These operators make targeted local modifications to a schedule, such as reordering jobs or shifting a vehicle’s parking slot, specifically to eliminate unnecessary crane movements and reduce the number of gantry startup events. Because the operators encode domain knowledge about which changes are likely to help, they refine solutions far more efficiently than random mutation. Third, the algorithm incorporates a destruction-reconstruction local search mechanism, in which part of a promising solution is deliberately dismantled and rebuilt in a different way. This aggressive intensification step pushes the search deeper into high-quality regions of the solution space while the rebuilding randomness helps it escape local optima, the deceptive peaks where simpler search methods tend to get trapped.

Numerical experiments built on realistic terminal operation scenarios put the framework to the test. The results showed that the improved algorithm produces high-quality trade-off solutions, achieving significant reductions in energy consumption while maintaining operational efficiency, according to the study. In practical terms, the approach gives terminal operators a menu of schedules rather than a single prescription: one end of the frontier favors the fastest possible completion, the other favors the leanest energy footprint, and intermediate points quantify exactly how much time must be sacrificed to save a given amount of energy. That kind of explicit quantification is precisely what decision makers need when terminals face both tight vessel departure windows and mounting pressure to cut emissions.

The significance of the work extends beyond the container yard. Ports are under intensifying scrutiny for their environmental impact, and yard equipment represents one of the largest controllable energy loads in terminal operations. Previous studies have integrated energy considerations into port equipment scheduling, but the authors note that the energy cost of gantry startups has received relatively limited attention despite its magnitude. By proving that startup-aware scheduling can be solved effectively with evolutionary computing, the study opens a path for terminals to retrofit their dispatch software with energy intelligence without replacing hardware. The savings would compound across thousands of daily crane cycles at a major terminal.

More broadly, the research is a case study in how hybrid intelligence, combining evolutionary search with heuristic and local-search techniques, can crack industrial scheduling problems that defeat both pure mathematical programming and off-the-shelf metaheuristics. The authors describe their results as confirming the effectiveness of integrating evolutionary computing and heuristic search for intelligent decision support in complex industrial scheduling systems. As automation spreads through global supply chains, from automated guided vehicles to twin stacking cranes, the lesson is that the smartest systems will be those that understand the machinery they orchestrate, down to the energy spike of a single gantry startup, and that treat speed and sustainability not as rivals to be traded blindly but as dimensions to be balanced with mathematical precision.

Subject of Research: Bi-objective optimization of integrated yard crane scheduling and vehicle positioning considering gantry startup energy consumption at container terminals

Article Title: Integrated yard crane scheduling and vehicle positioning considering gantry startup and energy consumption

Article References: Hu, R., He, X., Hu, H., Jin, J., & Liang, Y. (2026). Integrated yard crane scheduling and vehicle positioning considering gantry startup and energy consumption. Applied Intelligence, 56(14), Article 415. https://doi.org/10.1007/s10489-026-07463-z

Image Credits: AI Generated

DOI: 10.1007/s10489-026-07463-z

Keywords: yard crane scheduling, container terminals, energy consumption, gantry startup, vehicle positioning, NSGA-II, bi-objective optimization, evolutionary algorithm, mixed-integer programming, port logistics, heuristic search, makespan

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