A memetic ant colony system algorithm for multiple machine scheduling in additive manufacturing with orientation selection of parts and energy costs ​

Imagine a factory floor where machines do not cut away material to shape a part, but instead build it up, layer by layer, from a digital blueprint. This is additive manufacturing, a process often called 3D printing, which has revolutionized how we create everything from aircraft components to medical implants. Because these machines can produce complex shapes without molds, they offer incredible flexibility. However, this flexibility comes with a logistical puzzle. When a factory has several of these machines running at once, and a large order of different parts needs to be made, the manager must decide two difficult things at the same time: which parts should be grouped together to print in a single batch, and how those parts should be rotated on the machine bed to fit as many as possible. Furthermore, these machines are energy hogs; the lasers and heaters that fuse the material consume vast amounts of electricity, making the cost of running them a major concern for both the environment and the bottom line.

For years, researchers have tried to solve this scheduling puzzle, mostly focusing on how to finish the work as quickly as possible. They have developed various computer programs to figure out the best way to pack parts into batches and assign them to machines. Yet, a significant gap remained in the research. Most studies ignored the fact that a single part can often be printed in several different orientations, each changing how much space it takes up and how much energy it consumes. Additionally, few studies have prioritized saving energy over saving time, even though energy costs are rising and sustainability is becoming a critical goal for modern industry.

A team of researchers from the University of Seville in Spain has now tackled this complex problem with a new approach that combines two powerful computational strategies. They created a sophisticated algorithm designed to handle the dual challenges of packing parts efficiently and minimizing the energy required to print them. Their method, which they call a memetic ant colony system, draws inspiration from how real ant colonies find the shortest path to food. In nature, ants leave behind a chemical trail called pheromones; the more ants that travel a successful path, the stronger the scent becomes, guiding others to follow. The researchers translated this behavior into a computer program where virtual "ants" explore millions of possible ways to group and orient parts. As the program runs, it learns which combinations of parts and rotations lead to the best results, reinforcing those successful patterns while discarding the inefficient ones.

To make this system even more effective, the researchers added a second layer of intelligence. Once the virtual ants propose a solution, a local search procedure steps in to fine-tune it. This step acts like a meticulous inspector, making small adjustments—such as rotating a single part or swapping two parts between batches—to see if the energy cost can be lowered further. By combining the broad exploration of the ant colony method with this precise local refinement, the algorithm can navigate the massive number of possibilities involved in scheduling these machines without getting stuck in a suboptimal solution.

The team tested their new algorithm using a wide range of scenarios, including standard test cases from previous studies and new, more complex scenarios where parts could be printed in two or three different orientations. They compared their results against the best-known solutions from existing methods and against exact mathematical models that are known to find the perfect answer but are too slow to run on large problems. The results were striking. In tests designed to minimize the average cost of production, the new algorithm found better solutions than the existing methods in nearly half of the cases and matched the best results in the rest. When the goal was to finish the work as quickly as possible, the algorithm again outperformed previous methods, finding faster schedules for many of the test cases.

Perhaps the most significant finding relates to energy. When the researchers allowed the algorithm to choose from multiple orientations for each part, the energy savings were substantial. In scenarios with two alternative orientations, the average energy cost dropped by about 3.3 percent. When three orientations were available, the savings increased to nearly 6 percent. In some specific cases involving three machines, the reduction reached as high as 9.5 percent. These numbers might seem small at first glance, but in an industrial setting where machines run continuously, such reductions translate into massive savings in electricity bills and a significant decrease in the carbon footprint of the manufacturing process.

The study also revealed an important trade-off. When the scheduling focused strictly on finishing the job as fast as possible, the energy costs often skyrocketed, increasing by more than 20 percent on average compared to schedules designed specifically to save energy. In the most extreme cases, with six machines running, the energy penalty for prioritizing speed over efficiency could reach 36 percent. This finding suggests that simply trying to print faster is not always the most efficient strategy. Instead, a balanced approach that considers both time and energy, and that takes advantage of the flexibility to rotate parts, offers a much smarter path forward.

The researchers validated their findings by running the algorithm on a standard computer processor, completing the complex calculations in a matter of minutes or hours, whereas the exact mathematical models often failed to find a solution within a reasonable timeframe. This demonstrates that the new method is not only effective but also practical for real-world factories that need to make decisions quickly. By proving that considering alternative part orientations can significantly lower energy costs without sacrificing speed, this work provides a clear roadmap for manufacturers looking to make their additive production lines more sustainable and cost-effective. The study concludes that while the problem of scheduling these machines is incredibly complex, the right combination of intelligent search and local refinement can unlock efficiencies that were previously out of reach.