The Geometry of the Circular Economy

The fundamental shift in the architecture of economic activity that the circular economy brings with it is increasingly taking on the contours of a distinct geometric dimension. It's not just the mindset and habits of producers and consumers that are being transformed—the very spatial architecture of waste flows is changing: from the micro level of packaging, forms, and tools for municipal solid waste accumulation to the macro level of urban arteries, rethinking ergonomics and installing production lines along which waste moves. Geometry is ceasing to be a metaphor or discipline and becoming a working tool in shaping a culture of responsible behavior among producers and consumers, and in substantiating technical and economic proposals in interdisciplinary closed-loop economy projects in an era of rapid artificial intelligence (AI) development.

The Geometry of Packaging: Why Shape Matters

The fate of packaging on the sorting line is largely predetermined by its shape. Flat, flexible containers—film, bags, wrappers—represent the main challenge for optical scanners. They're difficult to identify and even harder to separate precisely using air jets. Rigid, three-dimensional packaging—bottles, cans, trays—sorts far more efficiently. Multi-layer packaging like carton beverage containers, composed of cardboard, aluminum, and plastic, has remained a stumbling block for recyclers for decades.

The response to this challenge has been a convergence of two strategies:

• Simplifying geometry and rethinking the composition of the material itself.
• Implementing digital marking that allows equipment to "see" through the form.

The Holy Grail 2.0 project, which brought together brands and technology companies, demonstrated that digital watermarks—invisible markers applied across the entire surface of packaging—deliver sorting accuracy of approximately 90% and higher even under challenging industrial conditions, with contamination and material overlap¹. During trials at the Hündgen facility in Germany, detection efficiency ranged from 86.7% to 93.6%².

In parallel, the mono-material direction is developing. Packaging manufacturer Mondi conducted a series of trials proving that flexible pouch packaging (category 05 PP, 7) and trays made from mono-material polypropylene are successfully recognized and directed into the correct sorting stream at modern waste processing facilities. Tests conducted jointly with the Dutch National Test Centre for Circular Plastics (NTCP) modeled real-world scenarios and confirmed that top film and thermoformed semi-rigid trays consistently end up in the right fraction³.

For packaging that cannot be simplified, artificial intelligence technologies become the key solution. Tetra Pak planned to invest £1.4 million in deploying computer vision systems based on British startup Recycleye at sorting facilities across the UK, training them to specifically identify multilayer carton packaging in mixed waste streams⁴.

The Circpack service by Veolia uses RFID tags (radio frequency tags) to test the recyclability of new packaging types under real-world conditions—samples with radio tags are introduced into the general waste stream at a facility in Ochtendung, Germany. This technology creates a feedback loop between sorting and packaging design, allowing manufacturers to adjust their designs at early stages⁵.

According to data from PPK REO, some organizations in Russia handling municipal solid waste (MSW) are beginning to use computer vision technology to improve MSW sorting quality. Its implementation is also aimed at automating data collection, which can be distorted when filling out 2-TP waste forms⁶. According to research by Bashkatov D.A., Rusinov R.A., and others, the cost of implementing an AI system at enterprises can reach approximately 190 million rubles. In the authors' view, major expense categories include: a robotic line (3 units) at 84 million rubles (44.2% of total costs), robotic AI stations (3 units) valued at 66 million rubles (34.7%), data collection, cleaning, and annotation for AI training at 21 million rubles (11%), service maintenance at 6 million rubles per year (3.1%), and technical maintenance at 5 million per year (2.6%)⁷According to research by CEWEP, the use of AI systems in municipal solid waste sorting can reduce processing time by 60%, decrease workload by 40%, and increase the volume of fractions suitable for recycling by 10%⁸.

Urban Geometry: Flow Graphs and Movement Arteries

If packaging design determines its fate once it hits the bin, then urban geometry and well-planned flow graphs determine how efficiently waste reaches recycling facilities. In this mathematical model, streets become edges, while container sites and landfills become vertices, constrained by limiting parameters (garbage truck capacity, noise pollution schedules in residential areas, and the equipment and accessibility of waste collection points)⁹. The choice of mathematical apparatus depends directly on development density.

In neighborhoods with high container density, specialists solve the Capacitated Arc Routing Problem (CARP), where garbage trucks must travel along every street in the service zone. In sparsely developed areas, the problem transforms into the Vehicle Routing Problem (VRP)—specific points must be visited, but the path between them can be arbitrary.

Particularly strong results come from applying the classic Chinese Postman Problem, which solves the challenge of traversing all graph edges with minimal repetition.

 A study conducted in Cajamarca, Peru, showed that optimizing municipal solid waste collection routes based on weighted Eulerian graph theory reduced the total average route distance by 66.6%¹⁰.

An even more comprehensive approach was demonstrated in the Çiğli district of Izmir, Turkey. GIS modeling with adaptation of a standard VRP solver for arc routing tasks and prohibition of U-turns to simulate real traffic conditions reduced collection time by 16.94%, distance by 21.47%, fuel consumption by 24.57%, and CO₂ emissions by 29.5%¹¹.

In the Bulgarian city of Montana, the ROSE dynamic routing platform, which analyzes data from container fill-level sensors, reduced weekly garbage truck mileage by 6-10%, while weekly CO₂ emissions dropped by approximately 15 kg for a pilot zone of 80 containers¹².

V. Mavrin and I. Makarova proposed a decision support system (DSS) for fleet management that reduced total logistics costs by 40.64% compared to the baseline scenario through precise calculation of optimal vehicle composition¹³.

In Russia, similar approaches are being applied at the local level. Simulation modeling in the Krasnoselsky district of Saint Petersburg identified suboptimal collection points, making it possible to redistribute them and reduce transportation costs by up to 1 million rubles per month¹⁴.

Thinking Encoded in Geometry

A common thread runs through all these cases: the circular economy demands not merely technological solutions, but a transformation in responsible thinking among both producers and consumers at every stage of a product's lifecycle. Packaging geometry ceases to be purely a matter of marketing and convenience. It becomes a factor determining the very possibility of returning material to the cycle. Designing urban space and waste flow networks—from collection points to sorting centers—is evolving into an independent engineering discipline at the intersection of municipal management, logistics, and applied mathematics, with computer science contributing through the development of specialized services and applications.

The contours of this new reality are already emerging. Packaging is designed not for the supermarket shelf, but for the sorting line. Garbage truck routes are calculated not by routine schedules, but by data from fill-level sensors. Urban planning begins to account not only for human traffic flows, but also for the arteries through which waste moves as a resource. It is in this geometric reassembly of familiar processes and meanings that the architecture of the circular economy takes shape.