⚡ electrical engineering

Quantum-Inspired Evolutionary Optimization for CO2 Sensor Placement on the UCF Campus: Mathematical Formulation and Baseline Validation

This paper presents a quantum-inspired evolutionary optimization framework for placing 11 CO2 sensors on the UCF campus with strict spatial constraints, achieving a 72.73% coverage of high-traffic pedestrian corridors—double the current baseline—while establishing a scalable methodology for municipal sensor network deployment and calibration.

Original authors: Eswara Sai Kumar Kandula, Phani Raja Bharath Balijepalli, Utkarsh Singh, Soheil Sabri, Azadeh Vosoughi, Haofei Yu, Roopesh Mathur, Abhishek Chopra, Rut Lineswala

Published 2026-08-06

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Eswara Sai Kumar Kandula, Phani Raja Bharath Balijepalli, Utkarsh Singh, Soheil Sabri, Azadeh Vosoughi, Haofei Yu, Roopesh Mathur, Abhishek Chopra, Rut Lineswala

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to listen to a bustling city square, but you only have a handful of tiny, low-cost microphones. You want to know exactly where the loudest conversations are happening so you can understand the city's mood. This is the world of urban sensing, a field where scientists use networks of small devices to monitor things like air quality. The challenge isn't just having the microphones; it's figuring out exactly where to hang them. If you put them in the middle of a quiet park, you'll hear nothing interesting. If you put them inside a building, they won't work at all. This is a giant puzzle called combinatorial optimization, which is just a fancy way of saying "finding the best arrangement out of a huge number of possibilities."

To solve this, researchers often use evolutionary algorithms, which are like digital versions of natural selection. They create a bunch of random solutions, see which ones work best, mix them together, and repeat the process until they find a winner. Recently, scientists have started borrowing ideas from quantum mechanics—the weird physics of tiny particles—to make these algorithms even smarter. Instead of just picking one spot at a time, these "quantum-inspired" tools can look at many possibilities at once, like a super-fast explorer checking every path in a maze simultaneously. This matters because getting air quality data right helps cities make better decisions about public health, traffic, and where to build new parks.

The Great Sensor Hunt on the UCF Campus

Now, let's zoom in on a specific adventure: placing carbon dioxide (CO2) sensors on the University of Central Florida (UCF) campus. The researchers faced a tricky situation. They had a budget for exactly 11 sensors, and each sensor could "see" in a circle with a radius of 223 meters. But the campus wasn't an empty field; it was a complex maze of buildings, lakes, and dense forests. You can't stick a sensor inside a wall, in the middle of a lake, or deep in a thick patch of trees where it would get blocked from the sky and the wind.

The team asked a simple but hard question: Where should we put these 11 sensors to catch the most CO2 from people walking around?

The Old Way vs. The New Way

Before this study, the campus had 11 sensors already installed. The researchers checked how well they were doing. It turned out they were covering only 36.29% of the high-traffic walking paths where students and staff actually breathe the air. The old placement was like trying to watch a soccer game by standing in the empty bleachers far away from the field; it gave a general view of the whole stadium but missed all the action.

The researchers wanted to do better. They built a digital map of the campus and used a special computer program called Quantum-Inspired Evolutionary Optimization (QIEO). Think of this program as a super-smart game player that doesn't just guess; it uses "quantum" tricks to explore millions of possible sensor locations in seconds.

The Rules of the Game

The computer had to follow strict rules, or "constraints," to make sure the solution was real-world ready:

No Go Zones: Sensors couldn't be placed inside buildings, water, or dense forests.
The Footprint Rule: Even if the center of the sensor was safe, its "view" (a 223-meter circle) couldn't overlap too much with forbidden areas. For example, the view could overlap with a forest by no more than 15%, but it had to stay completely clear of buildings and water.
The Goal: Maximize the number of "priority points"—spots along busy walkways where people are most likely to be exposed to CO2.

The Big Discovery

When the QIEO program ran its simulations, it found a new arrangement for the 11 sensors that was dramatically better.

The Result: The new layout covered 72.73% of the busy walking paths.
The Comparison: This is exactly 2 times (or 2×) better than the current setup!
The Bonus: It also beat a standard "greedy" computer method (which just picks the best spot one by one without looking ahead) by a small but significant margin, reaching 67.82% coverage.

The researchers showed that the new spots were packed tightly along the main "veins" of the campus where people walk, rather than spread out evenly across the whole map. The old sensors were spread out to get a general background reading of the whole campus, but the new ones focused on the specific places where people are actually walking and breathing.

The "How Many Do We Need?" Question

The team also asked a second question: If we want to cover a certain percentage of the campus, what is the minimum number of sensors we need? This is called the "Inverse Problem."

They ran the numbers and found a surprising truth about money and efficiency:

To cover 40% of the walking paths, you only need 6 sensors.
To cover 50%, you need 7 sensors.
To cover 60%, you need 9 sensors.
To cover 70%, you need 11 sensors.

Here is the kicker: The current campus has 11 sensors but only covers 36.29%. The new plan shows that with just 6 sensors placed in the right spots, you could actually cover 40.99% of the paths. This means the university could potentially cut their sensor budget by nearly half (from 11 down to 6) and still get more useful data about where people are breathing. Or, if they keep all 11, they get double the coverage.

Why This Matters

The study didn't just find a better map; it proved that how you place sensors changes everything.

It's not just math: The researchers made sure the sensors could actually be installed. They checked that every new spot was near a walkway, far from buildings, and safe from trees.
It's not magic: They didn't claim to solve the problem for the whole world. They showed that for this specific campus, using this specific method, they could double the effectiveness.
It's a trade-off: The old sensors were good for seeing the "big picture" of the whole campus. The new sensors are better for seeing the "hotspots" where people are. Both are useful, but they do different jobs.

In the end, this paper shows that by using smart, quantum-inspired math to respect the physical rules of the world (like not putting sensors in lakes), cities and universities can get much more value out of their air-quality networks. It's a reminder that sometimes, the best way to solve a problem isn't to buy more gadgets, but to think harder about where you put the ones you already have.

Technical Summary: Quantum-Inspired Evolutionary Optimization for CO2 Sensor Placement on the UCF Campus

Problem Statement
The proliferation of low-cost Internet-of-Things (IoT) platforms has made dense urban carbon dioxide (CO2) monitoring feasible; however, optimizing the placement of a finite sensor budget within complex municipal geometries remains a non-trivial combinatorial challenge. Traditional approaches often rely on simplified spatial domains or deterministic Geographic Information System (GIS) heuristics that struggle to scale with high-resolution candidate grids and complex, non-convex exclusion zones (e.g., buildings, water bodies, and dense vegetation). Furthermore, existing evolutionary formulations frequently utilize scalar penalties to discourage infeasible placements, allowing environmental violations to persist within the search population. This study addresses the specific challenge of placing $N=11$ circular-footprint sensors (radius $R=223$ m) on the University of Central Florida (UCF) campus. The goal is to maximize weighted pedestrian-priority coverage while strictly adhering to structural siting constraints that exclude buildings, water, and forest-class vegetation, thereby ensuring the resulting network is physically deployable and methodologically sound.

Methodology
The research proposes a structurally compliant optimization framework that integrates geospatial data processing, demand modeling, and a Quantum-Inspired Evolutionary Optimization (QIEO) algorithm.

Geospatial Filtering and Candidate Discretization:
Unlike traditional methods that apply soft penalties, this framework employs a rigorous spatial screening pipeline. The study domain is discretized into a deterministic 30 m grid. A candidate point is admitted to the search space only if it satisfies strict center-level criteria (e.g., distance to buildings between 5–140 m, distance to walkways $\le$ 90 m) and footprint-level intersection filters (overlap with buildings $\le$ 35%, water $\le$ 5%, and forest vegetation $\le$ 15%). This converts environmental siting rules from soft penalties into structural guarantees, ensuring the optimizer searches exclusively within a pre-validated set of 502 feasible locations.
Demand Modeling:
The coverage objective is defined as a demand-weighted Maximum Coverage Facility Location Problem (MCFLP). Rather than optimizing for uniform area coverage, the study prioritizes pedestrian exposure. Approximately 5,230 priority points are generated along walkable corridors, weighted by pedestrian density (derived from Kernel Density Estimation). The objective is to maximize the weighted fraction of these points falling within at least one sensor footprint.
Optimization Engine (QIEO):
The study utilizes a Quantum-Inspired Evolutionary Optimization algorithm. Unlike classical Genetic Algorithms (GAs) where individuals represent single deterministic solutions, QIEO utilizes qubit superposition ( $\alpha|0\rangle + \beta|1\rangle$ ) to maintain a probabilistic representation of the search space. This allows for broader global exploration in early generations. The algorithm employs quantum rotation gates to dynamically update probability amplitudes based on the best-performing individual, collapsing the superposition toward optimal discrete coordinates. A "snapping" mechanism maps continuous algorithmic outputs to the nearest valid candidate in the pre-filtered grid, enforcing spacing constraints (targeting 1.5R separation) and structural compliance.
Problem Formulation:
The study bifurcates the problem into two modes:
- Direct Problem: Maximizes coverage for a fixed budget of $N=11$ sensors.
- Inverse Problem: Determines the minimum number of sensors required to achieve specific coverage thresholds (40%, 50%, 60%, 70%), generating a hardware-versus-coverage calibration curve.

Key Contributions

Structural Constraint Enforcement: The introduction of a footprint-filtered deterministic candidate grid that embeds building, water, and vegetation exclusions directly into the search space. This eliminates the need for post-hoc manual adjustments and mathematically guarantees that any solution produced is physically deployable.
Baseline Deconstruction and Validation: A rigorous benchmarking of the optimized configuration against the currently deployed UCF campus network (11 sensors).
Hardware Scalability Analysis: The development of an inverse-problem formulation to construct a transferable calibration curve linking IoT capital investment (sensor count) to expected pedestrian-priority coverage.

Results

Coverage Improvement: The QIEO-optimized placement of 11 sensors achieved 72.73% weighted priority-point coverage. This represents a 2× improvement over the currently deployed baseline network (36.29%) and a 4.91% improvement over an unconstrained greedy heuristic baseline (67.82%).
Constraint Satisfaction: Post-hoc validation confirmed that all optimized sensor positions strictly satisfied environmental constraints. No sensor centers breached building or water polygons, and vegetation overlap remained within the 15% threshold (peaking at exactly 15% for one sensor).
Convergence and Efficiency: The algorithm demonstrated robust convergence with a standard deviation of only 0.20% across 10 independent runs. It located the optimal solution in approximately 195 seconds on a standard desktop workstation, contrasting with the intractability of brute-force enumeration (estimated at >361 million years for the same search space).
Inverse Problem Findings: The inverse sweep revealed a nonlinear relationship between sensor count and coverage. Achieving 40% coverage required only 6 sensors, while reaching 70% required 11. Notably, the optimized 6-sensor configuration (40.99% coverage) outperformed the existing 11-sensor baseline (36.29%), suggesting a potential 45% reduction in hardware costs for equivalent or better exposure monitoring.
Operational Trade-offs: The study identified a fundamental divergence in design objectives: the baseline network prioritized broad geographic representativeness (mean spacing 420 m), whereas the QIEO solution prioritized high-density pedestrian corridors (mean spacing 348 m).

Significance and Claims
The paper claims that this work bridges the methodological gap between empirical geospatial mapping and advanced metaheuristic optimization. By converting complex municipal siting geometries into structural constraints rather than soft penalties, the framework ensures that optimization results are not just mathematically optimal but operationally viable.

The study positions the UCF campus deployment as a "validated unit cell" for hierarchical metro-scale extensions. The primary significance lies in providing municipal planners with a quantitative framework to balance marginal hardware investments against expected pedestrian exposure coverage. The inverse-problem calibration curve serves as a policy instrument, demonstrating that strictly enforcing spatially explicit optimizations can drastically reduce IoT capital expenditure (CAPEX) without sacrificing monitoring resolution. The authors emphasize that while the optimized locations are candidates for deployment, they must still undergo site-specific calibration and field validation, and the current study focuses on geometric coverage rather than direct CO2 flux reconstruction. Future work is identified as necessary for scaling to metropolitan areas, integrating 3D microclimate dynamics, and incorporating mobile sensor architectures.