🔍💡 AI-Powered Coevolution for Optimizing Power Systems | #Sciencefather #researchers #algorithm

🌍⚡ A Dueling Double Deep Q Network-Assisted Cooperative Dual-Population Coevolutionary Algorithm for Solving Multi-Objective Combined Economic and Emission Dispatch (CEED) Problems

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🔍 Abstracted Intelligence for a Sustainable Grid

In the evolving landscape of smart power systems, achieving a sustainable balance between economic efficiency and environmental responsibility remains a grand challenge. The Combined Economic and Emission Dispatch (CEED) problem epitomizes this dual objective—minimizing fuel costs while simultaneously reducing toxic emissions. Conventional optimization techniques falter under the burden of CEED's nonlinear, multi-modal, and multi-objective nature.

This research introduces a novel, hybrid intelligent framework:

Dueling Double Deep Q-Network Assisted Cooperative Dual-Population Coevolutionary Algorithm (D3QN-CDPCA)—a next-generation optimizer that marries deep reinforcement learning with evolutionary computation for optimal power dispatch.

 

⚙️ Core Innovation at a Glance

Component	Purpose	Distinctive Advantage
🎯 Dual-Population Coevolution	Two interlinked populations optimize cost and emissions in parallel.	Promotes diversity and balanced trade-off discovery.
🧠 Dueling Double Deep Q-Network (D3QN)	Intelligent controller for adaptive decision-making.	Reduces overestimation bias and boosts learning precision.
🔁 Cooperative Strategy Learning	Reinforces beneficial knowledge exchange across populations.	Prevents premature convergence and stagnation.
📊 Pareto Archive Management	Dynamic update of non-dominated solutions.	Ensures high-quality, well-distributed Pareto front.

🌐 How the Algorithm Works: Step-by-Step Workflow

1. Population Initialization
   Two evolutionary populations are seeded—one targeting economic cost, the other environmental emission. Randomized yet constraint-aware.

2. Objective Evaluation
   Individuals are assessed using non-convex cost and emission functions under system constraints, including transmission losses and ramp-rate limits.

3. State Formation & D3QN Action
   The D3QN interprets the system’s dynamic state: population diversity, dominance spread, generation count, and convergence indicators.
   It selects adaptive actions: adjusting genetic operator intensity, enabling cross-population migration, or exploiting promising regions.

4. Coevolutionary Evolution
   Populations evolve independently but periodically exchange elite solutions as determined by the D3QN policy.

5. Pareto Front Construction
   A global archive is updated in real-time to preserve and enhance non-dominated, high-fidelity solutions using crowding distance and elitism.

6. Termination & Results
   Upon reaching convergence or iteration limit, the algorithm yields a high-resolution Pareto-optimal front reflecting an optimal cost-emission trade-off.

🧪 Why This Hybrid Model Excels

✅ Smart Exploration-Exploitation Balance: D3QN dynamically learns when to explore new regions or intensify exploitation.
✅ Resilient to Complexity: Effectively navigates CEED’s rugged and high-dimensional search space.
✅ Scalable & Adaptable: Easily extendable to dynamic dispatch, stochastic systems, or hybrid grids with renewables.

📈 Validation on IEEE Standard Systems

Benchmark simulations on IEEE-30 and IEEE-118 bus systems reveal:

• Superior Pareto front convergence compared to NSGA-II, SPEA2, and MOEA/D.

• Reduced emission levels without economic sacrifice.

• Faster convergence due to intelligent learning and coevolution.

• High Hypervolume & Spread metrics, proving diversity and quality.
  
  

🔮 Impact and Future Horizons

This work pioneers a new paradigm in power system optimization, harnessing the decision-making finesse of reinforcement learning with the robust search power of coevolutionary algorithms. It not only provides a tool for CEED but opens doors to AI-powered sustainable energy dispatch, smart grid resilience, and autonomous energy markets.

🏁 Conclusion

The D3QN-CDPCA is more than an algorithm—it’s an AI-augmented ecosystem for solving multi-objective dispatch problems in a manner that is smart, adaptive, and environmentally responsible. With deep learning driving cooperation and evolution, this approach sets a new benchmark for sustainable power optimization.

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🌐 Math-Driven UAV Rescue: Optimizing Pathways in Turbulent 3D Offshore Winds 🚁🔢 | #Sciencefather #researchers #algorithm

🚁 Mathematics in Motion: Empowering Multi-UAV Rescue Missions in Turbulent 3D Offshore Environments

A Scalable, Coatis-Inspired Path Planning Framework Driven by Intelligent Optimization

Dive into the world of mathematical optimization with an innovative Coatis-inspired algorithm designed for multi-UAV rescue operations. Navigating complex 3D wind fields, UAVs solve real-time geometric optimization challenges—ensuring energy-efficient, collaborative rescues. This cutting-edge method combines swarm intelligence, vector calculus, and dynamic modeling to revolutionize offshore missions. 🌊🔍🧮

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🌊 The Real-World Challenge:

Rescue operations at sea face the harshest conditions known to man—chaotic 3D wind fields, unpredictable ocean dynamics, and rapidly evolving emergency zones. In such unforgiving environments, deploying single UAVs is no longer viable.

We ask:

✳️ How can we mathematically orchestrate dozens of UAVs to navigate, search, and rescue—autonomously, collaboratively, and safely—within these dynamic 3D spaces?

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🧠 Our Mathematical Breakthrough:

We introduce a novel path planning method for collaborative UAV fleets using an enhanced Improved Coatis Optimization Algorithm (ICOA)—a metaheuristic inspired by the adaptive, social foraging patterns of coatis in the wild.

But this isn’t just biomimicry—this is math in action.

Our framework blends:

• ✅ Multi-objective Optimization Theory

• ✅ Vector Field Analysis for wind modeling

• ✅ Graph Theory for swarm coordination

• ✅ Entropy-Controlled Search Mechanics

• ✅ 3D Spatial Obstacle Mapping with Dynamic Constraints

• ✅ Lévy Flights and Evolutionary Perturbation Techniques

Each UAV becomes an autonomous agent solving a geometrically constrained optimization problem in real-time, communicating with its swarm, reacting to wind vectors, and avoiding collision—all governed by deeply mathematical principles.

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📈 Key Results – Quantified Intelligence

Our method is benchmarked against traditional algorithms (PSO, ACO, COA) and shows:

Metric	ICOA Performance
🚀 Rescue Response Time	↓ 27% faster
🔋 Energy Consumption	↓ 31% lower
🧭 Path Optimality (3D)	↑ 34% improved
🔗 UAV Fleet Scalability	↑ Highly robust (>50 UAVs)
💨 Wind Adaptation Accuracy	↑ Dynamic modeling support

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🌐 What Makes It Unique?

This work isn’t just engineering—it’s a mathematical ecosystem brought to life:

🔹 UAV paths become geodesics in wind-perturbed vector spaces.
🔹 Wind fields are treated as deformable potential functions in a dynamic optimization landscape.
🔹 Swarm behavior emerges from decentralized consensus and graph dynamics.
🔹 Real-time re-optimization ensures adaptive intelligence during the mission.

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🎯 Why It Matters:

In an era where climate change increases maritime disasters, this method empowers UAVs to become intelligent rescue agents—mathematically grounded, nature-inspired, and operationally scalable.

We aren’t just sending drones—we’re deploying mathematical agents of hope.

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🔬 Target Applications:

• Maritime disaster search & rescue

• Offshore platform evacuations

• Shipwreck analysis & survivor location

• Oceanic surveillance in hostile conditions

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🧮 Math is the Engine. Rescue is the Mission.

A new frontier where applied mathematics becomes airborne.

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🌿📉 Mathematical Modeling of UFLP Using Binary Grasshopper Swarms | #Sciencefather #researchers #algorithm

🧮🦗 A Binary Grasshopper Optimization Algorithm for Discrete Mathematical Modeling in UFLP

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🔷 1. Introduction: The Mathematical Challenge

The Uncapacitated Facility Location Problem (UFLP) is a classic in operations research, where the objective is to determine:

• Which facilities to open, and

• How to assign each customer to exactly one facility,
  such that the total cost (facility opening + service costs) is minimized.

Let:

• $F = \{1,2,\dots,m\}$: potential facility sites

• $C = \{1,2,\dots,n\}$: customer locations

• $f_i$: cost to open facility $i$

• $c_{ij}$: cost to serve customer $j$ from facility $i$

Objective function:

$$\textbf{Minimize } Z = \sum_{i=1}^{m} f_i x_i + \sum_{i=1}^{m} \sum_{j=1}^{n} c_{ij} y_{ij}$$

Subject to constraints:

• Each customer assigned once:

  $$\sum_{i=1}^{m} y_{ij} = 1 \quad \forall j$$

• Assignments only from open facilities:

  $$y_{ij} \leq x_i \quad \forall i, j$$

• Binary variables:

  $$x_i, y_{ij} \in \{0, 1\}$$

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🧠 2. Nature-Inspired Intelligence: The Grasshopper's Strategy

The Grasshopper Optimization Algorithm (GOA) simulates the swarming behavior of grasshoppers. The mathematical model includes:

$$X_i = \sum_{j=1}^{N} s(d_{ij}) \cdot \hat{d}_{ij} + G + W$$

Where:

• $s(d)$ = social interaction force

• $G$ = gravity force

• $W$ = wind influence

This model is continuous, but we apply a binary transformation to adapt it to combinatorial optimization problems like UFLP.

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🔁 3. Binary Transformation: Sigmoid Discretization

To convert real-valued solutions into binary form, we apply a sigmoid transfer function:

$$T(X) = \frac{1}{1 + e^{-X}}$$

Then use a threshold:

$$x_i^{t+1} = \begin{cases} 1 & \text{if } rand() < T(X_i^t) \\ 0 & \text{otherwise} \end{cases}$$

This maps the grasshopper's real-valued position into binary — indicating whether a facility is open (1) or closed (0).

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🎯 4. Fitness Function: Evaluating the Binary Solution

Each binary vector $\mathbf{x}$ encodes facility decisions. The fitness is:

$$f(\mathbf{x}) = \sum_{i=1}^{m} f_i x_i + \sum_{j=1}^{n} \min_{\substack{i=1\\x_i=1}}^m c_{ij}$$

To handle constraint violations, a penalty function is added:

$$f_{\text{penalized}}(\mathbf{x}) = f(\mathbf{x}) + \lambda \cdot V(\mathbf{x})$$

Where $V(\mathbf{x})$ counts constraint violations and $\lambda$ is the penalty weight.

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⚙️ 5. Algorithmic Workflow: Step-by-Step

Step	Description
1. Initialization	Generate random binary solutions (grasshopper swarm)
2. Evaluation	Compute fitness using cost function
3. Position Update	Apply GOA movement equations and binary mapping
4. Repair	Fix constraint violations or penalize them
5. Iteration	Repeat until stopping criteria are met
6. Output	Return the best-found binary solution

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✨ 6. Why It Works: Mathematical Elegance Meets Natural Design

• ✅ Binary Logic meets Biological Motion

• ✅ Efficient in large, high-dimensional spaces

• ✅ Flexible and robust in real-world logistics

• ✅ Aesthetic fusion of swarm intelligence and combinatorial math

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💭 Final Remark

The Binary Grasshopper Optimization Algorithm offers a visually intuitive, mathematically sound, and biologically inspired approach to solving the UFLP. It bridges nature and mathematics in a dynamic optimization framework — where every grasshopper's leap echoes a decision in facility planning.

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🌍 Calling Visionary Researchers: Apply for the Best Academic Researcher Award! 🏆 | #Sciencefather #researchers #mathscientists

Step Into the Global Spotlight: Celebrate Your Groundbreaking Research with the Best Academic Researcher Award ! 🌍🏆

🌱 Introduction: Recognizing Excellence in Research

The Best Academic Researcher Award honors those whose innovative ideas, game-changing discoveries, and unwavering dedication propel research forward. A beacon of academic excellence, this award acknowledges scholars who push the boundaries of knowledge, spark new conversations, and ultimately shape the future of academia. 🔬🌍

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🏅 About the Award: Where Visionaries are Celebrated

This prestigious award shines a spotlight on researchers who don’t just follow trends—they create them. With a commitment to transforming ideas into impactful solutions, the Best Academic Researcher Award celebrates those who have significantly advanced their field, whether through groundbreaking research, multidisciplinary collaboration, or a lifelong commitment to the pursuit of knowledge. 🧠✨

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🎯 Eligibility Criteria: Who Can Apply?

To be considered for this remarkable honor, you must meet the following criteria:

• 🎓 Qualifications: A PhD or equivalent in your area of expertise.

• 📑 Publications: A minimum of three peer-reviewed articles published in high-impact journals.

• 🌍 Age Limit: No age restrictions—this award recognizes talent from early-career scholars to seasoned researchers.

• 🔬 Active Involvement: You must be deeply involved in research, mentorship, and academic discourse.

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💡 Evaluation Criteria: What Makes an Award-Winning Researcher?

Our esteemed panel of experts evaluates nominees based on the following principles:

• 🚀 Innovation: Is the research pioneering? Does it bring new perspectives and methods to the field?

• 🔍 Scholarly Impact: How has the research influenced future academic pursuits?

• 🌐 Interdisciplinary Relevance: Does the work bridge multiple fields, opening new areas for collaboration and discovery?

• 🌍 Real-World Application: How does the research solve tangible problems or improve society?

• 📝 Publication & Citations: How widely acknowledged and cited is the research in academic circles?

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📑 Submission Guidelines: Your Path to Recognition

To apply for the Best Academic Researcher Award, you’ll need to submit the following:

• 🖋 Biography (max. 500 words): A detailed look at your academic journey, research contributions, and influence.

• 📑 Research Abstract (max. 300 words): A clear, concise summary of your most impactful research.

• 📂 Supporting Documents:

  • Full research papers and publications

  • Citation reports

  • Letters of recommendation from peers or mentors

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🌟 Recognition & Rewards: What You’ll Gain

Winning the Best Academic Researcher Award is not just about accolades—it's about unlocking new opportunities:

• 🏅 Award Trophy & Certificate: A prestigious symbol of your research excellence.

• 🌍 Conference Invitations: Present your findings at top global academic events and network with the world’s leading scholars.

• 🌐 Global Collaboration: Opportunities to collaborate with institutions and researchers across the globe.

• 📰 Media Recognition: Your research will be featured in leading academic publications and widely circulated journals.

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🌱 Community Impact: Advancing Science for All

This award honors researchers who not only contribute to their fields but also mentor the next generation of scholars, fostering a culture of collaboration and scientific inquiry. Your research is more than a collection of papers—it is a step towards solving the world’s most pressing challenges. 🌍✨

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🚀 Lead, Innovate, Inspire

The Best Academic Researcher Award is a call to all trailblazers—apply now and take the first step towards global recognition and endless possibilities. Your ideas, your research, your future. Let’s shape the world together! 🌟🔍

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Optimizing IIoT Sensing via Chaos-Based Enhanced Sparrow Search | #Sciencefather #researchers #algorithm

🌐 An Enhanced Sparrow Search Algorithm Using Chaos and Elite Reverse Learning for IIoT Communication Optimization

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As the Industrial Internet of Things (IIoT) transforms manufacturing, logistics, and automation, the need for ultra-efficient sensing and communication optimization becomes vital. Traditional routing and energy-balancing methods struggle to handle the growing complexity of IIoT networks—this is where intelligent metaheuristics come in.

The Sparrow Search Algorithm (SSA)—inspired by the foraging behavior of sparrows—offers a powerful foundation. This work introduces a next-generation enhancement of SSA using chaotic dynamics and elite reverse learning to tackle IIoT challenges head-on.

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🧠 What Makes This Algorithm Special?

✅ 1. Chaos Theory – Smarter Exploration

• 🔁 Chaotic Mapping (like Logistic or Tent maps) replaces randomness in population initialization.

• 💡 Outcome: Better diversity, faster convergence, and escape from local optima.

✅ 2. Elite Reverse Learning – Smarter Selection

• 🌟 Identifies elite (best) solutions.

• 🔄 Generates their reverse counterparts, expanding the solution space creatively.

• 🎯 Outcome: Improves precision, robustness, and search efficiency.

✅ 3. Dynamic Strategy – Adaptive Intelligence

• 🔄 Adjusts balance between exploration (global search) and exploitation (local refinement) in real time.

• 🧭 Leads to a more intelligent, context-aware optimization flow.

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🔧 Applied to IIoT: Real-World Use Cases

The enhanced algorithm tackles key IIoT communication and sensing problems:

⚙️ Optimization Target	💼 Application in IIoT
🛰️ Sensor Deployment	Strategic placement for full coverage with minimal redundancy
🛣️ Routing Path Optimization	Shortest, most energy-efficient communication routes
🔋 Energy Conservation	Extend battery life of sensors and nodes
⏱️ Latency Minimization	Enable faster data transmission in real-time systems
📶 Bandwidth Allocation	Efficient frequency use across crowded networks

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📊 Performance Highlights

🧪 Metric	🌟 Enhanced SSA Result
🔄 Convergence Speed	Faster than standard SSA, PSO, GWO
🎯 Solution Accuracy	Consistently achieves lower cost and better configurations
🔁 Robustness	Stable across varied IIoT topologies and noise conditions
🕒 Runtime Efficiency	Reduced computational complexity

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🌈 Why It Stands Out

• ✅ Integrates chaos theory for exploration diversity

• ✅ Applies elite reverse learning to boost exploitation accuracy

• ✅ Adapts dynamically for changing IIoT conditions

• ✅ Outperforms traditional and even advanced metaheuristics

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🏁 Conclusion

The Chaos and Elite Reverse Learning–Enhanced Sparrow Search Algorithm is not just an incremental improvement—it's a game-changer for IIoT sensing and communication optimization. Whether it's reducing energy consumption, optimizing sensor deployment, or ensuring real-time reliability, this hybrid strategy delivers high-performance results in even the most complex industrial networks.

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A Mind Beyond Measure | #Sciencefather #researchers #Winner

🎉 Congratulations to Dr. Mansi Subhash Palav: Winner of the Best Researcher Award at the Math Scientist Awards!

In a constellation of brilliant minds, one star shone the brightest. At the prestigious Math Scientist Awards, the spotlight found its true match — Dr. Mansi Subhash Palav, whose name now echoes with the rare distinction of Best Researcher. A mathematician, a mentor, a visionary — she is more than a scholar; she is a movement.

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🏅 The Award: When Dedication Meets Destiny

This moment is not merely a win — it is a whisper from the universe acknowledging decades of unshaken resolve. The Best Researcher Award bestowed upon Dr. Palav celebrates not just her exceptional intellect but the integrity, insight, and impact that define her work.

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📐 Mathematical Mastery: Sculpting the Language of Nature

With every formula she explores, Dr. Palav speaks the secret language of the universe. Her groundbreaking research in partial differential equations, advection-diffusion problems, Burgers’ equations, and numerical techniques such as B-spline collocation and finite elements, unveils order in complexity and elegance in computation.

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📚 Scholarly Impact: Beyond Borders and Boundaries

Her research travels farther than ink on paper — it resonates across continents. With numerous international journal publications, book chapters in Springer and CRC Press, and over 17 global conference presentations, her ideas move with momentum and precision.

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🎓 Excellence Etched in Credentials

A scholar in every sense, Dr. Palav holds prestigious qualifications: CSIR-UGC NET (JRF & LS), GATE, and SET Maharashtra. These achievements are not just accolades — they are evidence of a mind honed for mastery.

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🌱 Mentorship & Magic: Nurturing New Thought

As a visiting faculty and subject expert, she does more than teach — she ignites. Dr. Palav’s academic reach inspires students to dream deeper and climb higher, carrying forward the torch of scientific curiosity.

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🔭 Future Vision: Mathematics Meets Tomorrow

From modeling pollution transport to exploring image encryption, she stands where pure math dances with applied science. She doesn’t just solve equations — she envisions revolutions.

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🌹 A Standing Ovation

Congratulations, Dr. Mansi Subhash Palav. With every theorem you prove and every young mind you guide, you not only change the field — you reshape the future.

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