Computational Problem-Solving Tools

In Operations Research, solver choice is critical. While commercial options like CPLEX and Gurobi often dominate, there’s a strong ecosystem of open and freely available solvers worth knowing. The COIN-OR suite offers solid options like Cbc for MILP, Clp for LP, and Ipopt for nonlinear problems. Google OR-Tools is excellent for combinatorial optimization, routing, and CP/SAT, and includes its own LP/MIP solvers such as GLOP. GLPK, one of the most established open-source solvers, remains a go-to for LP and MIP—particularly in teaching and prototyping—though it can struggle with very large or complex problems. For quadratic programs, OSQP is a fast and reliable option, while OjAlgo provides a Java-based library for LP, QP, and MIP. Modeling frameworks like Pyomo and PuLP make it easy to define models and switch between solvers. While open-source solvers may not always match the performance of commercial ones on very large instances, they continue to advance rapidly and are invaluable for research, prototyping, and even production workflows. Which solvers do you typically use in your work? I'd love to hear what’s been working well for others.

Large Language Models (LLMs) have made big leaps in tackling complex reasoning tasks, thanks to techniques like Chain-of-Thought (CoT) prompting. CoT works by breaking problems into step-by-step reasoning, like how humans think. While it’s super effective, CoT can also be pretty slow and resource-heavy because of the detailed output it generates. Here’s where Chain of Draft (CoD) comes in. Inspired by how people often jot down quick drafts or shorthand notes, CoD gets LLMs to produce shorter, more focused reasoning outputs. The result? Faster responses, lower computational costs, and no compromise on accuracy. How CoD Works Researchers put CoD to the test on tasks like arithmetic, common-sense, and symbolic reasoning. They compared it to CoT and traditional methods, where the model gives a direct answer without showing its reasoning. The results were impressive: CoD often matched or even outperformed CoT in accuracy while slashing the number of tokens generated by up to 92.4%. That means less processing time and fewer resources used—huge wins for efficiency. Why It Matters CoD isn’t just faster; it’s also a game-changer for real-world uses. Its ability to reduce latency and computational demands makes it ideal for resource-limited situations or applications that need real-time responses. Think of real-time systems, interactive tools, or any scenario where speed and cost matter. Key Takeaways LLMs: AI models that understand and generate human-like text. CoT: A method where LLMs think step-by-step, but with long, detailed outputs. CoD: A new approach that creates concise, informative outputs for faster reasoning. Token: The smallest piece of text, like a word or character. Latency: The time it takes for a system to respond. By introducing CoD, researchers have unlocked a smarter, more efficient way to use LLMs. It’s a practical, real-world-friendly approach that could make these models even more accessible and useful.

🚀 Computational Physics: The Power of Science and Computing Computational Physics integrates physics, applied mathematics, and computer science to solve complex problems through numerical simulations. For professionals in modeling, machine learning, or data science, mastering this field unlocks groundbreaking applications. --- 🔍 What is Computational Physics? Many physical problems lack exact solutions, requiring numerical methods to obtain approximate answers. Computational Physics enables us to: ✔ Solve differential equations in complex systems. ✔ Simulate phenomena that can't be tested in labs. ✔ Model chaotic systems like climate and turbulence. ✔ Process and interpret vast scientific data. --- ⚙ Key Methods and Techniques 📌 Finite Difference (FDM), Finite Element (FEM), and Finite Volume (FVM) – Essential for engineering, fluid dynamics, and electromagnetism. 📌 Molecular Dynamics (MD) & Monte Carlo (MC) – Used in biophysics and materials science. 📌 Numerical Linear Algebra – LU decomposition, FFT, and conjugate gradient methods for efficient computations. --- 🌍 Applications of Computational Physics 🔭 Astrophysics & Cosmology – Simulating black holes, galaxy evolution and finding new exoplanets. ⚛ Particle Physics & Quantum Mechanics – Modeling high-energy collisions. 🌪 Computational Fluid Dynamics (CFD) – Applied in weather forecasting and aerodynamics. 🔬 Materials Science – Simulating semiconductors, nanotechnology, and superconductors. 🤖 Machine Learning & Physics – Neural Networks for solving PDEs and accelerating simulations. --- 🛠 Essential Tools & Programming Languages 💻 Languages – Python (NumPy, SciPy), C/C++, Fortran, Julia. 📊 Software & Frameworks – MATLAB, COMSOL, OpenFOAM, LAMMPS, GROMACS, ROOT. --- 🚀 Future Trends & Challenges ⚡ High-Performance Computing (HPC) – Enabling precise simulations. 🧠 AI in Physics – Implementing Physics-Informed Neural Networks (PINNs). 💡 Quantum Computing – Potential breakthroughs in quantum mechanics. --- 🔗 Conclusion From exploring the universe to predicting climate patterns and designing materials, Computational Physics is a powerful tool shaping science and technology. Mastering scientific programming and numerical modeling is an excellent starting point. 💬 Have you worked with Computational Physics before? Or interested in learning more? Let’s discuss in the comments! 👇

Alibaba Researchers Propose START: A Novel Tool-Integrated Long CoT Reasoning LLM that Significantly Enhances Reasoning Capabilities by Leveraging External Tools Researchers at Alibaba have proposed a new AI tool called START, which stands for Self-Taught Reasoner with Tools. Rather than relying solely on internal logic, START integrates an external Python interpreter to assist with reasoning tasks. The model is built on a fine-tuned version of the QwQ-32B model and employs a two-fold strategy to improve its problem-solving skills. First, it uses a method called Hint-infer. Here, the model is encouraged to include prompts like “Wait, maybe using Python here is a good idea,” which signal that it should perform computations or self-check its work using external tools. Second, the model undergoes a fine-tuning process known as Hint Rejection Sampling Fine-Tuning (Hint-RFT). This process refines the model’s reasoning by filtering and modifying its output based on how effectively it can invoke external tools. The result is a model that is not only capable of generating a logical chain of thought but also of verifying its steps through external computation........ Read full article: https://lnkd.in/gAQtawwb Paper: https://lnkd.in/gj8nB-GT

Flow-DPO: A Multi-Agent Framework for Better Math Problem Solving Flow-DPO uses two LLMs that collaborate to solve math problems step-by-step by learning from each other's mistakes. 1️⃣The Answer LLM generates solution chunks. 2️⃣The Stop LLM decides when the solution is complete. The system tests different solution paths (random rollouts) and compares outcomes. If paths differ (e.g., correct vs incorrect), they form a training pair to improve the models in real time through Direct Preference Optimization (DPO). This approach allows the models to adapt and improve continuously. Key Highlights: Challenge: Math reasoning is tough for LLMs due to a lack of detailed, structured training data. Solution: Flow-DPO enables flexible, incremental reasoning steps, improving accuracy over predefined methods. Results: Significant accuracy improvements were observed: Llama-3-8B-Instruct: +20% accuracy in 2000 instances. Phi-3-medium: Accuracy rose from 79% to 83%. ☑️Why It Works: Multi-agent collaboration outperforms single-model methods. Real-time learning with small reasoning chunks enhances performance. Incremental verification improves outcomes compared to checking only the final answer. Compatible with other improvement techniques for further optimization. https://lnkd.in/em8i6pqB

🔔 #ALERT Knowledge Augmented Complex Problem Solving with Large Language Models: A Survey ➡️ Complex problem solving is framed from both cognitive science (human-centered trace) and computational theory (algorithm design) perspectives. ➡️ Key challenges for LLMs in this space are multi-step reasoning, effective domain knowledge integration, and reliable result verification. ➡️ Methodologies discussed include enhancing Chain-of-Thought reasoning via data synthesis and self-correction, leveraging external knowledge bases (RAG, KGs), and employing diverse verification tools (LLM-as-a-judge, symbolic, experimental). ➡️ The survey maps these challenges and advancements to specific domains: software engineering, mathematics, data science, and scientific research, highlighting domain-specific complexities. ➡️ Future directions emphasize addressing data scarcity, reducing computational costs, improving knowledge representation, and developing more robust evaluation frameworks for complex, open-ended problems. Large Language Models demonstrate capabilities for complex problem solving by approximating human-like reasoning and integrating computational tools. However, deploying them effectively in real-world scenarios requires overcoming significant hurdles. The survey highlights that while progress has been made in areas like multi-step reasoning through techniques like Chain-of-Thought and self-correction, challenges remain in handling complex sequences and ensuring high accuracy. Integrating specialized domain knowledge is critical, moving beyond pre-training to using external sources and agent-based approaches. Furthermore, reliable verification of solutions, especially in domains lacking clear outcomes, necessitates a combination of LLM-based, symbolic, and experimental methods. The path forward involves refining these core capabilities and tailoring solutions to the unique demands of different technical fields. If you are keeping track of where the industry and the implementation of the AI is at! This article from ANTgroup and Zhejiang University is for you. #LLMs #TechnicalSurvey #ProblemSolving #ArtificialIntelligence