From Vaccine Biology to Lagrangian Math: Lagrange Elementary Optimisation (LEO) | Prof. Tarik A. Rashid | Dr. Tarik Ahmed Rashid
Public Research / 4 Min Read
From Vaccine Biology to Lagrangian Math: Lagrange Elementary Optimisation (LEO)
In computer science, global optimisation problems that are difficult to solve are always there. The aim is always the same: obtain the best solution (the global optimum) without using too many resources (computers). For this, biologists rely on nature for answers. The genetic algorithms simulate Darwinian evolution, and the swarm intelligence algorithms mimic the way in which animals forage. But a brand new algorithm is published in the journal Neural Computing and Applications that goes on a rather different path. Developed by researchers Aso M. Aladdin and Tarik A. Rashid, LEO (Lagrange Elementary Optimisation) is a self-adaptive meta-heuristic algorithm, blending the biological precision of human vaccinations with the rigorous framework of traditional mathematical duality.
Inspiration: Blood Immunity & Mathematical Cliffs
LEO is unique in that it combines a phenomenon from health care with higher-level calculus.
Vaccine Immunity & The Albumin Quotient
After getting a vaccine, the immune system generates antibodies and develops a reservoir of a type of white blood cells. These memory cells can immediately identify and neutralise the virus again in the future. In medicine, this defence is measured by the ratio of Albumin Level in CSF and Blood (Albumin Quotient). A drop in this quotient and a corresponding increase in certain serum parameters will mean that the blood-brain barrier is in good condition and the immune system is healthy. LEO models its optimisation strategy using this process, where candidate solutions are represented as immune cells, and the solutions with the highest immunity (best fitness score) survive.
They have a mathematical side, too: Lagrange Duality
The search behaviour is introduced to the LEO algorithm by biology, and the stopping power by calculus in the form of the Lagrangian Dual Function. Suppose you want to go to the top of a steep cliffside, but there is a strict physical restriction that prevents you from doing so. The Lagrange multiplier method, used in mathematics, is a way to convert a complicated, constrained problem into a non-constrained one by finding the point of tangency between the curves. The duality gap property is a strict geometric relationship between a problem with restricted boundaries and an ideal baseline that makes LEO a smart algorithm because it doesn't just wander around. It finds a correct and definite answer.
The Step-by-Step Details of How LEO Works
The LEO is developed based on a framework of a Genetic Algorithm, but adds to this by using a hybrid design:
· Initialisation: The algorithm initialises a population of 100 search agents representing human blood serum with random blood serum traits.
· Descending Sort: Agents get rated according to a fitness function based on the Albumin Quotient model and then sorted from best to worst fitness.
· Subpopulation Splitting: The sorted population is split in half. The best half is prioritised, so the algorithm will focus on the most promising half.
· Lagrangian Problem Crossover: Crossover parents use an operator based on the Lagrange multiplier principle, so that it can traverse the boundaries and find multiple local peaks.
· Gaussian Mutation: Agents randomly vary themselves to keep them diverse and jump out of local traps.
· Iteration: The loop is repeated until a global optimum position has been fixed.
The Power of LEO
The developers subjected LEO to exhaustive testing, running it under 19 classic test functions and 10 newer standard test functions that are quite competitive. LEO was benchmarked against classic and modern algorithms, such as Genetic Algorithms, Particle Swarm Optimisation, and Whale Optimisation Algorithm. The results were extremely impressive. LEO consistently outperformed widely cited algorithms over most of the test functions. The statistical analysis verified that LEO's fine-tuning of exploitation and broad phase exploration was excellent.
Real-World Practical Applications
The researchers were able to successfully use LEO to address two separate practical challenges:
Neurological Healthcare
The pathological immunoglobulin G fractions of the human nervous system were evaluated using LEO. It is important to measure these values in the CSF with precision to help diagnose autoimmune neurological diseases such as multiple sclerosis. Each of these pathogenic values was successfully optimised for LEO without regard for sex or fluid volume, or both.
Cyber-Physical Security in Industry
Modern manufacturing systems are digital networks that are tightly coupled and, which are therefore, susceptible to cyber-attacks. The researchers created a Cyber-Physical-Attack Mitigation System (CPAMS) based on a complex probabilistic framework, where an equilibrium matrix was used to model the system. With 300 iterations, LEO successfully minimised vulnerability over time while updating and isolating infected nodes.
The Essential Conclusion
More broadly, the LEO algorithm is a nice example of the fluid nature of boundary crossings between scientific domains. Anchoring the adaptive nature of biological immunity within the strictures of Lagrangian calculus, Aladdin and Rashid have created a powerful tool that can address some of the toughest problems in engineering.
Aladdin, A. M., & Rashid, T. A. (2023). A New Lagrangian Problem Crossover—A Systematic Review and Meta-Analysis of Crossover Standards. Systems, 11(3), 144. https://doi.org/10.3390/systems11030144
Rashid, T. A. "Computer Science & Artificial Intelligence," 2026. Available: tarikrashid.com.