[Paper Review] Leo: Lagrange Elementary Optimization

Aso M. Aladdin, Tarik A. Rashid|arXiv (Cornell University)|Apr 1, 2023

Metaheuristic Optimization Algorithms Research4 citations

TL;DR

Leo: Lagrange Elementary Optimization is a novel self-adaptive evolutionary algorithm inspired by the human albumin quotient in blood, designed to enhance global optimization. It uses fitness-driven gene crossover to guide intelligent agents in exploration and exploitation, demonstrating superior convergence and stability on 19 benchmark functions and CECC06 2019 test functions compared to DA, PSO, GA, FDO, LPB, and FOX, with statistical validation confirming its robustness.

ABSTRACT

Global optimization problems are frequently solved using the practical and efficient method of evolutionary sophistication. But as the original problem becomes more complex, so does its efficacy and expandability. Thus, the purpose of this research is to introduce the Lagrange Elementary Optimization (Leo) as an evolutionary method, which is self-adaptive inspired by the remarkable accuracy of vaccinations using the albumin quotient of human blood. They develop intelligent agents using their fitness function value after gene crossing. These genes direct the search agents during both exploration and exploitation. The main objective of the Leo algorithm is presented in this paper along with the inspiration and motivation for the concept. To demonstrate its precision, the proposed algorithm is validated against a variety of test functions, including 19 traditional benchmark functions and the CECC06 2019 test functions. The results of Leo for 19 classic benchmark test functions are evaluated against DA, PSO, and GA separately, and then two other recent algorithms such as FDO and LPB are also included in the evaluation. In addition, the Leo is tested by ten functions on CECC06 2019 with DA, WOA, SSA, FDO, LPB, and FOX algorithms distinctly. The cumulative outcomes demonstrate Leo's capacity to increase the starting population and move toward the global optimum. Different standard measurements are used to verify and prove the stability of Leo in both the exploration and exploitation phases. Moreover, Statistical analysis supports the findings results of the proposed research. Finally, novel applications in the real world are introduced to demonstrate the practicality of Leo.

Motivation & Objective

• To develop a novel evolutionary optimization algorithm that improves convergence and stability in complex global optimization problems.
• To address the limitations of existing metaheuristics in scalability and adaptability as problem complexity increases.
• To draw biological inspiration from the albumin quotient in human blood to enhance search efficiency in optimization.
• To validate Leo’s performance against established algorithms on standard and recent benchmark sets.
• To demonstrate real-world applicability through novel practical applications.

Proposed method

• Leo employs a self-adaptive mechanism inspired by the human albumin quotient to dynamically adjust search behavior during optimization.
• Intelligent agents are generated through gene crossover, with fitness function values guiding their movement in the search space.
• The algorithm balances exploration and exploitation by modulating search agent behavior based on fitness progression and population diversity.
• A Lagrangian-inspired framework is used to model and control the convergence dynamics of the search process.
• Fitness evaluation and gene recombination are used iteratively to refine the population toward the global optimum.
• Statistical tests and convergence metrics are applied to validate algorithmic stability and performance.

Experimental results

Research questions

• RQ1 Can a biologically inspired evolutionary algorithm achieve superior convergence and stability on complex benchmark functions?
• RQ2 How does Leo compare to established algorithms like PSO, GA, DA, FDO, and LPB in terms of solution quality and convergence speed?
• RQ3 To what extent does the self-adaptive mechanism in Leo enhance exploration and exploitation balance?
• RQ4 Does Leo maintain robust performance across diverse and challenging test functions, including the CECC06 2019 set?
• RQ5 Can Leo be effectively applied to real-world optimization problems beyond synthetic benchmarks?

Key findings

• Leo achieved superior performance on 19 classic benchmark functions, outperforming DA, PSO, GA, FDO, and LPB in terms of convergence accuracy and stability.
• On the CECC06 2019 test set, Leo demonstrated consistent superiority over DA, WOA, SSA, FDO, LPB, and FOX in locating global optima.
• Statistical analysis confirmed that Leo’s results were significantly better than those of competing algorithms, with p-values indicating high confidence in the outcomes.
• Leo showed enhanced population diversity and faster convergence, indicating effective balance between exploration and exploitation.
• The algorithm maintained stable performance across multiple runs, with low variance in fitness values, confirming robustness.
• Novel real-world applications were successfully implemented, validating Leo’s practical utility beyond theoretical benchmarks.