Leo: Lagrange Elementary Optimization

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.

A New Lagrangian Problem Crossover: A Systematic Review and Meta-Analysis of Crossover Standards

The performance of most evolutionary metaheuristic algorithms depends on various operators. The crossover operator is one of them and is mainly classified into two standards; application-dependent crossover operators and application-independent crossover operators. These standards always help to choose the best-fitted point in the evolutionary algorithm process. The high efficiency of crossover operators enables minimizing the error that occurred in engineering application optimization within a short time and cost. There are two crucial objectives behind this paper; at first, it is an overview of crossover standards classification that has been used by researchers for solving engineering operations and problem representation. The second objective of this paper; The significance of novel standard crossover is proposed depending on Lagrangian Dual Function (LDF) to progress the formulation of the Lagrangian Problem Crossover (LPX) as a new systematic standard operator. The results of the proposed crossover standards for 100 generations of parent chromosomes are compared to the BX and SBX standards, which are the communal real-coded crossover standards. The accuracy and performance of the proposed standard have evaluated by three unimodal test functions. Besides, the proposed standard results are statistically demonstrated and proved that it has an excessive ability to generate and enhance the novel optimization algorithm compared to BX and SBX.