A novel algorithm named LEJaya is introduced in this paper. LEJaya is an advanced optimization algorithm that builds upon the EJaya method. LEJaya employs a two-phase structure: Adaptive Enhancement and EJaya to effectively balance exploration and exploitation within the search space, crucial for handling constraints in complex optimization tasks. The algorithm’s performance was assessed on a set of 10 constrained benchmark functions. To validate its efficacy, LEJaya was compared against five prominent metaheuristics: TLBO, EJaya, Jaya, Particle Swarm Optimization, and Genetic Algorithm on constrained functions. Each algorithm underwent thirty trials across 1000 iterations, with evaluations based on metrics such as best solution, mean, standard deviation, CPU time, and rank. The findings reveal that LEJaya excels in handling constraints, often reaching the global optimum and surpassing other algorithms, establishing it as a strong method for constrained optimization problems.