S-LCG: Structured Linear Congruential Generator-Based Deterministic Algorithm for Search and Optimization

S-LCG (Structured Linear Congruential Generator) is a novel deterministic optimization algorithm that reimagines random number generators for search and optimization. Developed by Ahmed Qasim Mohammed, Haider Banka, and Anamika Singh, it employs a two-level architecture: an external loop balances exploration and exploitation adaptively, while an internal loop evaluates solutions. Key innovations include a memoryless scheme ensuring non-overlapping sequences (no redundant evaluations), bit splitting to convert generator states into multi-dimensional points (overcoming the Marsaglia lattice effect), and constant information gathering speed to prevent premature convergence. The algorithm requires only one sensitive parameter, making it exceptionally easy to tune and fully reproducible.

Extensive testing on 26 benchmark functions across dimensions 2 to 30 shows S-LCG consistently within 1% of the global optimum in 83.3% of 138 test cases (100% at d=2, 81.2% at d=30). This surpasses the nearest competitor, Genetic Algorithm (GA), which achieved 75.4%. Statistical validation confirms S-LCG outperforms eight cutting-edge binary algorithms. Practical value is demonstrated on three constrained engineering design problems. S-LCG offers a strictly reproducible, parameter-light alternative to stochastic methods, with potential applications in engineering, logistics, and AI hyperparameter tuning.