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

2026-05-06

AI Summary

This work proposes a deterministic bilevel optimization algorithm based on a Structured Linear Congruential Generator (S-LCG) to address redundancy in fitness evaluations, premature convergence, and imbalance between exploration and exploitation inherent in conventional optimizers. The outer loop employs an adaptive mechanism to dynamically balance exploration and exploitation, while the inner loop leverages bit-decomposed mappings of LCG states to generate multidimensional candidate solutions. A memoryless scheme is introduced to avoid redundant evaluations, effectively mitigating the Marsaglia lattice effect. Requiring only a single parameter to tune and maintaining a constant information acquisition rate, the method prevents premature convergence. Evaluated on 138 instances across 26 benchmark functions, it achieves solutions within 1% of the global optimum in 83.3% of cases (100% for 2D and 81.2% for 30D problems), significantly outperforming eight state-of-the-art binary optimizers, and demonstrates practical efficacy on three real-world constrained engineering problems.

Abstract

This study presents a novel deterministic optimization algorithm based on a special variant of the Linear Congruential Generator (LCG). While conventional algorithms generally operate within the search space, the introduced technique follows a two-level architecture. In particular, an external loop that adaptively balances between exploration and exploitation, while the internal loop evaluates solutions. It is motivated by the intrinsic structure of the generator, the reason behind naming it the Structured Linear Congruential Generator (S- LCG). which enjoys a number of unique characteristics as follows: 1) a memoryless scheme, which ensures non-overlapping sequences based on distinct seeds, thus ensuring no evaluation redundancy; 2) bit splitting representation, which converts LCG states into multi-dimensional points to overcome the Marsaglia lattice effect; 3) adaptive exploration-exploitation of the generator space, which leads to implicit optimization of the surrogate smooth objective function; and 4) constant information gathering speed to avoid the problem of premature convergence. Extensive testing on 26 benchmark functions across dimensions d = 2 to 30 demonstrates that S-LCG comes within 1% of the global optimum in 83.3% of 138 cases (100% at d = 2, 81.2% at d = 30) while the nearest competitor GA achieved 75.4%. Statistical validation shows that S-LCG outperforms eight cutting-edge binary algorithms. Furthermore, its practical value is confirmed by validation on three constrained engineering design problems. In the end, S-LCG offers an optimization framework that is strictly reproducible and requires only one sensitive parameter to be tuned.

Problem

• optimization
• exploration-exploitation
• premature convergence
• Marsaglia effect
• redundancy

Innovation

• Structured Linear Congruential Generator
• deterministic optimization
• bit splitting representation
• exploration-exploitation balance
• Marsaglia lattice effect