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

TL;DR

This paper introduces S-LCG, a deterministic optimization algorithm based on a structured variant of the Linear Congruential Generator, demonstrating high accuracy and efficiency across benchmark functions and engineering problems.

Contribution

The paper proposes a novel structured LCG-based algorithm with unique features like memoryless sequences and adaptive exploration, outperforming existing algorithms in optimization tasks.

Findings

Achieves within 1% of the global optimum in 83.3% of benchmark cases

Outperforms eight state-of-the-art binary algorithms statistically

Validated on three constrained engineering design 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.