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.

翻译：本研究提出了一种基于线性同余生成器（LCG）特殊变体的新型确定性优化算法。传统算法通常仅在搜索空间内运行，而本技术采用双层架构：外层循环自适应平衡探索与开发，内层循环评估解方案。该算法受生成器内在结构启发，故命名为结构化线性同余生成器（S-LCG），其具备以下独特特性：1）无记忆机制，确保基于不同种子的序列无重叠，从而避免评估冗余；2）位拆分表示法，将LCG状态转化为多维点以克服马尔萨利亚格点效应；3）生成器空间的自适应探索-开发平衡，隐式优化替代平滑目标函数；4）恒定信息收集速度，避免早熟收敛问题。在维度d=2至30的26个基准函数上的广泛测试表明：在138个测试案例中，S-LCG有83.3%的案例达到全局最优值的1%以内（d=2时100%，d=30时81.2%），而最接近的对比算法GA仅达75.4%。统计验证显示S-LCG优于八种前沿二进制算法。此外，在三个约束工程设计问题上的验证进一步证实其实用价值。最终，S-LCG提供了一个严格可复现且仅需调节单个敏感参数的优化框架。