Sine Cosine Optimization Algorithms for Global Problem Solving

The Sine Cosine Algorithm (SCA) is a population-based optimisation technique that harnesses trigonometric sine and cosine functions to navigate complex search spaces. By iteratively adjusting candidate solutions through periodic oscillations, SCA balances global exploration and local exploitation to locate optimal or near-optimal solutions. During each iteration, the algorithm updates the position of each solution according to sine or cosine operators modulated by adaptive parameters, enabling both broad searching and fine-tuning phases. Its conceptual simplicity, ease of implementation and rapid convergence have led to widespread application across engineering design, scheduling, route planning and resource allocation. However, the basic SCA may suffer from premature convergence and reduced diversity in large-scale or highly multimodal problems. Recent developments have thus focused on self-adaptive weighting, chaotic mappings, hybrid strategies and learning-based enhancements to bolster the algorithm’s robustness, improve convergence accuracy and avoid local optima. The global significance of these advances is evident in their ability to address ever-growing problem sizes, stringent constraint sets and real-world uncertainties, making SCA variants a versatile tool for both academic and industrial applications.

Research from Nature Portfolio

Two recent studies have extended the SCA framework to hybrid metaheuristic models for real-world optimisation. One approach couples a multi-verse optimiser with the sine cosine mechanism to tackle large-scale discrete time–cost trade-off problems in construction management. By integrating data exchange across explorers and exploiters, the hybrid model outperforms classic metaheuristics in balancing project duration and expenditure on medium and large instance sets. A second innovation merges roulette wheel selection with opposition-based learning into an advanced sine cosine model. This integration dynamically adjusts selection pressure and enhances population diversity, yielding superior performance on modern benchmark suites and diverse engineering case studies. Both contributions demonstrate how strategic hybridisation elevates global search capabilities while maintaining efficient convergence for complex optimisation tasks.

Research from all publishers

Recent contributions outside the portfolio have introduced self-adaptive weight and social strategies to improve exploration–exploitation balance in SCA. By employing dynamic weight adjustment and social interaction rules, the enhanced model significantly boosts convergence precision and robustness on benchmark test functions and competitive suites. Another work focuses on elite individual collaborative search, utilising chaotic population initialisation and multi-strategy guidance to prevent stagnation. Alternating local and global search strategies alongside greedy selection has led to faster convergence and improved solution accuracy in mechanical design optimisation experiments. Complementing these algorithmic improvements, a comprehensive survey has mapped the breadth of SCA research, covering chaotic, binary, multi-objective and hybrid variants. This review highlights emerging trends, identifies key performance bottlenecks and proposes future research directions, thereby providing a valuable roadmap for the next generation of SCA-based optimisers.

Sine Cosine Optimization Algorithms for Global Problem Solving publication trend

The graph below shows the total number of articles in sine cosine optimization algorithms for global problem solving across all publications each year (not limited to Nature Index journals).

Technical terms

Sine Cosine Algorithm (SCA): A metaheuristic that employs sine and cosine functions to update solution positions for optimisation.

Metaheuristic algorithm: An overarching optimisation strategy that guides subordinate heuristics to explore and exploit search spaces.

Global exploration: The phase of an algorithm dedicated to broadly sampling the search space to avoid premature convergence.

Local exploitation: The phase of an algorithm focused on intensively refining solutions in promising regions.

Opposition-based learning: A technique that enhances diversity by simultaneously evaluating candidate solutions and their opposites.

Roulette wheel selection: A probabilistic selection method where solutions are chosen based on fitness-proportional probabilities.

Benchmark test functions: Standardised mathematical functions used to assess and compare optimisation algorithm performance.

References

1. Solving large-scale discrete time–cost trade-off problem using hybrid multi-verse optimizer model. Scientific Reports (2023).
2. Enhancing engineering optimization using hybrid sine cosine algorithm with Roulette wheel selection and opposition-based learning. Scientific Reports (2024).
3. Improved Sine Cosine Algorithm for Optimization Problems Based on Self-Adaptive Weight and Social Strategy. IEEE Access (2023).
4. Sine Cosine Algorithm for Elite Individual Collaborative Search and Its Application in Mechanical Optimization Designs. Biomimetics (2023).
5. A comprehensive survey on the sine–cosine optimization algorithm. Artificial Intelligence Review (2022).