AQSCA hybrid algorithm boosts global optimisation with innovative sine-cosine and chaotic techniques

A novel hybrid metaheuristic, AQSCA, integrates sine-cosine dynamics, Levy flights, and chaotic sequences to enhance exploration and exploitation, outperforming conventional algorithms in high-dimensional and real-world engineering problems.

The Sine Cosine Algorithm (SCA), initially proposed by Mirjalili, represents a novel, population-based metaheuristic optimizer designed to solve complex real-world optimization problems through the mathematical properties of sine and cosine trigonometric functions. This algorithm dynamically adjusts the spatial distance between the best solution identified so far and each candidate solution during iterations, guiding the population towards a global optimum. A key feature of SCA lies in its balance between exploration and exploitation phases, achieved via sine and cosine-based position updates and fewer model parameters than traditional metaheuristics. Through this mechanism, SCA probes promising search regions effectively while maintaining computational simplicity. The position update equations involve random parameters that facilitate movement around the current best and new trial solutions, governed by a switch parameter deciding between sine and cosine influences, and other parameters that vary over iterations to balance search intensification and diversification.

Building on these fundamentals, recent research advanced the optimization capabilities of the AQUILA algorithm by hybridizing it with modified sine-cosine manipulation schemes, culminating in the AQSCA hybrid algorithm. This approach leverages the diversified probing ability of SCA to enhance AQUILA’s strengths in exploration and exploitation. The integration introduces dynamically adjusted inertia weights inspired by Particle Swarm Optimization’s heuristics, allowing the algorithm to adapt search intensity based on the fitness landscape dynamically. Additionally, the hybrid incorporates Levy flight mechanisms to further diversify solution candidates, facilitating escape from local optima, and introduces chaotic number sequences generated by the Ikeda map, which enhances population diversity via their ergodic and stochastic properties. Such complex hybridization methodologies build on prior successful attempts to amplify the search efficiency of base optimizers through SCA’s trigonometric functionalities.

A thorough time complexity analysis reveals that despite integrating these advanced techniques, the AQSCA retains the same overall computational complexity as the original AQUILA method, namely O(T·N·D), where T is the number of iterations, N is the population size, and D is the dimensionality of the problem. This ensures the hybrid maintains computational efficiency while enhancing performance.

Extensive numerical experiments validate the superiority of AQSCA across benchmark functions with diverse characteristics and dimensionalities, including 30D and hyper-dimensional (up to 500D) unimodal and multimodal optimization problems. It surpasses several well-known algorithms such as Multi-Verse Optimization, Spotted Hyena Optimization, Jaya Optimization, and the original AQUILA in both convergence rate and solution accuracy. The hybrid shows marked improvements in global search capability and robustness, consistently achieving or nearing global optima across a wide variety of test functions. Wilcoxon signed-rank statistical tests confirm the significance of its performance gains over competitors. Moreover, experimentation with CEC-2013 and CEC-2022 benchmark suites underscores AQSCA’s adept balance of exploration and exploitation, ensuring effective convergence on complex and composite problem landscapes where algorithms frequently struggle with local optima or irregular search spaces.

Crucial to the algorithm’s success is its dynamic balancing of exploration and exploitation, rigorously analysed through convergence behavior on shifted benchmark functions. These tests reveal that AQSCA maintains high exploration in early iterations to avoid entrapment in local optima and gradually shifts focus to exploitation for solution refinement. The combined hunting behaviour of AQUILA and the oscillatory adjustments of the SCA contribute to this adaptive search strategy, enabling robust performance across diverse problem types. Ablation studies further illustrate that the hybrid’s strength arises from the synergy between its components, with standalone variants showing diminished accuracy and robustness.

The practical utility of AQSCA extends to real-world constrained engineering design problems, including heat exchanger network design, industrial refrigeration system optimization, and automotive side impact structure design. In these complex, nonlinear, and highly constrained contexts, AQSCA outperforms several leading metaheuristic and gradient-based methods, consistently delivering more accurate and reliable feasible solutions. Statistical comparisons and convergence analyses demonstrate its superior capability in navigating intricate constraint landscapes without parameter tuning, thus enhancing its applicability to engineering optimization challenges.

Furthermore, AQSCA proves remarkably effective in the domain of chemical equilibrium modelling via Gibbs Free Energy (GFE) minimization, a highly nonlinear and non-convex global optimization problem vital for energy systems design and analysis. Compared against over thirty metaheuristic algorithms, AQSCA consistently achieves better or comparable equilibrium compositions and GFE minima in multiple gas-phase reaction systems under varying temperatures and pressures. It demonstrates high success rates in satisfying atom balance constraints and maintains robustness across diverse operational conditions. These results highlight the hybrid’s adaptability and precision in solving thermodynamically complex chemical equilibrium problems that pose significant challenges for conventional deterministic methods.

In summary, the AQSCA algorithm epitomizes a state-of-the-art hybrid metaheuristic that intelligently combines the sine-cosine-based adaptive search of SCA with the aerial hunting-inspired strategies of AQUILA, reinforced by Levy flights and chaotic number sequences. This amalgamation enables fast convergence, avoidance of local traps, and reliable global solutions across a broad spectrum of high-dimensional, constrained, and real-world optimization problems, as well as nonlinear chemical equilibrium calculations. The algorithm’s design reflects a sophisticated balance of exploration and exploitation phases, underpinned by dynamic parameter tuning and advanced randomization techniques, which collectively elevate its optimization performance and applicability.

📌 Reference Map:

• ^[1] (Nature Scientific Reports) – Paragraphs 1-12, 14-25
• ^[2] (ScienceDirect) – Paragraph 1
• ^[3] (Springer) – Paragraph 1, Paragraph 2
• ^[4] (PMC) – Paragraph 1, Paragraph 7

Source: Noah Wire Services

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