A new quantum differential squirrel search algorithm for global optimization problem

doi:10.1007/s10586-025-05571-y

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A new quantum differential squirrel search algorithm for global optimization problem

2025-09-29

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DOI：10.1007/s10586-025-05571-y

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Abstract

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Complex optimization problems are often multimodal, high-dimensional, non-differentiable, and involve nonlinear interactions, making them difficult to solve. While many meta-heuristic algorithms have been developed, they often struggle with poor exploration and getting trapped in local optima. To address this limitation, this paper introduces a novel hybrid Quantum Differential Squirrel Search Algorithm (QDSSA), which is based on the Differential Squirrel Search Algorithm (DSSA) and Quantum-Behavior Particle Swarm Optimization (QPSO). Squirrel Search Algorithm (SSA) is an algorithm that simulates flying squirrels foraging, and DSSA is one of its improved versions. While DSSA has modified the weather monitoring mechanism of the Squirrel Search Algorithm to incorporate a crossover operator, it still faces the challenge of excessive randomness. The QPSO algorithm is integrated to enhance the global search capability of the algorithm, and a Horizontal Vertical Crossover Strategy is also introduced to accelerate the convergence speed. The proposed method is evaluated using the CEC2017 and CEC2022 test suites, and its performance is compared against other metaheuristic and state-of-the-art algorithms. Through the Wilcoxon rank sum test and Friedman test, it was determined that QDSSA achieved the highest ranking in all dimension tests of CEC2022, and ranked third, second, and first in the 10, 30, and 50 dimension tests of CEC2017, respectively. Additionally, QDSSA demonstrated superior performance in three real-world constrained engineering optimization problems. Furthermore, QDSSA was applied to a singular perturbation inverse problem and the five-parameter non-linear Muskingum model parameter estimation problem, with numerical results provided to illustrate the effectiveness of QDSSA. The method’s flexibility and robustness make it suitable for a wide range of parameter estimation problems.

Keywords:

Quantum Differential Squirrel Search Algorithm

Horizontal vertical crossover strategy

Optimization problem