As optimization problems grow more complex, traditional Differential Evolution (DE) algorithms face challenges like premature convergence, loss of population diversity, and inadequate local search ability in high-dimensional spaces. To address these issues, this paper introduces TSDE-SSA, a Two-Stage Differential Evolution algorithm with Squirrel Exploration. TSDE-SSA divides the optimization process into two phases: an early exploration phase and a later exploitation phase. In the exploration phase, it combines the strengths of DE/rand/1 and DE/best/2 mutation strategies with a self-adaptive mechanism for historical parameters. This enhances global exploration and swiftly identifies potential optimal solution regions. In the exploitation phase, it mimics the foraging behavior of the Squirrel Search Algorithm (SSA) and integrates DE crossover operations. By dynamically adjusting parameters like the scaling factor and gliding constant, it boosts local search accuracy and prevents premature convergence. CEC2017 and CEC2020 benchmarks show that TSDE-SSA surpasses three fundamental algorithms and five outstanding DE variants in convergence speed, precision, and stability. It also outperforms eight new meta-heuristic algorithms and shows strong applicability and reliability in five typical engineering design problems. In summary, TSDE-SSA balances global and local search effectively, offering an efficient and stable solution for complex optimization problems with broad application potential.
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