Solving the absolute value equation (AVE) is a nondifferentiable NP-hard and continuous optimization problem with a wide range of applications. Because its solutions have different forms, it is challenging to design the most efficient algorithm that can solve different AVEs without using overcomplicated technical improvement and problem-dependent objectives. Hence, this paper proposed an improved glowworm swarm optimization (GSO) algorithm with an adaptive step size strategy based on the sigmoid function (SIGGSO) that solves the AVEs. Seven test AVEs, including multisolution and high-dimensional AVEs, are selected for testing and compared with seven metaheuristic algorithms. The experimental results show that the proposed SIGGSO algorithm has higher solution accuracy and stability when seeking multiple solution of AVEs compared to the basic GSO. Moreover, it obtains competitive advantages on multisolution and high-dimensional AVEs compared with other metaheuristic algorithms and provides an effective method for engineering and scientific calculations.