Improved Glowworm Swarm Optimization Algorithm Based on Sigmoid Function for Absolute Value Equation

The absolute value equation (AVE) is a nondifferentiable NP-hard and continuous optimization problem with a wide range of application, including linear programming, quadratic programming, and game theory. The AVE has several solution forms, such as single-peak, multi-peak, and high-dimension. In view of the weaker performance in solving multi-peak and high-dimension AVEs, we propose an improved glowworm swarm optimization algorithm (GSO) based on the sigmoid function for solving AVEs in this study. The algorithm constructs an adaptive variable step-size based on the sigmoid function, which can effectively overcome the shortcomings of the basic GSO algorithm such as slow convergence in the early iterations, poor local search ability in the later iterations, and the tendency to easily fall into local peaks. Compared to the other GSOs with step-size improvement and other intelligent algorithms, our improved strategy includes advantages such as strong global search ability, high-calculation accuracy, and good stability for solving multipeak and high-dimensional AVEs, in particular