Optimization of Diagonal Recurrent Neural Networks using Genetic Algorithm, Particle Swarm Optimization, and Backpropagation Algorithm

This paper explores the application of three optimization algorithms for improving the performance of Diagonal Recurrent Neural Networks (DRNNs). DRNNs excel in processing time-series data due to their unique recurrent structure, but parameter optimization remains challenging. We focus on analyzing the implementation approaches and applicable scenarios of three mainstream optimization algorithms.

The Genetic Algorithm (GA) simulates biological evolution mechanisms to optimize DRNN parameters through selection, crossover, and mutation operations. The algorithm first generates a random population of parameters, calculates fitness functions (such as prediction error) for each individual, and preserves superior individuals for genetic recombination. Although convergence speed is relatively slow, GA effectively escapes local optima and is suitable for large parameter search spaces. In code implementation, key functions include population initialization, fitness evaluation, and genetic operators with dynamic mutation rates to handle complex error surfaces.

Particle Swarm Optimization (PSO) is inspired by bird flock foraging behavior, finding optimal solutions through particle cooperation. Each particle represents a set of network parameters, adjusting its flight direction by recording individual and global best positions. Compared to GA, PSO offers simpler implementation and faster convergence but requires careful tuning of parameters like inertia weight. Implementation typically involves position and velocity updates using social and cognitive components, with layered PSO strategies recommended for DRNN's recursive structure.

The Backpropagation (BP) algorithm, as a classic gradient descent method, adjusts network weights through error backpropagation. While computationally efficient, it easily falls into local minima. In practice, momentum terms or adaptive learning rates are often incorporated to improve performance. Code implementation requires careful handling of gradient computation through time (BPTT) for recurrent networks, with possible enhancements using second-order optimization methods like Levenberg-Marquardt.

Important implementation considerations: DRNN's recursive structure results in more complex error surfaces, suggesting the use of dynamic mutation rates (for GA) or hierarchical particle swarms (for PSO). For BP algorithms, second-order optimization methods can improve convergence. Practical applications should select appropriate optimization strategies based on data characteristics and real-time requirements – industrial time-series prediction typically prioritizes PSO, while complex nonlinear system modeling may consider combining GA for coarse tuning followed by BP for fine-tuning.