Ant Colony Optimization-Partial Least Squares Algorithm (AOC_PLS)

The Ant Colony Optimization-Partial Least Squares (AOC_PLS) algorithm is an intelligent computational method that combines Ant Colony Optimization (ACO) with Partial Least Squares (PLS) regression, primarily designed to address variable selection problems in high-dimensional datasets.

Algorithm Core Concepts Ant Colony Optimization (ACO): Simulates the pheromone accumulation principle during ant foraging behavior, employing probabilistic search mechanisms to progressively optimize variable subsets. When selecting paths (variables), ants tend to follow directions with higher pheromone concentrations, enabling efficient exploration of the solution space. In MATLAB implementation, this involves maintaining a pheromone matrix and using roulette-wheel selection based on pheromone levels and heuristic information. Partial Least Squares (PLS): Extracts latent variables from data while maximizing covariance between independent and dependent variables, addressing multicollinearity issues through dimensionality reduction. The algorithm typically uses the NIPALS (Nonlinear Iterative Partial Least Squares) method for component extraction, with cross-validation to determine optimal components.

Implementation Workflow Initialization Phase: Set colony size, initialize pheromone matrix, and configure PLS model parameters (e.g., number of latent components). Code implementation requires defining population parameters and creating data structures for tracking ant solutions. Iterative Optimization: Each ant probabilistically selects variable subsets based on pheromone concentrations and heuristic information (e.g., variable importance metrics), then evaluates subset performance using PLS prediction accuracy (typically through cross-validation RMSE). The selection process can be implemented using probability calculation functions and subset evaluation routines. Pheromone Update: High-performing variable combinations reinforce pheromone concentrations, guiding subsequent ants toward better solutions. This involves updating the pheromone matrix with evaporation and reinforcement rules, often implemented through matrix operations. Termination Conditions: The algorithm outputs the optimal variable subset upon reaching maximum iterations or convergence criteria, typically monitored through fitness value stabilization.

Application Advantages Highly suitable for high-dimensional data like spectroscopy and gene expression data, effectively eliminating redundant variables to enhance model interpretability and computational efficiency. Combines ACO's global search capability with PLS's statistical properties, demonstrating greater robustness compared to single-method approaches. MATLAB implementation benefits from built-in matrix operations for efficient PLS computation and custom functions for ACO metaheuristic optimization.

Implementation Considerations Parameters (e.g., pheromone evaporation coefficient, ant population size) require tuning based on data characteristics to prevent premature convergence. This can be automated through parameter sweep scripts or optimization techniques. MATLAB implementations should optimize matrix operations and memory management for handling large-scale datasets, potentially utilizing sparse matrix techniques for high-dimensional scenarios. Code structure should separate ACO optimization logic from PLS modeling components for maintainability, with modular functions for pheromone management and fitness evaluation.