Enterprise AI Analysis

Overview of Optimization Approaches

This study evaluates four key metaheuristic algorithms for MPC weight optimization:

• Particle Swarm Optimization (PSO): Particles (potential weight vectors) navigate a multi-dimensional search space, adjusting their positions and velocities based on their own best past performance and the swarm's global best. This collective learning enables efficient exploration without gradient information.
• Genetic Algorithm (GA): Inspired by natural selection, GA evolves a population of candidate solutions (chromosomes) over generations. Fitness assessment, reproduction (crossover), and random alterations (mutation) are used to find optimal or near-optimal solutions, balancing exploration and exploitation.
• Pareto Search: A multi-objective optimization method that identifies a set of non-dominated alternatives, known as the Pareto front. This approach is crucial for problems with conflicting goals, allowing decision-makers to visualize and understand optimal trade-offs rather than a single ideal solution.
• Pattern Search: A derivative-free optimization method that explores the search space by evaluating the objective function at points organized in a pattern around the current solution. It is particularly useful for noisy, discontinuous, or non-differentiable functions, as it does not require knowledge of derivatives.

Evaluating Optimization Effectiveness

The effectiveness of each metaheuristic algorithm is assessed primarily through two key metrics: tracking error and convergence speed. The loss function, defined by the squared norm of the tracking error and a regularization term for high weight values, quantifies performance. Error percentage is calculated as (Demand - Load) / Demand, ensuring robustness across various operating scenarios.

Convergence, influenced by the maximum number of iterations, determines how quickly an algorithm finds an optimal solution. Robustness is further ensured by analyzing parameter interdependencies, confirming that the tuning reflects a thorough and reliable search rather than an incomplete or biased outcome. Faster convergence and lower tracking error are critical for real-world enterprise applications like energy management in microgrids.