MATLAB Source Code for Load Balancing Scheduling Problem

In modern distributed computing environments, load balancing scheduling is one of the key technologies for improving system efficiency. The core objective is to reasonably distribute N computational tasks to M server nodes, minimizing the total completion time of all tasks. Here we explore implementation approaches using MATLAB.

The mathematical model of this problem can be described as: given the length (computational requirement) of each task and the processing speed of each node, the goal is to find a task-to-node assignment scheme that minimizes the completion time of the latest finishing node (makespan). This type of problem belongs to NP-hard problems and typically requires heuristic algorithms for solution.

Common solution approaches include: Greedy Algorithm: Assigns the current longest task to the currently least-loaded node (implementation in MATLAB would involve sorting tasks and tracking node loads) Genetic Algorithm: Uses population evolution to find approximate optimal solutions (requires chromosome encoding for task assignment and fitness evaluation based on makespan) Dynamic Programming: Suitable for exact solutions in small-scale problems (uses state transition equations for optimal substructure)

Key considerations for MATLAB implementation: Task lengths and node speeds can be represented using vectors/matrices When calculating node loads, element-wise division is required (task length ÷ node speed using ./ operator) The objective function should monitor the maximum node completion time using max() function on load vectors

Optimization directions may include: considering node heterogeneity, task priority constraints, or introducing real-time load feedback mechanisms. This problem has widespread application scenarios in cloud computing, edge computing, and related fields.