Reservoir optimization scheduling using PSO algorithm (MATLAB implementation)
In water resource management, cascade reservoir optimal dispatching is a common problem. This article describes how to solve this problem using Particle Swarm Optimization (PSO), and provides MATLAB code.
First, let us understand what is the cascade reservoir optimal dispatching problem. The problem is balancing water flow across multiple reservoirs to maximize irrigation, power generation, and other needs. The goal of the optimal scheduling problem is to reduce the amount of wasted water as much as possible and to improve the efficiency of water resource utilization as much as possible.
Next, we will introduce how to use the PSO algorithm to solve the cascade reservoir optimal dispatching problem. We assume that there are N reservoirs, each reservoir has a different input flow, and its output flow will flow into the downstream reservoir or channel. We use the formula to define the object function for each reservoir:
F = α × (1-δ) × U + β × (1-δ) × R + γ × δ
Among them, α, β and γ are adjustment parameters, U is the difference between the reservoir water level and the maximum water level, R is the remaining capacity at the current water level, δ is the balance coefficient of each reservoir at the current time point, and their sum should be Equal to 1, it means that at each time point, the water is distributed to each reservoir in a balanced manner.
Next, we will use the PSO algorithm to minimize this function. We will define a population of N particles. Each particle represents a possible solution and has a position vector and a velocity vector. In each iteration, each particle updates its own position according to its own position and velocity vector, and calculates its fitness function. Each particle also records its historical best position and the historical best position of the entire swarm.
The following is the implementation code in MATLAB:
function [best_position, best_fitness] = PSO(num_particles, max_iterations, alpha, beta, gamma)
%初始化粒子的位置和速度
particles_position = rand(num_parti