Quick-Start Guide to Solving Optimization Problems with Geatpy’s Genetic Algorithm

Getting Started Example

First, using the "solver mode" as a quick start to help you master building problems, defining algorithms, and solving them.

Example 1

Use a genetic algorithm with enhanced elite retention strategy to solve the following problem:

s.t.

where the decision variables and their ranges are defined.

import numpy as np
import geatpy as ea
# 构建问题
r = 1  # 目标函数需要用到的额外数据
@ea.Problem.single
def evalVars(Vars):  # 定义目标函数（含约束）
    f = np.sum((Vars - r) ** 2)  # 计算目标函数值
    x1 = Vars[0]
    x2 = Vars[1]
    CV = np.array([(x1 - 0.5)**2 - 0.25,
                   (x2 - 1)**2 - 1])  # 计算违反约束程度
    return f, CV

problem = ea.Problem(name='soea quick start demo',
                    M=1,  # 目标维数
                    maxormins=[1],  # 目标最小最大化标记列表，1：最小化该目标；-1：最大化该目标
                    Dim=5,  # 决策变量维数
                    varTypes=[0, 0, 1, 1, 1],  # 决策变量的类型列表，0：实数；1：整数
                    lb=[-1, 1, 2, 1, 0],  # 决策变量下界
                    ub=[1, 4, 5, 2, 1],  # 决策变量上界
                    evalVars=evalVars)
# 构建算法
algorithm = ea.soea_SEGA_templet(problem,
                                 ea.Population(Encoding='RI', NIND=20),
                                 MAXGEN=50,  # 最大进化代数。
                                 logTras=1,  # 表示每隔多少代记录一次日志信息，0表示不记录。
                                 trappedValue=1e-6,  # 单目标优化陷入停滞的判断阈值。
                                 maxTrappedCount=10)  # 进化停滞计数器最大上限值。
# 求解
res = ea.optimize(algorithm, seed=1, verbose=True, drawing=1, outputMsg=True, drawLog=False)

Analysis

From the code we can see that we first define an objective function, then create the problem, build the algorithm, and finally call optimize() to solve it. The @ea.Problem.single decorator makes the evalVars() function receive a one‑dimensional NumPy ndarray representing an individual’s decision variables. Inside evalVars() we compute the objective value with f = np.sum((Vars - r) ** 2).

Then we compute the constraint violation values with CV = np.array([(x1 - 0.5)**2 - 0.25, (x2 - 1)**2 - 1]). If a value is greater than 0, the corresponding constraint is violated; larger values indicate greater violation.

Line 15 calls Geatpy’s Problem constructor, where maxormins records whether each objective is to be minimized (1) or maximized (-1), and varTypes records variable types (0 for continuous, 1 for integer).

Line 24 instantiates a built‑in evolutionary algorithm class; the population encoding Encoding='RI' means “real‑integer mixed” encoding. NIND=20 sets the population size to 20.

Finally, line 31 calls ea.optimize(). seed=1 fixes the random seed; dirName='result' saves results to a folder named “result”. The returned dictionary res contains keys such as ObjV (best objective values) and Vars (corresponding decision variable values).

Alternative Implementation

r = 1  # 模拟该案例问题计算目标函数时需要用到的额外数据

def evalVars(Vars):  # 定义目标函数（含约束）
    ObjV = np.sum((Vars - r)**2, 1, keepdims=True)  # 计算目标函数值
    x1 = Vars[:, [0]]  # 把Vars的第0列取出来
    x2 = Vars[:, [1]]  # 把Vars的第1列取出来
    CV = np.hstack([(x1 - 0.5)**2 - 0.25, (x2 - 1)**2 - 1])  # 计算违反约束程度
    return ObjV, CV  # 返回目标函数值矩阵和违反约束程度矩阵

problem = ea.Problem(
    name='soea quick start demo',
    M=1,  # 目标维数
    maxormins=[1],  # 目标最小最大化标记列表，1：最小化该目标；-1：最大化该目标
    Dim=5,  # 决策变量维数
    varTypes=[0, 0, 1, 1, 1],  # 决策变量的类型列表，0：实数；1：整数
    lb=[-1, 1, 2, 1, 0],  # 决策变量下界
    ub=[1, 4, 5, 2, 1],  # 决策变量上界
    evalVars=evalVars)
# 构建算法
algorithm = ea.soea_SEGA_templet(problem,
    ea.Population(Encoding='RI', NIND=20),
    MAXGEN=50,  # 最大进化代数。
    logTras=1,  # 表示每隔多少代记录一次日志信息，0表示不记录。
    trappedValue=1e-6,  # 单目标优化陷入停滞的判断阈值。
    maxTrappedCount=10)  # 进化停滞计数器最大上限值。
# 求解
res = ea.optimize(algorithm,
                 verbose=True,
                 drawing=1,
                 outputMsg=True,
                 drawLog=False,
                 saveFlag=True)

References

http://geatpy.com/index.php/quickstart/